Hummer, Merritt-senior thesis final April 2010.pdf - CASTLE Lab ...

Greening the Grid: 

Optimal Tax Policy for 

Wind and Solar Technology 

Merritt S. Hummer 

April 2010 

Advisor: Professor Warren Powell 

Submitted in partial fulfillment 

of the requirements for the degree of 

Bachelor of Science in Engineering 

Department of Operations Research and Financial Engineering 

Princeton University

I hereby declare that I am the sole author of this thesis. 

I authorize Princeton University to lend this thesis to other institutions or 

individuals for the purpose of scholarly research. 

________________________________________ 

Merritt Hummer 

I further authorize Princeton University to reproduce this thesis by photocopying or 

by other means, in total or in part, at the request of other institutions or individuals 

for the purpose of scholarly research. 

________________________________________ 

Merritt Hummer 

ii

Abstract 

Wind and solar energy provided less than 1% of the United States total 

energy supply in 2008. Yet the nascent renewable energy industry is gaining 

momentum, and fast: the U.S. leapfrogged Japan to become the third largest 

photovoltaic market in the world after the country’s installed solar photovoltaic 

capacity soared 36% in 2009 alone [79]. The U.S. retained its top spot as the world’s 

largest wind energy producer, increasing its installed wind power capacity by 39% 

in 2009 [78]. 

Renewable energy capacity is poised to grow dramatically in the coming 

decades with the advent of technological improvements, government incentives, 

and the broader environmentalist movement. The Department of Energy set a goal 

to supply 25% of the nation’s electricity from wind energy by 2030. While it has not 

yet published a formal goal for solar power, the DOE has signaled its intentions by 

earmarking substantial funding for further research and development of solar 

technology. 

This thesis examines how the federal tax policy can be designed in a way that 

fosters the growth of wind and solar contributions to the electricity supply. 

Specifically, the thesis seeks to quantify and optimize the economic impact of two 

variables: a carbon tax and a tax credit for renewable energy installations in the 

residential sector. The model will project the cumulative cost or benefit to society of 

policy proposals—both real and hypothetical—in a single period and over time. 

iii

Acknowledgements 

I would like to thank my advisor, Professor Warren Powell, for giving me the 

freedom to explore this subject. While traveling through a labyrinth of potential 

thesis topics in the fall semester, Professor Powell never ceased to spark my interest 

by suggesting a new turn. Indeed, this thesis would not have been possible without 

his guiding hand and endless stream of new ideas. I am also indebted to Professor 

Hugo Simao, who helped to launch me into the land of senior theses. 

Thank you also to my friends and family for their support in this and all 

endeavors. To my parents, thank you for all the feedback you gave me along the 

way. Special thanks to my ORFE classmates, many of whom I have gotten to know 

well over the last four years. You comprise a dynamic, talented, and eclectic group 

of which I am proud to be a member! In particular, thank you, Daphne, Phoebe, 

Jaimeson, and Austin, for supplying a generous dose of levity when needed. 

Finally, thank you to Princeton University, and to the many people I do not 

have room to name here, for providing me with much more than a person could 

reasonably expect. 

iv

The habit of expression leads to the search for something to express. 

-‐ Henry Adams 

v

Table of Contents 

Abstract ..................................................................................................................... iii 

Acknowledgements.....................................................................................................iv 

1. Introduction to the Energy Problem...................................................................... 1 

1.1 The Current Renewable Energy Profile of the United States......................................................6 

1.2 Tax Subsidies for Renewable Energy ....................................................................................................8 

1.2.1 Residential Renewable Energy Tax Credit.......................................................................................9 

1.2.2 Residential Energy Efficiency Tax Credit .........................................................................................9 

1.2.3 State-wide Renewable Tax Credits................................................................................................... 10 

1.3 The Cost of Carbon ..................................................................................................................................... 10 

1.3.1 The Social Cost of Carbon..................................................................................................................... 10 

1.3.2 The Carbon Tax ........................................................................................................................................ 11 

1.4 Overview of the Thesis ............................................................................................................................. 13 

2. Methodology of Cost Comparison....................................................................... 14 

2.1 Foundations for this Approach ............................................................................................................. 15 

2.2 Factors Affecting Retail Electricity Prices in the United States............................................... 18 

2.3 Solar Photovoltaics..................................................................................................................................... 19 

2.3.1 Assumptions in Solar Calculations................................................................................................... 19 

2.3.2 Solar Energy Potential in the United States................................................................................. 21 

2.3.3 Peak Sun Hours and PV Modules ...................................................................................................... 23 

2.3.4 Installation and Maintenance Costs................................................................................................ 25 

2.3.5 Electricity Production of the PV Module........................................................................................ 28 

2.3.6 Overall Price of Solar Electricity in this Model ........................................................................... 29 

2.3.7 Government Incentives.......................................................................................................................... 30 

2.4 Wind Energy.................................................................................................................................................. 31 

2.4.1 Assumptions in Wind Calculations................................................................................................... 31 

2.4.2 Wind Energy Potential in the United States ................................................................................ 32 

2.4.3 Modeling Wind Energy using the Weibull Distribution.......................................................... 34 

2.4.4 Electricity Production of the Wind Turbine................................................................................. 36 

2.4.5 Installation and Maintenance Costs................................................................................................ 41 

2.4.6 Overall Price of Wind Electricity in this Model........................................................................... 43 

2.4.7 Government Incentives.......................................................................................................................... 44 

2.5 Retail Electricity .......................................................................................................................................... 45 

2.5.1 Regional Cost Discrepancies ............................................................................................................... 45 

2.6 Price Comparison of Electricity Sources........................................................................................... 47 

3. Applying Government Forces to the Electricity Market ....................................... 49 

3.1 The Quantitative Model............................................................................................................................ 51 

3.1.1 Decision Variables................................................................................................................................... 51 

3.1.2 Market Response...................................................................................................................................... 52 

3.1.3 The Cost Function and Constraints.................................................................................................. 53 

3.1.4 Incorporating Variability in Solar Costs........................................................................................ 54 

3.2 The Impact of Government Incentives on Electricity Allocation............................................ 62 

3.2.1 Impact of the Carbon Tax on Allocation........................................................................................ 62 

vi

3.2.2 Impact of the Renewable Tax Credit on Allocation .................................................................. 64 

3.3 The Impact of Government Incentives on Electricity Prices.................................................... 67 

3.3.1 Background on the Electricity Price-Carbon Tax Relationship........................................... 67 

3.3.2 Improvement upon Linearity in the Electricity-Carbon Tax Relationship ..................... 68 

3.4 Laying the Groundwork for Policy Optimization .......................................................................... 72 

4. Optimizing Environmental Tax Policy.................................................................. 74 

4.1 Structure of the Cost-‐Benefit Analysis in One Time Period...................................................... 75 

4.1.1 Government Net Revenue..................................................................................................................... 76 

4.1.2 Consumer Net Revenue.......................................................................................................................... 78 

4.1.3 Net Social Benefit..................................................................................................................................... 82 

4.1.4 Summary Table......................................................................................................................................... 82 

4.2 Calculating the Social Cost of Carbon ................................................................................................. 83 

4.3 Modeling Consumer Behavior ............................................................................................................... 85 

4.3.1 Inducement to Change Threshold..................................................................................................... 85 

4.3.2 Renewable Adoption Rate, or Switchover Rate.......................................................................... 88 

4.4 Declining Costs of Renewable Technology Over Time................................................................ 93 

4.4.1 Solar Photovoltaic Cost Trends.......................................................................................................... 93 

4.4.2 Wind Turbine Cost Trends................................................................................................................... 95 

5. Results of the Mathematical Model.................................................................... 97 

5.1 Net Savings to Society for One Time Period.................................................................................... 98 

5.1.1 Net Savings with Lockstep Technology Improvement............................................................. 98 

5.1.2 Optimal Policies in the One Period Model...................................................................................104 

5.1.3 Delinking Wind and Solar Technology Improvement Variables.......................................107 

5.2 Net Savings to Society Over Time ......................................................................................................111 

5.2.1 Net Cost to Society with Variable Rates of Technology Improvement ...........................111 

5.2.2 Optimal Policies in the Time Lapse Model..................................................................................115 

6. Summary and Conclusion ..................................................................................117 

6.1 Summary of the Thesis ...........................................................................................................................117 

6.2 Limitations of this Model.......................................................................................................................119 

6.3 Areas for Further Investigation ..........................................................................................................121 

6.4 Final Thoughts............................................................................................................................................122 

Appendix..................................................................................................................123 

References ...............................................................................................................134 

vii

For my parents

1. Introduction to the Energy Problem 

Ever since the Industrial Revolution took hold around the turn of the 

nineteenth century, progress has implied pollution: societal 

advancement and urban development have gone hand in hand with environmental 

damage, arguably the greatest externality of modernization. In the decades 

following industrialization, the atmospheric concentration of carbon dioxide, the 

most important greenhouse gas, rose 36% [28]. Almost the entire increase is due to 

human activities, primarily deforestation and the burning of fossil fuels [29]. 

The global community is at a crossroads in human history. With the long-‐ 

term well-‐being of the environment teetering on a precipice, the next phase of 

progress must correct the errors of the past. Forthcoming innovation must steer 

civilization away from the recklessness of former generations and toward 

sustainability and energy efficiency. The most important challenge of the twenty-‐

Introduction to the Energy Problem 

first century will be solving the energy problem: how can the global community 

sustain its rate of growth without causing a gradual death of the natural world? 

Moreover, as demand for the earth’s natural resources increases in response 

to growing populations and economies worldwide, the rate at which resources are 

replaced cannot keep up with the rate at which they are depleted. In other words, if 

developed and developing countries do not choose to alter their course out of 

concern for the environment, they will eventually be forced to change due to the 

scarcity of nonrenewable resources like petroleum, natural gas, and coal. 

Besides adverse environmental effects and scarce supply of fuels, there are 

also geopolitical forces at play to motivate the U.S. to reevaluate its current energy 

portfolio. Energy importers around the world, the U.S. included, are subjected to 

energy price volatility as a result of precarious political situations in oil exporting 

countries. Political instability even in countries considered “marginal oil suppliers” 

can cause major price spikes [37]. In October 2007, Turkey threatened to invade 

northern Iraq, and within two weeks the price of oil jumped $7 to $94.53 per barrel, 

despite the fact that Iraq 

produces less than 4% of the 

world’s oil supply per day [37]. 

The political circumstances in 

Saudi Arabia, Russia, and the 

United Arab Emirates—three of 

the top oil exporters globally— 

are hardly more predictable. 

Table 1. Major Oil Exporting Nations [39] 

Top World Oil Net Exporters, 2008 

(thousand barrels per day) 

Rank Country Exports 

1 Saudi Arabia 8,406 

2 Russia 6,874 

3 United Arab Emirates 2,521 

4 Iran 2,433 

5 Kuwait 2,390 

6 Norway 2,246 

7 Angola 1,948 

8 Venezuela 1,893 

9 Algeria 1,888 

10 Nigeria 1,883 

2


Clearly, the fragile political equilibria in oil supplying nations are inextricably tied to 

economic interests of importing nations. 

Fluctuating oil prices, an uneasy dependence on other nations, and 

environmental concerns have prompted the U.S. Department of Energy (DOE) to 

explore alternatives to its current energy mix. Part of the DOE’s multi-‐pronged 

strategy is to encourage citizens to transition to energy sources broadly defined as 

“renewable,” which applies to hydropower, geothermal, biomass, wind, and solar 

power. To that end, the Office of Energy Efficiency and Renewable Energy (EERE) is 

charged with leading federal research and development in energy efficiency and 

pursuing high-‐risk, high-‐value renewable energy projects that would not be carried 

out as aggressively by the private sector on its own [38]. 

Still, there is much progress to be made before the U.S. can reconcile its 

“addiction” to fossil fuels with a changing global landscape. Currently, fossil fuels 

provide the vast majority of energy consumed in the United States [23]. In 2009, the 

United States, second only to China, emitted 5.7 billion tons of carbon dioxide—a 

figure that is projected to grow by 0.3% each year through 2030 [30] [31]. All forms 

of renewable energy only supplied 7% of U.S. energy in 2008 despite attracting 

widespread attention from politicians, scholars, and the press. Solar and wind 

energy represented a mere 1% and 7% of that category, respectively, or less than 

1% of total U.S. energy supply together [4]. 

Despite the lackluster numbers in the renewable sector, the DOE has set 

ambitious goals: the “20-‐in-‐10” plan, announced by President George W. Bush in the 

2007 State of the Union address, seeks a 20% reduction in U.S. gasoline 

3


consumption by 2017. “20-‐in-‐10” is complemented by the “20% Wind Energy by 

2030” goal, which aims for a major increase in wind’s contribution to the U.S. 

electricity supply [40] [4]. Wind-‐generated electricity has gained traction since the 

formal 20% goal was published in an exhaustive July 2008 report. 

Renewable energy skeptics often point to the cost of solar and wind power as 

the biggest hindrance to the adoption of renewable technology. Indeed, experts 

generally agree that it is highly unlikely that the nation will be able to meet the 

DOE’s goals without some form of government intervention. One of the conclusions 

of Aghion, Hemous, and Veugelers’s [41] policy analysis is that even though the 

private market for green technology is ready to take off, “in the absence of the right 

push from government this will be difficult, if not impossible” [41]. Put another 

way, “governments must initially redirect market forces towards cleaner energy 

before market forces can take over” [41]. Ultimately, public intervention will be as 

critical as private initiative to the success of renewable energy. 

To accelerate the shift from fossil fuels to renewable energy, renewable 

technology must become cost-‐competitive with traditional fuels. There are three 

main ways in which the government can play a role in accomplishing this: 

• Providing subsidies or tax credits for renewable energy installations, making 

such investments more attractive to consumers. 

• Imposing a carbon tax on emissions of CO2, thereby increasing the cost of 

coal, petroleum, and natural gas. Alternatively, the government could set a 

cost on carbon via a cap-‐and-‐trade system whereby firms are allowed to buy 

and sell emissions credits in the marketplace; this “tax-‐free” model of 

4


distributing tradable pollution rights has become politically popular, 

especially after its documented success in reducing other pollutants, namely 

sulfur dioxide and nitrous oxide, in the United States [42]. 

• Contributing financial and human capital toward the research, development, 

and deployment of renewable energy technologies. The technology will 

become cheaper and more accessible as it improves. 

By utilizing these and other policies to induce a change in consumer behavior, 

governments in the United States and abroad will have a chance to meet clean 

energy targets of their choosing. 

As sustainable energy becomes more and more relevant in today’s world, the 

importance of developed nations recalibrating their energy portfolios cannot be 

understated. The world is in their hands. Notwithstanding the obvious moral 

reasons why developed countries should lead the green energy movement, doing so 

is also to their benefit; as President Obama put it in his State of the Union address on 

January 27, 2010, “The nation that leads the clean energy economy will be the 

nation that leads the global economy” [21]. As if to quell an unsettling fear to many 

Americans, he added, “And America must be that nation.” Already, the race has 

begun. 

5

1.1 The Current Renewable Energy Profile of the United States 


Not to anyone’s surprise, the U.S. is still heavily dependent upon fossil fuels 

to run its daily operations. The most recent data available shows that 84% of U.S. 

energy is supplied by fossil fuels. That number has remained steady in recent 

decades, but the Energy Information Administration projected that the share of 

fossil fuels in total energy consumption will drop to 78% by 2035 [45]. According to 

Rep. Henry A. Waxman (D), co-‐author of the American Clean Energy and Security 

Act of 2009 1 , “Our goal is to strengthen our economy by making America the world 

leader in new clean-‐energy and energy-‐efficiency technologies” [15]. 

As illustrated in Figure 1, renewable energy only represents a sliver of the 

energy supply at this point. Biomass power, or “power obtained from energy in 

plants and plant-‐derived materials,” supplied the majority of energy from the 

renewable sector in 

2008 [43]. Biomass 

materials include 

food crops, grassy 

plants, wood, 

residues from 

agriculture or 

forestry, alcohol 

Figure 1. The Role of Renewable Energy in the 

Nation's Energy Supply, 2008 [26] 

fuels, and municipal and industrial wastes [43]. One of the chief advantages of 

biomass power is its versatility: biomass can be used for direct heating, generating 

1 This bill has not yet been passed the Senate. It passed the house on June 26, 2009 [94]. 

6


electricity, or meeting transportation needs, in which case it is converted into liquid 

fuel [43]. It also provides an important service in waste management [43]. 

Hydropower, the other major component of the renewable sector in 2008, 

harnesses the energy in moving water. While there are many forms of hydropower, 

hydroelectric dams are the most common, largely because hydroelectricity can be 

Figure 2. Top Hydropower Producing States, 2007 [53] 

far less expensive than fossil 

fuel-‐generated electricity in 

areas well suited to building 

dams. Six percent of U.S. 

electricity was supplied by 

hydroelectricity in 2008; that 

number will likely rise in the 

future as the country builds 

out its hydroelectric capacity. Major hydroelectric dams in the United States are 

located in the Northwest, the Tennessee Valley, and on the Colorado River [43]. 

Approximately 31% of total U.S. hydropower is generated in Washington, which is 

home to the nation’s largest hydroelectric facility [44]. 

Wind, solar, and geothermal energy round out the renewable energy 

component. These renewable sources, while quite intuitive in nature, have proven 

difficult to master technologically, with each one presenting unique challenges. 

Wind is an inherently volatile resource that can supply an overabundance or a lack 

of energy at any time without warning, which prompts the need for stored energy to 

provide consistent power. Like wind power, solar power also varies by hour, 

7


season, and location, sometimes unpredictably, making a secondary energy source 

all but necessary. Finally, geothermal energy, which is simply heat from the earth, is 

captured beneath the earth’s surface. The drilling and exploration associated with 

geothermal energy makes for a very expensive, and sometimes unfruitful, 

enterprise. 

Together, wind, solar, and geothermal energy supplied 13% of renewable 

energy in 2008, or, equivalently, roughly 1% of the total U.S. energy supply. Yet 

there is reason to believe that contributions from these three sources, backed by 

technological advances and support from the federal government, will grow rapidly 

in the coming years. In theory, wind, solar, and geothermal sources offer enormous 

potential for meeting future energy demands; the obstacle will be to harness and 

distribute the energy in a cost-‐effective manner. 

1.2 Tax Subsidies for Renewable Energy 

If the government is so inclined, it may offer attractive subsidies to 

encourage consumer behavior that it deems favorable. Subsidies are a powerful 

means to ease financial burdens on consumers or to encourage spending in a certain 

area. Tax subsidies and incentives take a great many forms, the most attractive of 

which is the tax credit. Unlike tax deductibles, which only reduce taxable income, 

tax credits reduce the amount of taxes owed dollar for dollar. Currently, the federal 

government offers child and dependent care credits, education credits, and first-‐ 

time homebuyer credits, to name just a few [49]. In 2005, Congress enacted a 

personal tax credit for investment in renewable energy. 

8

1.2.1 Residential Renewable Energy Tax Credit 


The tax incentive of greatest interest here is the Residential Renewable 

Energy Tax Credit. It applies directly to American consumers, unlike the many tax 

breaks granted to corporations and industry. Originally created under the Energy 

Policy Act of 2005, it offers a 30% personal tax credit to Americans who install 

renewable technology in their homes; qualifying technologies include solar heating 

and solar electric technology, wind turbines, fuel cells 2 , and geothermal heat pumps 

[32]. The American Recovery and Reinvestment Act of 2009 further enhanced the 

Residential Renewable Energy Tax Credit by removing the original $2,000 

maximum credit amount for eligible technologies, bringing the credit to its most 

generous design since its inception [32]. 3 It is not due to expire until December 

2016. 

1.2.2 Residential Energy Efficiency Tax Credit 

The other federal tax credit offered to American consumers in the clean 

energy sector is the Residential Energy Efficiency Tax Credit. It provides a 30% 

personal tax credit for the cost of “upgrading the efficiency of a building’s envelope” 

[51]. Such home improvements include insulation materials or pigmented metal 

roofs designed to reduce a home’s heat loss and gain, advanced main air circulating 

fans, biomass stoves, and much more [51]. The Residential Energy Efficiency Tax 

Credit has a cap of $1,500, and it is set to expire in December 2010 [51]. 

2 Fuel cells are “electrochemical cells in which the energy of a reaction between a fuel, such as liquid 

hydrogen, as an oxidant, such as liquid oxygen, is converted directly and continuously into electrical 

energy” [50]. The exhaust of fuel cells consists only of water. 

3 This enhancement to the tax credit excludes fuel cell technology. 

9

1.2.3 State-‐wide Renewable Tax Credits 


In addition to federal tax incentives, many state governments offer their own 

tax breaks for renewable energy or energy efficiency. In total, twenty-‐two states 

offer personal tax credits for renewable energy [52]. 4 Of those, five states—Arizona, 

Maryland, Montana, New Mexico, and New York—offer more than one personal tax 

credit for renewable energy. In comparison, just thirteen states offer personal tax 

credits for energy efficiency [52]. 

1.3 The Cost of Carbon 

Despite its widespread usage in everyday publications, the “cost of carbon” is 

ambiguous and may refer to two distinct concepts: the social cost of carbon, and the 

carbon tax. For clarity’s sake, neither of these concepts will hereafter be called the 

“cost of carbon”; they will be referred to only by their more descriptive names. 

1.3.1 The Social Cost of Carbon 

The social cost of carbon (SCC) is formally defined as the marginal cost of 

emitting an additional unit of carbon (in the form of carbon dioxide) [5]. It is usually 

expressed in dollars per metric ton of carbon. It is calculated by quantifying the 

long-‐term environmental damage done by the additional unit of carbon, and 

discounting the damage to its present value in dollars. The SCC, therefore, can be 

interpreted as “a measure of the seriousness of climate change”: the more grim the 

4 Alabama, Arizona, Georgia, Hawaii, Idaho, Indiana, Iowa, Kentucky, Louisiana, Maryland, 

Massachusetts, Montana, New Mexico, New York, North Carolina, North Dakota, Oregon, Rhode 

Island, South Carolina, Utah, Vermont, and West Virginia [52]. 

10


assumptions about the environmental impact of carbon, the higher the SCC estimate 

will be. 

To complicate matters for policymakers, there is no single widely accepted 

SCC value. In fact, estimates of the SCC vary considerably. The not-‐for-‐profit 

Investor Responsibility Research Center projects that the SCC will be $28.24 per ton 

in 2012 [6]. Richard Tol, a leading authority on SCC research, estimates that the 

mean SCC is $23 per ton with a 1% chance that it exceeds $78 per ton [5]. Other 

estimates put the cost of carbon at a much higher price than that; the United Nations 

Intergovernmental Panel on Climate Change (IPCC) pointed out that there was a $98 

difference between the highest and lowest peer-‐reviewed estimates in 2005 [8]. 

According to the IPCC, peer-‐reviewed estimates of the SCC put its mean value at $43 

per ton with a standard deviation of $83 per ton in 2005 dollars [35]. 

The SCC value is critically important to shaping energy legislation, which will 

have a varying degree of impact based on SCC assumptions. The gap in estimates, 

however, is not likely to narrow anytime soon. The variance in SCC estimates is 

mostly attributable to different choices of discount rate, uncertainty about the 

science of climate change, and varying assumptions about future population growth, 

economic growth, and greenhouse gas emissions [5]. 

1.3.2 The Carbon Tax 

As is evident from its name, the carbon tax is not an economic measure but 

rather a government-‐imposed levy on carbon dioxide emissions. Importantly, the 

carbon tax is not strictly a tax per ton of carbon emitted; it is understood to be a tax 

per ton of carbon dioxide, which is only partially composed of carbon. As of this 

11


writing, there is no federal carbon tax in the United States. 5 Over a year ago, 

President Obama proposed climate legislation with an implicit tax of $13.70 per ton 

of carbon dioxide within a cap-‐and-‐trade framework, but Congress has yet to vote 

on a bill [46]. In comparison, many European nations successfully enacted carbon 

taxes as early as 1990. Sweden’s tax is the most expensive at $150 per ton 6 , but it 

appears not to have had a dragging effect on the local economy [47]. 

In a perfect market, the penalty for emitting one ton of carbon into the air 

should be set equal to the marginal damage done by the additional ton, i.e. the social 

cost of carbon. It would then become a Pigouvian tax, or a tax levied on market 

activity that generates negative externalities not internalized by the private market. 

However, because markets are imperfect and the value of the SCC is uncertain, many 

governments around the world question whether a carbon tax is warranted at all. 

In later chapters, the hypothetical range for a carbon tax in the U.S. is $0 to 

$100 per ton carbon dioxide. This is based upon estimates of the SCC in past 

literature. According to the IPCC Climate Change Synthesis Report in 2007, most 

models show that “global carbon prices rising to $20 to $80 per ton by 2030 are 

consistent with stabilization” of CO2 in the atmosphere in 2100 [8]. Admittedly, it is 

unlikely that the U.S. Congress would impose a steep carbon tax in the near future, 

but the range is extended to $100 per ton to allow for the possibility. 

5 However, certain districts in California and Colorado have adopted carbon taxes [47]. 

6 Fuels used for electricity generation are exempt from the carbon tax, and the industrial sector is 

mandated to pay only 50% of the tax [47]. 

12

1.4 Overview of the Thesis 


In analyzing government intervention in the solar and wind energy markets, 

this thesis will examine the interplay of government-‐sponsored tax credits and a 

potential carbon tax. Chapter 2 explains the methodology used for arriving at costs 

for wind and solar energy installations in each of the fifty states. Chapter 3 offers a 

cost function to minimize electricity costs incurred by residential consumers across 

the country, and it illustrates the effects of government intervention on the national 

electricity mix and price. Chapter 4 builds off of Chapter 3 by developing a cost-‐ 

benefit model to assess the impact of different tax policies. The results and 

subsequent analysis in Chapter 5 demonstrate the overall social benefit of varying 

degrees of government intervention in the solar and wind energy markets. Finally, 

Chapter 6 summarizes the results and suggests areas for further research. 

13

2. Methodology of Cost Comparison 

Prior to exploring the effects of hypothetical government policies on 

energy usage, it is necessary to gather relevant information about the 

state of energy usage today. The first objective in this methodology is to compute 

and compare the costs, state by state, of electricity from three different sources: 

solar photovoltaic (PV) panels, wind turbines, and conventional retail electricity, a 

proxy for fossil fuels. From there, the data will lead to conclusions about where 

renewable energy can have the greatest impact, and what degree of government 

intervention (if any) is required in order to achieve the desired change. 

This task is heavily reliant upon data at both regional and national levels. 

Fortunately, the Department of Energy website houses a massive aggregation of 

data that enables any dedicated researcher to answer myriad questions concerning 

energy costs in the United States. One of those questions—how to sensibly

Methodology of Cost Comparison 

regionalize energy sources by exploiting cost disparities for solar, wind, and retail 

electricity across the United States—is explored here. 

2.1 Foundations for this Approach 

Rather than analyze the costs of all five of the renewable resources, this 

chapter will conduct an in-‐depth study of wind and solar energy only. Wind and 

solar have a great deal in common: both are considered to have significant long-‐ 

term potential, and both are vastly untapped sources of energy, as noted in the 

introduction. Because electricity generation is the biggest market that wind and 

solar energy have in common, this analysis will focus solely on electricity in the 

United States, as opposed to other forms of energy like direct heating and powering 

vehicles. 7 This allows for the direct 

comparison of wind and solar to fossil 

fuel-‐generated electricity, which will 

hereafter be called “retail electricity.” 

Retail electricity implies “the 

final sale of power from an electricity 

provider to an end-‐use consumer” [48]. 

Quite simply, the average retail 

electricity price in New York reflects 

the price that everyday New Yorkers 

7 Solar energy is used both for direct heating and electricity generation, whereas wind energy is 

limited to electricity generation. 

Figure 3. U.S. Electric Power Industry 

Net Generation, 2008 [27] 

15


are paying per kilowatt-‐hour on electrical bills. Typically, a varying mix of energy 

sources provides retail electricity to any region and state; from an analytical point of 

view, it is therefore impractical, if not nearly impossible, to separate coal-‐generated 

electricity from natural gas-‐ and petroleum-‐generated electricity for any area. 

Instead, it makes more sense to treat the three as a package and then utilize retail 

electricity price data, which is readily available for every state and sector. Local 

retail electricity prices serve as a benchmark against which electricity prices from 

solar and wind energy are compared; in other words, solar and wind power are 

considered economically competitive when and if their price points decline to those 

of retail electricity. 

Of course, retail electricity in the United States is not a perfect proxy for fossil 

fuel-‐generated electricity. As Figure 3 shows, fossil fuels—coal, natural gas, and 

petroleum—represent 70% of electricity generated in the United States. The 

remaining 30% comes from nuclear power (20%), renewables (9%), and “other” 

(1%). However, given the vast complexity of the different electricity mixes servicing 

consumers across the United States and the lack of available data decomposing the 

prices within each mix, a consumer’s local retail electricity price is generally a fair 

substitute for the price the consumer would pay if 100% of the electricity in the U.S. 

were generated by fossil fuels. Also, nuclear and hydroelectric power are roughly 

cost-‐competitive with fossil fuels in the regions where they are currently used, so 

16


the combined 26% of electricity consumption from those sources does not skew the 

retail price data. 8 

Within the retail electricity market, this analysis will utilize data from the 

residential sector exclusively. Accordingly, the analysis will look only at electricity 

generated by solar and wind power for 

residential use. From now on, “solar 

energy” is defined as rooftop solar 

photovoltaic panels that are installed to 

provide electricity to individual homes. In a 

similar vein, “wind energy” is defined as 

small-‐scale, individual wind turbines for 

residential electricity production rather 

than large-‐scale wind farms. 

Figure 4. Residential Energy Use in 

Different Types of Homes [12] 

Additionally, only residences falling under the category of “single-‐family 

detached home” are considered so as to exclude apartments and other shared 

residential buildings where cost calculations per household are somewhat 

ambiguous. Given that the energy consumption of single-‐family detached homes 

accounts for 80% of total residential energy use, as shown in Figure 4, the analytical 

results will be representative of the residential sector at large [12]. 

8 The U.S. average levelized cost for plants entering service in 2016 is: $104.2/MWh for fossil fuel 

plants, $107.3/MWh for nuclear plants, and $114.1/MWh for hydropower facilities [91]. The 

definition of levelized cost is “the present value of the total cost of building and operating a 

generating plant over its economic life, converted to equal annual payments” [90]. 

17

2.2 Factors Affecting Retail Electricity Prices in the United States 


The three major components of the electricity price are the generation, 

transmission, and distribution of electricity. Yet the average breakdown shown in 

Figure 5 is just that: an average. For a number of reasons, states do not pay 

equivalent retail electricity prices per kilowatt-‐hour of electricity. In fact, the range 

is quite large. There are many sources of variability driving regional electricity 

prices [11]: 

• Fuel type – Electricity prices will vary based on the availability and type of 

fuels in the region. 

• Power plants – Construction and maintenance is more costly for certain 

kinds of plants. 

• Weather conditions impact demand for electricity and, in turn, electricity 

prices. 

• State regulations (or lack 

thereof) regarding pricing: 

“Some states are fully regulated 

by the Public Service 

Commissions, while in others 

there is a combination of 

unregulated prices (for 

generators) and regulated prices 

(for transmission and 

distribution)” [11]. 

Figure 5. Major Components of U.S. 

Average Electricity Price, 2008 [11] 

(Cents per kWh and Share of Total) 

18


In addition to regional variation, electricity prices also vary by sector and over 

time. Residential consumers tend to pay the steepest rates because distribution 

costs are higher for them than for industrial and commercial consumers. 

Seasonality also plays a role in electricity prices; during the summer or winter, 

when demand for cooling or air conditioning is highest, prices tend to be the most 

expensive. 

2.3 Solar Photovoltaics 

The government records retail electricity prices across the country at regular 

intervals, but this practice has not been extended to the renewable electricity sector 

just yet. As a relatively new product targeted at mainstream consumers, solar 

photovoltaic panels do not have well-‐documented per-‐kilowatt-‐hour prices on a 

state-‐by-‐state basis. The growing interest in the renewable energy industry, 

however, prompts the need for knowledge of regional solar technology prices; the 

paucity of available price data is resolved here by building an entire data set from 

the ground up. 

2.3.1 Assumptions in Solar Calculations 

This analysis does not consider solar thermal technology. Solar thermal 

collectors—including flat plate, evacuated tube, and parabolic dish collectors—are 

typically used to heat water in homes. Instead, the focus is on solar electric 

technology: photovoltaic (PV) panels that provide electricity to homes by converting 

solar radiation into direct current. Photovoltaic literally means “capable of 

producing a voltage when exposed to radiant energy, especially light” [25]. Whereas 

19


solar thermal collectors can only transfer heat from the sun, PV panels enable 

individuals to use computers, refrigerators, and other appliances integral to 

American modern life. Figure 6 illustrates the distinction between solar thermal 

collectors and photovoltaic panels. 

Figure 6. Comparison of solar photovoltaic cells 

and solar thermal collectors [20] 

The first assumption is that all homes have the roof surface area necessary to 

support a rooftop solar installation that could theoretically power 100% of its 

electricity needs, notwithstanding one obvious problem. In reality, most households 

would not want to be completely reliant on solar power, which, like wind power, can 

be unreliable depending on weather conditions. Solar power is naturally a 

complement to, but not a replacement of, other sources of energy. 

To that end, the second assumption is that PV panels are grid-‐connected, 

meaning that the PV panels provide electricity to the home while the sun is shining, 

but when the solar resource is unavailable or limited, electricity from the grid 

supplies the household’s electricity needs. Likewise, any excess electricity produced 

20


by the solar PVs is fed back into the grid. Connecting a solar electric system to the 

grid eliminates the need to purchase electricity storage devices like batteries. 

The third major assumption is that the lifespan of a solar PV panel is twenty 

years, which is the standard length of time that PV module manufacturers provide a 

warranty [54]. 

2.3.2 Solar Energy Potential in the United States 

Of course, the intensity of the sun varies greatly across the United States, 

which in turn affects the potential for solar energy use in different regions. The 

relative measure of sunshine that represents an area’s potential for solar energy is 

daily peak sun hours; a peak sun hour is one kilowatt-‐hour per square meter of 

sunlight. It is a better comparative measure than hours of sunlight per day because 

it accounts for both intensity and duration of sunlight. Figure 7 is a solar insolation 9 

map of the United States. Reddish tones essentially represent “dense” sunlight— 

that is, the sun provides more kilowatt-‐hours of energy per square meter per day in 

the red and orange states. 

Table 2. Average Peak Sun Hours Per Day [19] 

States with most peak sun States with least peak sun 

hours per day 

hours per day 

New Mexico, 6.77 Vermont, 2.95 

Arizona, 6.50 Illinois, 3.14 

Nevada, 6.20 New Hampshire, 3.40 

Wyoming, 6.06 New York, 3.58 

Hawaii, 6.02 Pennsylvania, 3.60 

California, 5.74 Connecticut, 3.63 

9 Insolation: Solar radiation received at the earth’s surface [55]. 

21


Peak sun hour data for all fifty states was compiled from the National Solar 

Radiation Data Base [19]. There are measurement stations in or near major cities 

throughout the United States. For states that have more than one primary station, 

the stations’ measurements are averaged. The states with the highest and lowest 

peak sun hours per day are represented in Table 2. Combined with data on annual 

residential electricity consumption in each of the fifty states [56], it is possible to 

calculate the PV panel wattage required to theoretically meet 100% of the electricity 

demand of a typical single-‐family home in each state. 10 The wattage of the PV panel 

is the major determinant of the cost of the solar electric installation. 

Figure 7. Solar PV Resource Map of the United States [7] 

10 When the sun is shining, the PV panels of the calculated wattage will be capable of meeting 100% 

of household demand. When the sunlight is limited or unavailable, the PV panels may not fully meet 

demand. 

22

€ 

€ 


Based on the insolation map alone, one could conjecture that solar energy is 

most economical in the Southwest, especially Arizona, New Mexico, southern 

California, and surrounding states. But the attractiveness of solar energy in any 

region will depend on the relative prices of other electricity sources, which is why 

building a regional price data set for renewable energy sources is so crucial. 

2.3.3 Peak Sun Hours and PV Modules 

where 

The formula that represents the PV module wattage required in each state is: 

W i 

elec 

solar d i 

= 1.15 ⋅ solar 

k i 

solar 

W i = PV wattage required to provide 100% of the average single-‐family 

€ 

home’s electricity consumption in state i (kW) 

elec 

d i = average daily electricity consumption of a single-‐family home in 

state i (kWh) 

solar 

k i = average peak sun hours per day in state i (hours) 

i = states 1, 2, …, 51 (including District of Columbia) 

€ A factor of 1.15 is included in the calculation to account for energy loss resulting 

from the conversion of direct current into alternating current, which is necessary in 

order to power most household appliances. 

Table 3. Average Electricity Consumption in Single-‐Family Homes [19] 

States with highest electricity States with lowest electricity 

consumption (kWh/month) consumption (kWh/month) 

Tennessee, 1,344 Maine, 530 

Alabama, 1,305 California, 580 

Louisiana, 1,276 Vermont, 592 

Kentucky, 1,217 New York, 604 

Virginia, 1,207 Rhode Island, 608 

23


For reference, electricity consumption data for average single-‐family homes 

in a selection of states is listed in Table 3. Homes in southern states tend to 

consume the most electricity per month, whereas homes in the Northeast and 

California consume the least amount of electricity. The discrepancy is large, with 

some southern states consuming more than twice as much electricity as California 

and Northeastern states. 

Climate is one of the major factors affecting regional electricity consumption. 

Hot summers require the use of more air conditioning and other space cooling, so 

homes in southern states tend to use more electricity in the summer. Cold winters 

also increase energy use for space heating, but most U.S. households rely on natural 

gas rather than electricity for heating. However, “in the South the reverse is true, 

meaning that households in southern states will tend to have a peak of electricity 

use in winter as well as in summer” [92]. Another factor influencing regional 

electricity consumption is the average age of the housing stock: “New homes, which 

are more prevalent in the South, tend to use more electricity” [92]. 

Conversely, the lower electricity consumption in Northeastern states is 

explained by cooler summers, which decrease electricity demand for air 

conditioning, and by a greater reliance on fuel oil for heating during the winters 

[93]. Additionally, New Englanders are “more likely to live in older buildings and in 

apartments than householders nationwide,” which usually means they live in 

smaller residences that require less electricity [93]. 

24

€ 

€ 

€ 

2.3.4 Installation and Maintenance Costs 


Solar electric installations are priced according to wattage capacity, so the 

formula for the average installation cost of a PV module capable of providing 100% 

household electricity consumption in state i is as follows: 

where 

solar solar solar 

C install,i = W i ⋅ c install 

solar 

= average 

€ 

cost of installing a residential PV module in state i ($) 

C install,i 

solar 

c install = average installation cost of the residential PV module ($/kW) 

solar 



Due to the technological advancement of PV panels, the average cost per 

kilowatt installed has fallen dramatically over the past several years. Today, the 

total installation cost 11 is around $7,000 per kilowatt for residential solar modules, 

or as low as $5,000 per kilowatt for utility-‐scale installations [57] [33]. The $7,000 

per kilowatt estimate is used here, although the installation cost might be lower for 

those who have the expertise to install the PV modules themselves. The economies 

of scale in PV installations are assumed to be negligible for residential modules, 

which tend to be quite small. 

Moreover, maintenance costs 12 also need to be incorporated into the total 

cost of the solar energy system. Even though the annual maintenance cost for solar 

PV panels is very low, it is the only other component of the total cost of a solar 

11 Includes solar module itself, plus inverter, mounts, racks, wiring, and labor for installation. 

12 Includes electrical inspections and replacement of inverters. 

25

€ 

€ 


electric system. A rule of thumb used in the PV industry is to expect annual 

maintenance costs of 2% of the initial capital cost [58]. Therefore, the present value 

of all future maintenance costs is represented by: 

where 

solar 

solar (0.02 ⋅ C install,i) 

1 

C mntc,i = 1 − 

r (1+ r) −n 

⎡⎡ ⎤⎤ 

⎢⎢ ⎥⎥ 

⎣⎣ ⎦⎦ 

solar € 

= present value of all maintenance costs over lifetime of the PV module 

C mntc,i 

in state i ($) 

r = interest rate (assume real interest rate of 2%) 

n = lifetime of the PV module (assume 20 years) 

solar 

C install,i defined as above 

€ 

Based on historical trends, a nominal long-‐term interest rate of 5% and an inflation 

€ 

rate of 3% are projected in the future, resulting in a real long-‐term interest rate r of 

€ 

€ 

2% [62]. 

Combining the installation and maintenance costs, the average total cost of 

the solar PV installation in state i over its lifetime is represented by: 

where 

€ 

solar solar € solar 

, C install,i, 

C mntc,i ≥ 0 

C total,i 

solar solar solar solar 

C total,i = C install,i(1− 

β ) + C mntc,i 

β solar = federal investment tax credit for residential solar installations, 

0 ≤ β solar ≤1 

26


Because tax credits imply a dollar-‐for-‐dollar reduction in the income taxes a person 

must pay, the effective cost of the wind installation is simply the percentage (1-‐tax 

credit) of the original installation cost. 

Appendix A-‐1 provides a list of the installation costs, maintenance costs, and 

total costs 13 using this methodology for all 51 states. 14 The calculations show that 

solar PV systems capable of meeting 100% of household need are cheapest in New 

Mexico, due to the combination of intense sunlight and lower-‐than-‐average 

electricity consumption in that state. Still, with a price tag of $32,000, a PV module 

in New Mexico is not cheap. In other states, however, PV installations of this kind 

appear so expensive as to be infeasible: in Alabama, Tennessee, and West Virginia, 

PV modules meeting the specifications described would cost over $100,000, which 

is far more than the average consumer would spend on retail electricity bills in an 

entire lifetime. 15 

The range in costs demonstrates that the economic practicality of solar 

power varies greatly across the United States. It is important to note, however, that 

households could install modules far smaller than those discussed in this analysis 

and in some cases achieve a reduction in their electrical bills. Here, the assumption 

that households will build modules to meet 100% of their electric need is solely for 

13 

For now, assuming the absence of any subsidy from the federal or state government. 

14 

Including the District of Columbia. 

15 

At this point, two things to bear in mind are that this number reflects neither investment tax 

credits nor expected price declines of PV modules. The latter is discussed in Section 4.2.1. 

27

€ 

€ 

€ 


purposes of comparison, so that data of a solar-‐powered home can be juxtaposed to 

that of wind-‐powered and fossil fuel-‐powered homes. 

2.3.5 Electricity Production of the PV Module 

The next step is to find the total electricity produced by a solar PV system 

over its useful life. Using previously defined variables, this is simply: 

where 

solar solar solar 

E total,i = 0.87W i ⋅ k i ⋅ 365n 

solar 

= the 

€ 

total output of electricity over the lifespan of the solar PV module 

E total,i 

for the average residential single-‐family home in state i (kWh) 

solar 



solar 

k i = average peak sun hours per day in state i (hours) 

n = lifetime of the PV module (assume 20 years) 

The total output is reduced by approximately 13% due to energy loss in the 

€ 

conversion of direct current into alternating current. Also, the peak sun hour data 

k solar is daily, hence n, measured in years, must be adjusted by a factor of 365 (days 

per year). Finally, plugging W into the equation, the total output value E for the 

average module in each state matches the home’s expected electricity consumption 

in state i over that time period, or 

elec 

365n ⋅ d i 

just as intended. After all, consumers will want to spend just enough money to 

install a PV module sized to€ meet their electricity consumption—no more and no 

less. 

28

€ 

2.3.6 Overall Price of Solar Electricity in this Model 


Having calculated the total cost of the PV module over its lifetime as well as 

the total output of electricity over its lifetime, the price per kilowatt-‐hour of 

electricity generated by the solar PV system in state i follows as such: 

where 

p i 

solar 

solar C total,i 

= 

solar 

E total,i 

solar 

p i = overall price per kilowatt-‐hour of electricity that consumers will pay 

€ 

over lifespan of the PV module in state i ($/kWh), 

solar 

p i ≥ 0 

Calculations for output of electricity and overall price per kilowatt-‐hour by 

state are included in Appendix A-‐1. Not surprisingly, the€ solar-‐generated electricity 

prices are cheapest in states with the greatest number of peak sun hours per day, 

and are most expensive in states with the fewest number of peak sun hours per day. 

Table 4 provides the “tails” of the overall price calculations. The calculations 

confirm the expectation that states with abundant sunshine have a natural price 

advantage because more solar radiation is captured per square foot of photovoltaic 

panel per day. Consumers in less sunny states (i.e., states with fewer peak sun 

hours) are forced to purchase larger, and therefore more expensive PV systems in 

Table 4. Solar-‐Generated Electricity Prices 

States with highest solar States with lowest solar 

electric prices ($/kWh) electric prices ($/kWh) 

Vermont, 0.37 New Mexico, 0.16 

Illinois, 0.35 Arizona, 0.17 

New Hampshire, 0.32 Wyoming, 0.18 

New York, 0.31 Nevada, 0.18 

Pennsylvania, 0.31 Hawaii, 0.18 

29


order to capture a comparable amount of energy from the sunlight to meet their 

electricity needs. 

On the whole, the weighted average price of solar-‐generated electricity 16 

from residential PV modules is $0.25/kWh without any government tax incentive, 

which remains much higher than the “baseline” price of retail electricity of 

$0.11/kWh. Chapter 4 will explore how improvements in PV technology, combined 

with different levels of a tax credit, can significantly reduce the price of solar 

electricity. 

2.3.7 Government Incentives 

As discussed in the introduction, a substantial federal tax credit of 30% is 

available to those who install PV modules in their homes. Taking advantage of the 

federal tax credit in addition to any state-‐specific tax incentives can lower the cost of 

installation to the point that, in some areas, the price of solar electricity competes 

with retail electricity. For example, in Arizona, solar electricity costs $0.17/kWh in 

the absence of any tax credit; with a 30% tax credit, the price paid by the consumer 

drops to $0.13/kWh, and with an aggressive 50% tax credit, the price drops even 

further to $0.10/kWh, which is the average price for retail electricity in the state. 

One can easily see how effective the tax credit is as an instrument to 

influence consumers. Chapter 3 will explore in greater depth how the level of the 

renewable energy tax credit in addition to a carbon tax influences the relative prices 

of solar, wind, and retail electricity. 

16 The price is weighted over the 51 states. 

30

2.4 Wind Energy 


Within the last couple of decades, wind energy has developed a following 

within the United States. But like solar PVs, wind turbines have yet to penetrate the 

mainstream market (though many believe they are on the verge of doing so). As a 

result, no state-‐by-‐state price data for wind energy yet exists. To address this need, 

the approach used to build the solar price data set is adapted for wind energy. 

2.4.1 Assumptions in Wind Calculations 

To remain consistent with the approach taken to solar calculations, the wind 

energy in this study is limited to “small wind,” or the use of wind turbines for 

individual homes. As is true across the renewable energy sector, installation costs 

are dependent upon scale: generally, the larger the wind or solar installation, the 

cheaper the resulting electricity will be per kilowatt-‐hour. Thus, to eliminate 

variance in costs due to scale, only small-‐scale wind turbines intended for 

residential use are considered. 

Three main assumptions regarding small wind turbines are made to parallel 

the solar calculation approach. The first is that the single-‐family homeowners in 

this study are willing to devote some space on their property to a wind turbine. It 

may be in the backyard, the front yard, or anywhere they like so long as the wind 

turbine is built to provide enough electricity to meet 100% of the home’s electricity 

demand. Secondly, as with the PV modules, all residential wind turbines are 

assumed to be on-‐grid. When the wind is blowing, the homeowner will use the 

turbine-‐generated electricity, but when winds are low or no wind is blowing at all, 

the owner can rely upon electricity from the grid. If excess electricity is generated 

31


by the turbine, it is sent to the utility to be transferred to a neighbor [22]. The third 

assumption is that the wind turbines have a lifespan of twenty years, which is 

consistent with objective assessments of the useful life of turbines on the market 

today [59]. However, the American Wind Energy Association has suggested that the 

actual operating life of a typical wind turbine may be much longer than that [60]. 

2.4.2 Wind Energy Potential in the United States 

Wind energy is akin to solar energy in that its “potential” in a given state or 

region is determined by one thing: the area’s average wind speed. (For solar power, 

the analogous metric was the area’s peak sun hours.) Of course, a number of factors 

determine a region’s wind speed, like height above sea level, proximity to a 

coastline, and local terrain, to name just a few—but ultimately, only the wind speed 

matters. 

The National Renewable Energy Laboratory (NREL) created a wind resource 

map (Figure 8), wherein the states with orange and pink coloring have “fair” to 

“good” wind energy potential. “Excellent,” “outstanding,” and “superb” wind 

potential ratings are primarily reserved for coastlines, with some “excellent” ratings 

peppered throughout the country, particularly in the Midwest region. Data from the 

American Wind Energy Association (AWEA) in Table 5 corroborates the visual 

display of the wind resource. The AWEA estimates that the United States could 

potentially generate 10.8 billion megawatts from its onshore wind resources on an 

annual basis, which is more than twice as much electricity as the U.S. consumes 

annually [17]. However, today, the “installed wind power fleet” generates just 48 

32

Figure 8. Wind Energy Resource Map [3] 

Table 5. Top States for Wind Energy Potential [17] 

States with greatest 

wind energy 

potential 

Annual wind 

energy potential 

(billions of kWh) 

North Dakota 1,210 

Texas 1,190 

Kansas 1,070 

South Dakota 1,030 

Montana 1,020 

Nebraska 868 

Wyoming 747 

Oklahoma 725 


33


billion kilowatt-‐hours of electricity—that’s only a tiny fraction (less than one-‐half of 

one percent) of the generation potential in any of the windiest states in Table 5 [17]. 

By contrast, the wind resource map clearly shows that a large portion of the 

country remains white, representing little or no wind potential in those areas. 

(White areas have been assigned a wind power class of 1 or 2 by the NREL, and only 

classes 3 through 7 are represented by color on the map.) As the wind energy cost 

calculations will soon show, the white states are at a huge cost disadvantage when it 

comes to installing wind turbines. 

2.4.3 Modeling Wind Energy using the Weibull Distribution 

Given the volatile nature of wind as a natural resource, it is helpful to think of 

wind speed in a state as a distribution rather than as a discrete average value. Past 

literature has demonstrated that wind speeds can be modeled by the Weibull 

distribution, the shape of which reflects the behavior of wind: light and moderate 

winds are fairly common, but strong gales are relatively infrequent. The Weibull 

probability density function is given by 

where [18] 

P(V ) = k 

c 

⎛⎛ V 

⎜⎜ 

⎝⎝ c 

⎞⎞ 

⎠⎠ 

k −1 

⎟⎟ 

exp − V ⎛⎛ 

⎜⎜ 

⎝⎝ c 

⎞⎞ ⎛⎛ k⎞⎞ 

⎜⎜ ⎟⎟ ⎟⎟ 

⎝⎝ ⎠⎠ ⎠⎠ 

P(V) = the probability 

€ 

of occurrence of speed V 

k = the dimensionless Weibull shape parameter 

c = the Weibull scale parameter 

34


The scale parameter c indicates how ‘windy’ the location is overall. 17 The 

shape parameter indicates how dense the wind distribution is around the mean 

speed. A shape parameter of 1 represents a “heavy tails” region with lots of low 

speed winds combined with high speed winds, whereas a shape parameter of 3 

represents a region with wind speeds consistently around the median. Typical wind 

behavior, however, is best represented by a shape parameter of 2, under which 

condition the Weibull distribution is referred to as the Rayleigh distribution [18]. 

More formally, the parameters can be evaluated using the equations [9] 

−1 −1.086 

ki = (σi V i ) 

−1 

V i = ci Γ(1+ ki ) 

where V i is the annual mean wind speed in state i and σi is the variance of the 

monthly means. However, 

€ 

because wind speed variance data broken down by state, 

€ 

as opposed to region, is unavailable, two reasonable assumptions are made in order 

to apply the Weibull function: 

• The U.S., as a whole, has a Weibull shape parameter of 2. Due to the 

lack of wind volatility data available at the state (as opposed to 

regional) level, this constant parameter is used for all states. 

• The gamma function in V i when k = 2 is approximately equal to 1, so 

V i ≈ c i . 18 This simplifying assumption allows for NREL mean wind 

€ 

data by state to be the direct input into the Weibull model. 

17 € 

To come up with c values for every state, each state was first assigned a wind class per the wind 

resource map from the NREL. This is, of course, a somewhat subjective method because wind 

potential is not defined along state lines, and it is often the case that a mix of wind classes make up a 

single state. In such cases, the wind classes are averaged to come up with a reasonable state-‐wide 

wind classification. Appendix A-‐3 lists the wind class assignments by state as well as their 

corresponding c (i.e., average wind speed) values. 

18 

Γ(n) = (n-‐1)!, so Γ(1+(1/k)) = Γ(1+(1/2)) = (1/2)! = .89. 

35


Figures 9 and 10 show the Weibull PDFs for two very different states from a 

wind energy perspective: Alabama, which has virtually no wind energy potential 

according to the NREL map, and Montana, one of the top states for wind energy. The 

MATLAB code in Appendix A-‐4 was used to generate these graphs. Having assumed 

a constant shape parameter across the country, similar graphs can be generated for 

other states merely by adjusting the scale parameter. The Weibull PDFs shown 

below are useful representations of wind speed, for wind is so inconsistent as to 

render a simple average uninformative. 

Figure 9. Alabama Wind Distribution 

2.4.4 Electricity Production of the Wind Turbine 

Figure 10. Montana Wind Distribution 

Once armed with wind distributions for each of the 51 states, the next task is 

to compute the electricity generation of a wind turbine over its lifetime, which will 

depend primarily on two variables: the distribution of wind speeds in the state, and 

the size of the wind turbine in the state, measured by rotor diameter. Rotor 

diameters of small, residential-‐use wind turbines are generally ten meters or less 

[16]. Just like with the solar calculations, the assumption here is that consumers 

36

€ 

€ 

€ 

€ 

€ 


will install wind turbines powerful enough to meet 100% of their residential 

electricity needs per year. 

As defined in Hasan [9], the electrical energy generated over the course of 

one year by the wine turbine is obtained from the equation 

where 

wind 

E annual,i 

wind 

E annual,i 

∫ 

V 2 

wind wind 

= Wi (V )Ti (V )dV 

V 1 

€ 

= annual electricity generated by the wind turbine in state i (kWh) 

wind 

Wi (V ) = power output of the wind turbine as a function of wind speed V in 

state i (kW) 

wind 

Ti (V ) = number of hours in a year during which the wind blows with 

speed V in state i (hours) 

V 1 = cut-‐in speed (the minimum speed at which the wind turbine will 

generate useable power, usually around 3 meters per second) 

V 2 = cut-‐out speed (the speed at which the wind turbine ceases to function 

and shuts down, usually around 20 meters per second for small wind 

turbines [14]) 

Consequently, the total electricity generated by the wind turbine in state i over the 

course of its useful life is 

turbine. 

wind wind 

E total,i = n ⋅Eannual,i 

, where n is the lifetime of the wind 

The annual 

€ 

number of hours during which V ≥ Vx is given by the equation [9] 

€ 

wind −1 k 

Ti (V ≥Vx ) = 8760 exp {− (Vx ci ) } 

37

€ 

€ 

€ 

€ 

€ 

€ 


where the factor 8760 represents the number of hours in a year. The effective 

power output 19 in kilowatts from a wind turbine, W(V), is given by the AWEA 

formula [61] 

where 

ρ air 

A i 

0.5⋅ρ wind air ⋅A i ⋅ Cperf ⋅V 

Wi (V ) = 3 ⋅ Ngen ⋅ Ngear 1000 

= air density (1.225 kg/m 

€ 

3 ) 

= average rotor swept area required to meet a typical household’s 

electricity needs in state i: π*(rotor radius) 2 (unit: square meter) 

C perf = coefficient of performance of the wind turbine, also known as capacity 

factor (35% for a good design, but 59% is the theoretical maximum, 

known as the Betz limit) 

N gen = generator efficiency (80% for a grid-‐connected induction generator) 

N gear = gearbox/bearings efficiency (95% for a good design) 

The only variable in the W(V) calculation that changes from state to state is 

A i , the rotor swept area of the wind turbine. The ideal rotor swept area for state i— 

that is, the 

A i required in order for the wind turbine to yield precisely 100% of the 

average household’s electricity consumption—is determined by setting the integral 

€ 

E equal to the average annual electricity consumption per household in state i, and 

then solving for 

€ 

A i , as follows: 

€ 

19 After efficiency losses. 

365d i 

∫ 

elec 

V2 = Wi 

V1 wind wind 

(V )Ti (V )dV 

38


However, in practice, consumers in the market cannot specify their rotor 

swept area to a precise decimal unless they order a customized wind turbine, which 

is unlikely. To address this, the MATLAB code in Appendix A-‐4 returns the matrix 

EnergyProduced, which lists, by state, annual electricity output from a range of 

commercially available wind turbine sizes. Because wind turbines are usually 

manufactured and sold with no smaller than one-‐half meter increments in rotor 

diameter, the matrix simulates the real-‐life process of a consumer selecting the wind 

turbine that most closely meets, but probably does not exactly meet, his or her 

household’s electricity need. 

In North Dakota, for example, a 7-‐meter diameter wind turbine (with a 38.48 

m 2 swept area) is the size that most closely meets the average North Dakota home’s 

electricity needs. Inputting 38.48 m 2 for 

A NorthDakota , the W(V)T(V) function for North 

Dakota is shown in Figure 11. 20 The final step is to compute the integral 

wind 

E annual,ND 

€ 

from the cut-‐in speed (3 m/s) to the cut-‐out speed (20 m/s). For North Dakota, the 

EnergyPerYearND integration returns 13,070 kWh produced€ per year, which is 

approximately equal to the 12,936 kWh consumed per year by the average single-‐ 

family home in North Dakota, as intended. This method is repeated for all fifty-‐one 

states. 

In the wind turbine industry, turbines are typically advertised by their power 

rating, as distinct from their effective power output. The effective power output 

formula used above yields a realistic measure of the power a consumer can expect 

20 The accompanying MATLAB code to produce this plot is included in Appendix A-‐4. 

39

Figure 11. W(V)T(V) Function for North Dakota 


from a wind turbine of a certain size. The advertised power rating, on the other 

hand, is essentially an overstatement of the turbine’s realistic production; 

troublingly, there are no standards to which turbine manufacturers must comply 

regarding the wind speeds they use in their power rating calculations. Nor do 

turbine manufacturers account for generator and gearbox efficiency, both of which 

lower the expected power output of a wind turbine. Instead, turbine manufacturers 

use a more “ideal” version of the W(V) formula: 

wind 

0.5⋅ρ wind air ⋅A i ⋅ Cperf ⋅V 

Power Rating = W rating,i = 3 

1000 

where all variables are defined as before, except that V is set equal to 10 meters per 

second (m/s), 

€ 

a wind speed in the upper quartile for most regional wind 

distributions. Turbine manufacturers use a high wind speed—sometimes even 

higher than 10 m/s—to advertise the power their turbines are capable of producing, 

40

€ 

€ 


but not necessarily the power the turbines achieve frequently throughout the day. 

Power ratings become relevant in the next section because turbine prices are 

usually set according to the manufacturer’s power rating despite the lack of explicit 

industry-‐wide standards. 

Appendix A-‐3 provides a listing of wind classes, corresponding annual mean 

wind speeds, turbine rotor diameters, turbine power ratings required to meet 

electricity need, and integrations of 

wind 

E annual,i 

2.4.5 Installation and Maintenance Costs 

for all of the states. 

€ 

Similar to solar energy, the greatest expense associated with wind energy is 

the up-‐front capital cost of the technology. Also like solar energy, the cost of a wind 

turbine installation is directly proportional to the wattage of the installed system. 

The one-‐time installation cost for a wind turbine is represented by the equation 

where 

wind wind wind 

C install,i = W rating,i⋅ 

c install 

wind 

C install,i = average cost of installing a residential wind turbine in state i ($) 

€ 

wind 

c install 

= average installation cost of the turbine per kilowatt-‐hour ($/kW) 

wind 

W rating,i = the kilowatt rating of the wind turbine by its manufacturer (kW) 

While 

wind 

c install can vary significantly depending on the scale of the project, the 

€ 

average cost in 2009 for residential-‐sized wind installations was $4,000 per kilowatt 

[63]. € 21 (This compares favorably to residential PV panels, which are installed for 

$7,000 per kilowatt.) Most homeowners will need wind turbines of at least five 

kilowatts in order to provide a sufficient amount of electricity to their homes; this 

21 Prices range from $1,000 per kilowatt for utility-‐scale installations to $5,000 per kilowatt for very 

small wind installations. 

41

€ 


puts the approximate lower bound of a wind turbine installation at $20,000, which, 

for the average homeowner, is a hefty upfront payment no matter its benefits. 

The present value of all maintenance costs for the residential turbine is 

modeled in the same way as maintenance costs for a PV module. That is, 

where, as before, 

wind 

wind (0.02 ⋅ C install,i) 

1 

C mntc,i = 1− 

r (1+ r) −n 

⎡⎡ ⎤⎤ 

⎢⎢ ⎥⎥ 

⎣⎣ ⎦⎦ 

wind € 

= present value of all maintenance costs over lifetime of the wind 

C mntc,i 

turbine in state i ($) 

r = interest rate (assume real interest rate of 2%) 

n = lifetime of the wind turbine (assume 20 years) 

€ 

Combining the installation and maintenance costs, the average total lifetime cost in 

€ 

dollars of the wind turbine in state i is represented by: 

€ 

where 

wind wind € wind 

, C install,i, 

C mntc,i ≥ 0 

C total,i 

wind wind wind wind 

C total,i = C install,i(1− 


β wind = federal investment tax credit for residential wind turbines, 0 ≤ β wind ≤1 

A notable difference between the total costs by state of the solar electric 

€ 

€ 

versus the wind electric systems is, interestingly enough, symbolic of the difference 

between the sun and wind as natural resources: the sun, which shines in all states 

indiscriminately (albeit with varying levels of irradiation), gives rise to total solar 

electric costs which are relatively consistent around a nationwide mean. The wind, 

on the other hand, is distributed much less evenly across the states, resulting in 

42

€ 


wide disparities in wind electricity costs. As an example, a wind turbine can be 

installed for as little as $14,852 in California, a Class 3 wind state—yet a wind 

turbine producing the same amount of electrical output per year would cost $27,617 

in Connecticut, a Class 2 wind state. 22 

Perhaps coincidentally, in addition to having very little wind as a resource, 

Class 1 states tend to consume more electricity per year than the average state. The 

combination of these two factors drives wind energy costs up considerably. Clearly, 

there are certain states—like Alabama, Georgia, and Kentucky—that are unlikely 

candidates for wind energy, absent heavy government subsidies or a dramatic 

reduction in technology costs. 

2.4.6 Overall Price of Wind Electricity in this Model 

Having computed the cost and energy generation data for each state, the 

pieces are now put together to arrive at the end result. The overall price per 

kilowatt-‐hour of electricity generated by the wind turbine in state i is: 

where 

p i 

p i 

wind 

wind C total,i 

= wind 

E total,i 

= C wind wind wind 

install,i(1 

− β ) + C mntc,i 

V2 wind wind 

n Wi (V )Ti (V )dV 

∫ 

V 1 

wind 

= € overall price per kilowatt-‐hour of electricity that consumers will 

pay over lifespan of the wind turbine in state i ($/kWh), 

€ 

wind 

p i ≥ 0 

22 The cost disparity is solely due to the difference in the wind resource in California and 

Connecticut. California, which has a lot of wind, will generate more electricity per wind turbine than 

other states. To compensate for the lesser wind resource, consumers in Connecticut must install 

larger wind turbines to produce the same amount of energy as consumers in California. 

43


One can see that the wind calculations follow a similar form to the solar 

calculations in Section 2.3. Likewise, the wind calculations yield the same intuitive 

results as the solar calculations. States with the greatest wind energy potential (per 

Table 5) have the lowest overall wind-‐generated electricity prices (per Table 6), and 

vice versa. The figures in Table 6 demonstrate that wind energy tends to be quite 

polarized: wind-‐generated electricity is so effective in some states that it is cost-‐ 

competitive with fossil fuels already, whereas in other states wind-‐generated 

electricity is more than twenty times the price of retail electricity. In the latter 

states, consumers must build enormous wind turbines in order to catch the limited 

energy available in the wind. The expense is far from recouped, even over a twenty-‐ 

year-‐plus useful life of a wind turbine. 

State-‐by-‐state calculations for installation costs, maintenance costs, total 

costs, and overall per-‐kilowatt-‐hour prices are listed in Appendix A-‐3. 

2.4.7 Government Incentives 

Table 6. Overall Cost of Wind-‐Generated Electricity 

States with highest wind 

electricity prices 

($/kWh) 

States with lowest wind 

electricity prices 

($/kWh) 

Alabama, 2.12 Montana, 0.10 

Kentucky, 2.12 Idaho, 0.11 

Louisiana, 2.12 North Dakota, 0.12 

Mississippi, 2.12 Nevada, 0.12 

Florida, 2.12 Wyoming, 0.12 

Unlike solar energy, wind energy has achieved “grid parity,” or cost 

competitiveness with fossil fuels, in some states without the help of a tax incentive. 

44


However, for the large number of states where wind energy is on the cusp of 

reaching grid parity, a tax credit can move the needle. Indeed, wind energy installed 

capacity has been growing at a faster and faster rate as wind turbines become more 

economical. For example, in a state like Maine, which has a higher-‐than-‐average 

retail electricity price of 16.5¢ per kilowatt-‐hour, a 30% tax credit brings down the 

price of wind-‐generated electricity from 17.7¢ to 13.7¢ per kilowatt-‐hour, allowing 

the renewable source to beat the retail price. 

2.5 Retail Electricity 

Because retail electricity data is readily available on the Energy Information 

Administration website, there is no need to build estimates from the ground up à la 

solar and wind calculations. For reference, the average retail prices of electricity in 

2008 for all fifty-‐one states has been reproduced in Appendix A-‐2. What will 

henceforth be called the “baseline” price of electricity is $0.11 per kilowatt-‐hour, the 

weighted average cost of retail electricity for residential consumers in the U.S. in 

2008. The median retail electricity price in 2008 was $0.09 per kilowatt-‐hour, 

suggesting that some states with larger weights have higher electricity prices. 

California and New York, which have two of the highest retail electricity prices 

nationwide, are prime examples. 

2.5.1 Regional Cost Discrepancies 

Just as solar and wind energy have regional cost disparities, so too does the 

price of retail electricity vary with region. Areas of the country with coal deposits, 

like Wyoming, Kentucky, and West Virginia, tend to have cheaper retail electricity 

45


on average. Coal is, after all, the cheapest fossil fuel, and it makes up almost half of 

retail electricity generation in the U.S. Table 7 shows that all but three of the top ten 

coal-‐producing states have retail electricity prices below the national median. 

As a region, the Northwest—primarily Idaho, Washington, Oregon—claims 

the cheapest electric rates in the nation. Unlike the rest of the country, a significant 

portion of electricity in the Northwest comes from hydropower thanks to the 

region’s numerous dams. In contrast, states in the Northeast typically pay the 

highest electrical bills. Of the ten most expensive electrical rates in the country, all 

but three (Hawaii, Alaska, and California) belong to Northeastern states, as Table 8 

shows. 

State 

Table 7. Electricity Prices and Coal Production [67] [56] 

Percent of 

Total U.S. Coal 

Production 

Retail 

Electricity Price 

(cents/kWh) 

Rank in Price of 

Retail Electricity 

(1 = cheapest) 

Montana 25.4 8.77 18 

Illinois 16.5 10.12 31 

Wyoming 14.4 7.75 8 

West Virginia 8 6.73 2 

Kentucky 6.3 7.34 5 

Pennsylvania 6.1 10.95 34 

Ohio 4 9.57 29 

Colorado 3.6 9.25 23 

Texas 2.7 12.34 39 

Indiana 2.1 8.26 14 

Though there is some debate as to why the Northeast experiences higher 

retail prices, some argue that it stems from “a deliberate policy of favoring cleaner 

(and more expensive) sources of electricity” [68]. Others blame the population 

46


density of the region, suggesting that the rates are excessive due to transmission 

congestion [68]. Regardless, there is no question that there are marked price 

discrepancies from state to state. 

Table 8. Most Expensive Retail 

Electricity Prices, By State (2008) [56] 

State 

2.6 Price Comparison of Electricity Sources 

Retail 

Electricity Price 

(cents/kWh) 

Hawaii 24.12 

Connecticut 19.11 

New York 17.10 

Maine 16.52 

Massachusetts 16.23 

Alaska 15.18 

New Hampshire 14.88 

California 14.42 

Vermont 14.15 

New Jersey 14.14 

The cost methodology introduced in this chapter provides a framework for 

building a data set not otherwise available for analysis and manipulation. As 

frontier technologies, wind turbines and solar PVs simply do not have nearly as 

much compiled data available to the public as do traditional sources of energy. But 

by boiling down solar electricity, wind electricity, and retail electricity to a 

comparable measure—the “overall” price of electricity per kilowatt-‐hour—this 

methodology serves as a springboard for further analysis. A recurring theme 

throughout the forthcoming chapters is that of exploiting cost disparities between 

47


regions for the good of both society and the environment. The comparable price 

metric is crucial in that it is the single most important determinant of market forces, 

which will ultimately accept or reject solar and wind technologies. 

48

3. Applying Government Forces to the Electricity Market 

In Chapter 2, electricity prices from different sources were calculated in 

the absence of government intervention. But in the real world, 

governments can enact legislation to manipulate consumer decision making for the 

good of society, and they do so often. The commonly cited justification for wielding 

government power in such a way is “market failure,” or the inability of a market to 

allocate resources efficiently. Markets left to their own devices may ignore 

externalities imposed on society at large—like pollution—by free and private 

economic activity. Following that line of thought, the argument can be made that 

energy in its various forms is currently mispriced because social costs are not built 

into market prices. In the context of this energy problem, the two main tactics used

Applying Government Forces to the Electricity Market 

to address the mispricing of energy are the carbon tax (explicit or implicit 23 ) and the 

tax credit (one of many forms of a subsidy). Both are powerful levers with which 

the government can alter market prices. 

Such influence in the electricity market is particularly meaningful due to the 

price inelasticity of electricity; that is to say, as the price of the electricity increases 

or decreases, the quantity consumed remains relatively constant. Consumers’ 

inability to live without electricity and producers’ price monopoly in some states 

(which leaves consumers with no cheaper substitutes) are both causes of the 

inelasticity of demand for electricity. In the case of the California Electricity Crisis in 

2001, upticks in the per-‐kilowatt-‐hour price of electricity prompted a call for 

government intervention from an otherwise helpless public [64]. In brief, 

Americans are keenly aware of the price of electricity due to its necessity. 

The price-‐altering effects of government incentives, therefore, are crucial to 

the future of renewable energy. As a pair, the carbon tax and the renewable tax 

credit motivate the same directional shift: transitioning from fossil fuels to “clean” 

energy. Yet they do so in opposite ways (by penalizing or rewarding consumers) 

and with arguably different rates of success. Notwithstanding the philosophical or 

political underpinnings of legislators’ preferences for one method to the other, this 

chapter will examine the impact of the carbon tax and renewable tax credit in 

conjunction as well as the isolated impact of each on its own. 

23 An explicit carbon tax is a levy on an emitted ton of carbon dioxide regardless of its source. An 

implicit carbon tax could exist in a cap-‐and-‐trade framework, whereby the government distributes a 

certain number of carbon credits to power plants and allows the plants to trade the credits amongst 

themselves, resulting in a market-‐driven price for one ton of carbon dioxide emissions. 

50

€ 

€ 

3.1 The Quantitative Model 


This model assumes that three different sources of electricity are available to 

every household in the United States: the local utility, a residential PV module, and a 

residential wind turbine. It is assumed that the three different sources are perfect 

substitutes, meaning that there is no differentiation in quality among them. 

Consequently, consumers will always prefer the least expensive option. Chapter 4 

will account for consumer behavior that departs from this assumption. 

3.1.1 Decision Variables 

In this model, the government is the decision-‐making agent. The degree to 

which it manipulates prices in the electricity market will influence consumers’ 

choices, also known as the “market response.” The three major decisions made by 

the government in this model are represented by 

c carbon = the “cost of carbon,” a government-‐enforced tax on emissions of 

carbon dioxide ($/ton CO2) 

β wind = federal tax credit for wind installations 

β solar = federal tax credit for solar installations 

The carbon tax might more appropriately be called the “cost of carbon 

€ 

dioxide,” because the amount of tax owed is based on tons of carbon dioxide 

emitted, not carbon alone. Yet the media and politicians have colloquialized the 

phrase “cost of carbon,” so it will be used as it is intended. 

Even though the Residential Renewable Energy Tax Credit is currently 

designed to provide equivalent incentives for wind and solar energy, the solar and 

51

€ 

€ 


wind tax credits are treated as separate decisions here should the government 

decide to disjoin them. 

3.1.2 Market Response 

Consumers are also decision-‐making agents in the sense that they must 

choose a preferred source of electricity. But because their decisions are greatly 

influenced by the actions of the government, consumer decisions are relegated to 

market response variables rather than decision variables. 

Prices are calculated at a state-‐wide level, so the model predicts that all 

households within a state will respond in the same way to the relative pricing of 

retail, wind, and solar electricity. In aggregate, the market response variables are 

represented by 

retail carbon 

µ i (c ) = the proportion of the electricity portfolio allocated to retail 

electricity in state i 

wind wind 

µ i (β ) = the proportion of the electricity portfolio allocated to wind 


solar solar 

µ i (β ) = the proportion of the electricity portfolio allocated to solar 


€ 

Treating retail, wind, and solar electricity as perfect substitutes would lead to 100% 

of households within a given state selecting the cheapest source of electricity. 

However, Section 3.1.4 complicates this result by incorporating variability of solar 

electricity prices into the model. 

Ultimately, 

€ 

retail wind 

µ i , µi , and 

€ 

solar 

µ i are determined by the relationship of the 

prices of retail, wind, and solar electricity. Indirectly, then, each of the market 

52

€ 

€ 

€ 

€ 


response variables is dependent on all three decisions: the carbon tax, the wind 

turbine subsidy, and the solar PV subsidy. For clean notation purposes, the market 

response variables are written as functions of the government decisions that most 

contribute to each of the variables. For retail electricity, that is the carbon tax; for 

wind electricity, the wind turbine subsidy; and for solar electricity, the solar PV 

subsidy. The method to calculate each of the market response variables is 

developed in Section 3.1.4. 

3.1.3 The Cost Function and Constraints 

The cost function for the residential electricity price in state i is given by 

€ 

F( c carbon , β wind , β solar ) = 

wind wind wind wind solar solar 

µ i (β ) ⋅ p i (β ) + µi (β ) ⋅ ˆ 

such that 

€ 

and where 

€ 

c carbon ≥ 0 

1 ≥ β wind ≥ 0 

1 ≥ β solar ≥ 0 

wind wind wind 

wind wind C install,i(1− 


p i (β ) = wind 

E total,i 

retail cabon 

p i (c ) = p pretax,i 

solar solar 

p i (β ) + µi 

retail carbon retail cabon 

(c ) ⋅ p i (c ) 

= the average wind electricity price in state i ($/kWh) 

retail + c carbon 

CO2 mi = the average retail electricity price in state i after the 

implementation of the carbon tax ($/kWh) 

53

€ 

€ 

where 


CO2 mi = the ratio of electricity produced in state i to the 

output of CO2 from burning of fossil fuels to 

generate electricity in state i (kWh/ton CO2) [65] 

solar solar 

p ˆ i (β ) = the “achievable” solar electricity price in state i based on a 

Note that 

solar 

p i 

normal distribution ($/kWh) 

solar 

p ˆ i is used instead of 

solar 

p i , the average price of solar electricity in 

state i. If were used, the optimal solution would lead to the complete exclusion 

€ 

€ 

of solar power; households would choose between the other two options because, 

€ 

when comparing deterministic average prices, either wind or retail electricity is 

cheaper than solar electricity in every state. However, it is not necessarily the case 

that wind or retail electricity is always cheaper than solar electricity. There are 

myriad factors affecting renewable electricity inputs that influence the ultimate 

price a household pays. These sources of variability naturally lend themselves to a 

distribution for the price of renewable electricity rather than a deterministic 

average value. The lower tail on a solar price distribution in state i may match or 

beat the average price of wind electricity in the state; hence, to exclude solar 

electricity from the optimal solution would be misleading. Section 3.1.4 discusses 

the method for overcoming this problem. 

3.1.4 Incorporating Variability in Solar Costs 

Wind and solar electricity pricing is something of a curiosity in the United 

States. Note that in Figure 12, the weighted average price of wind electricity in the 

U.S. far exceeds the weighted average price of solar electricity. Harkening back to 

54


the data in Chapter 2, it is apparent that the small group of states with very 

expensive wind electricity skew the data. To a smaller degree, the same effect 

influences solar electricity data. Figure 13 24 provides a more realistic price 

comparison: once the states with impractically high prices for wind and solar 

electricity are excluded, the weighted average prices drop significantly—and the 

positions of wind and solar energy flip, with average wind electricity prices beating 

average solar electricity prices in all but one scenario. 25 Evidently, it would require 

an aggressive tax credit for the average price of solar electricity to match that of 

wind electricity with no tax credit. 

Figure 12. Price Comparison of Electricity Sources 

24 The * on Figure 13 indicates that the graph does not represent a true weighted average national 

price, but rather a weighted average price that has been “cleaned” of impractical states. 

25 As seen in Figure 13, the scenario is a 0% tax credit for wind installations combined with a 50% 

tax credit for solar installations. This is highly unlikely. 

55


Incorporating solar PVs into the optimal electricity portfolio is neither 

impossible nor impractical, however; modeling solar electricity prices as a 

distribution will illustrate as much. There are many dimensions of variability that 

might interact to make solar PVs a cheaper option than wind turbines for some 

consumers. For instance, an experienced, practical consumer is more likely to 

obtain cheaper credit, negotiate a better deal with a PV installation contractor, and 

know where to go to purchase inexpensive parts for repair and maintenance. Aside 

from market savvy, some consumers will happen to live in towns that have more 

peak sun hours per day than their state’s average, making a solar PV panel a 

relatively wiser investment. Others might require smaller PV panels than their 

state’s average by virtue of using electricity more conservatively or living in more 

energy efficient homes by design. 

Figure 13. Price Comparison of Electricity Sources 

(excluding upper quartile prices) 

56


These factors illustrate that there is not a single estimated price for solar 

electricity, but rather a range of costs that reflects individual practicality in addition 

to attributes of the physical environment. To reflect the noise in these factors, 

several variables in the 

p i 

solar 


= 

solar 

E total,i 

calculation are treated as normal 

distributions. 26 They are the daily electricity consumption of a single-‐family home, 

€ 

the peak sun hours per day, the installation cost of a solar module per kilowatt, the 

useful lifetime of a solar module, and the present value of all future maintenance 

costs, as follows: 

€ 

€ 

€ 

d ˆ elec elec 2 

i ~ N(d i , 4 ) 

k ˆ solar solar 2 

i ~ N(k i , 0.75 ) 

solar solar 2 

c ˆ install ~ N(c install, 

1000 ) 

ˆ 

n solar ~ N(n solar , 5 2 ) 

C ˆ solar solar 2 

mntc,i ~ N(C mntc,i, 

2000 ) 

The variables included 

€ 

in the model are deemed to be the most significant 

contributors to variability € in solar electricity prices within a state. Yet there are 

numerous other variables that could affect the price per kilowatt-‐hour of the PV 

module over the course of its life. The following factors also play a role in the 

efficiency of the PV module and consequential pricing of solar electricity [20]: 

€ 

• The orientation of the PV module toward the sun – the optimal 

orientation in locations above the equator is southward 

• The inclination of the roof – the average optimal angle is 35 degrees 

26 (1− β 

As a reminder, solar 

p i = 

solar solar 

solar solar 0.02c install,i 1 

)(W i c install) 

+ 1− 

r (1+ r) −n 

⎡⎡ ⎤⎤ 

⎢⎢ ⎥⎥ 

⎣⎣ ⎦⎦ is the expanded form of 

solar solar 

0.87W i k i ⋅ 365n 

€ 

p i 

solar 


= 

solar 

E total,i 

57

€ 


• The PV technology itself – how advanced and modern it is 

However, the encumbrance of incorporating every possible source of price 

variability prohibits the inclusion of less impactful factors. The five aforementioned 

variables will suffice to meet the needs of this analysis. 

Now, finding a threshold value at which solar costs compete with wind costs 

is a matter of comparing the normal distribution of the solar price 

deterministic wind price 

€ 

wind 

p i . More formally, one solves for 

solar wind 1 

fi ( p i ) = solar 

σi Φ p ⎛⎛ 

i 

⎜⎜ 

⎝⎝ 

€ 

€ 

⎞⎞ 

⎟⎟ 

⎠⎠ 

wind solar 

− µi 

solar 

σi solar 

fi in 

solar 

p ˆ i to the 

which is the z-‐score 27 of the average wind cost in state i on the solar price 

€ 

distribution for state i. The z-‐score is then converted into a percentile that 

represents the percentage of state i’s electricity portfolio that can be transferred 

from wind electricity to solar electricity at no additional cost. The consumers who 

are able to achieve lower-‐tail solar prices probably have a number of the normally 

distributed variables working to their advantage. 

New Mexico will serve as an example case of this method. The means of the 

normally distributed solar price inputs in New Mexico are 

solar 

k NM = 6.77 hours, 

solar 

c install = $7,000, 

n solar = 20 years, and 

elec 

d NM = 21 kWh, 

solar 

C mntc,i = $11,514. 

€ 

The MATLAB code in Appendix A-‐5 plots the solar electricity price distribution for 

€ 

€ 

New Mexico based on the means and variances€ of the input variables. The 

distribution is shown in Figure 14. The vertical red line and blue line mark the 

average price of wind and retail electricity in New Mexico, respectively. This visual 

27 A measure of the distance in standard deviations of a sample from the mean. 

58


demonstrates that solar electricity can and should be included in the state’s 

electricity portfolio from an economic point of view so long as the households 

utilizing solar electricity are beneath a threshold percentile on the price 

distribution. 

Figure 14. Distribution of Solar Electricity Price 

Generalizing this method across all of the states, the 

SolarAllocationByState m-‐file (included in Appendix A-‐6) returns two 

vectors that give the percentiles of deterministic wind and retail electricity prices on 

the solar price distribution for each state. A percentile of “1” in either vector 

suggests that the entire solar electricity price distribution falls below the average 

price of wind or retail electricity, depending on the vector. 

The states returning percentiles of 1 in the wind vector are those with decent 

solar energy potential but little wind energy potential, like Alabama, Georgia, and 

South Carolina. (Hence, wind electricity prices fall on the upper-‐tail of the solar 

59


price distribution.) The states returning high percentiles in the retail vector are 

those with decent solar energy potential or inordinately expensive retail electricity, 

or some combination of both. (The higher the deterministic retail price, the higher 

its percentile on the solar distribution.) Such states are California, Hawaii, Arizona, 

North Carolina, Tennessee, New York, and Louisiana. Appendix A-‐6 includes a 

comprehensive listing of all states and the corresponding wind and retail 

percentiles on their respective solar price distributions. 

Incorporating solar variability into the cost function, the optimal solution is 

no longer a binary allocation of “0” or “1” to a single source in each state, but rather 

a division of allocation between two energy sources (solar and retail or solar and 

wind). One limitation of this model is that because wind and retail prices 

are treated as deterministic values rather than as distributions, the model precludes 

the possibility of states choosing a blend of wind and retail electricity as their 

electricity sources. Table 9 provides a snapshot of optimal allocations in each state. 

60

State 

% 

Retail 


Table 9. Optimal Electricity Allocations by State 

(No Carbon Tax and No Tax Credit) 

% 

Wind 

% 

Solar 

State 

% 

Retail 

% 

Wind 

% 

Solar 

.AL 97.8 0 2.2 .MT 0 90.6 9.4 

.AK 0 91.1 8.9 .NE 98.1 0 1.9 

.AZ 91.3 0 8.7 .NV 0 83 17.1 

.AR 96.9 0 3.1 .NH 0 89 11 

.CA 0 83.3 16.7 .NJ 0 57.9 42.1 

.CO 93.7 0 6.3 .NM 88.5 0 11.5 

.CT 0 80.3 19.7 .NY 0 86.2 13.8 

.DE 96.6 0 3.4 .NC 93.2 0 6.8 

.DC 97.5 0 2.5 .ND 98.3 0 1.7 

.FL 95.3 0 4.7 .OH 90.1 0 9.9 

.GA 97.7 0 2.3 .OK 96.7 0 3.3 

.HI 0 0 100 .OR 97.8 0 2.2 

.ID 97.9 0 2.1 .PA 97.2 0 2.8 

.IL 97.9 0 2.2 .RI 0 90.3 9.7 

.IN 98.1 0 1.9 .SC 95.8 0 4.2 

.IA 97.1 0 2.9 .SD 96.9 0 3.1 

.KS 97.4 0 2.7 .TN 97.3 0 2.7 

.KY 98.4 0 1.6 .TX 92.2 0 7.8 

.LA 96.0 0 4.0 .UT 97.6 0 2.4 

.ME 0 77.3 22.7 .VT 0 90.1 9.9 

.MD 96.1 0 3.9 .VA 96.4 0 3.6 

.MA 0 83.7 16.3 .WA 97.0 0 3.0 

.MI 96.2 0 3.8 .WV 98.3 0 1.7 

.MN 96.2 0 3.8 .WI 94.6 0 5.4 

.MS 98.1 0 1.9 .WY 92.3 0 7.7 

.MO 97.9 0 2.1 

61


3.2 The Impact of Government Incentives on Electricity Allocation 

To minimize the cost function in Section 3.1, households will prefer 

whichever source of electricity is cheapest for them. The government, then, is 

charged with the task of understanding how potential policies will affect the price of 

electricity from different sources. Using the methodology developed thus far, one 

can project how the electricity portfolio allocations as well as the electricity prices 

will respond to varying levels of government intervention. 

3.2.1 Impact of the Carbon Tax on Allocation 

First, it is important to note that while the maximum carbon tax in this study 

is $100 per ton CO2, no serious proposal to Congress has yet exceeded $13.70 per 

ton CO2. It is interesting as an academic exercise to explore hypothetical scenarios 

with a carbon tax above $13.70, but the likelihood of a bill with a high carbon tax 

making its way through Congress in the near term is slim. 

That said, a number of conclusions can be drawn from Figures 15-‐17 on the 

following page. These illustrations show how the optimal nationwide electricity mix 

changes according to a varying carbon tax. Additionally, the three graphs represent 

three different levels of the renewable tax credit: a zero tax credit, a moderate tax 

credit (30%), and an aggressive tax credit (50%). Figures 15-‐17 support the 

expectation that as the carbon tax and renewable tax credit increase, more 

consumers will opt for renewable energy sources. 

Yet there is a more nuanced interpretation of these figures that may have 

implications for policy decisions. As the illustrations plainly show, an increasing 

carbon tax causes a steady decline in the national allocation to retail electricity. 

62


Figure 15 

Figure 16 

Figure 17 

63


Households will begin switching to clean sources as the price of carbon-‐based retail 

electricity rises above that of renewable electricity. But the implementation of a tax 

begs a question about trade-‐offs: what incremental social benefit to the country (in 

the form of less pollution and greater national security) justifies a palpable increase 

in retail prices? Moreover, what target electricity mix should the government hope 

to achieve by implementing a carbon tax of $X per ton? Figures 15-‐17 hint at the 

answers to these questions, which will be more fully developed in Chapter 4. 

In the first scenario (no tax credit), the fact that less than half of the country 

will use renewable electricity even with a $90 carbon tax (see Figure 15) suggests 

that the carbon tax, at some level, may backfire: imposing a tremendous tax burden 

of $90 per ton on consumers is only sufficient to induce a large minority of 

households to switch electricity sources. It is very likely that, in this scenario, a high 

carbon tax does more economic harm than societal good. Finding the point at which 

the economic burden justifies the social benefit is crucial to designing a policy 

solution. For now, it is sufficient to note that the tax, while effective in inducing 

consumer behavior, must be moderated lest the burden outweigh the benefit. 

3.2.2 Impact of the Renewable Tax Credit on Allocation 

Figures 15-‐17 indicate that the renewable tax credit is perhaps even more 

influential than the carbon tax as a policy tool. To investigate this further, Figures 

18 and 19 hold the carbon tax constant, isolating the change induced by the tax 

credit. Assuming the government continues on its current path of providing the 

same tax credit for all renewable technology ( 

€ 

β solar = β wind ), Figures 18 and 19 

present the projected national electricity mix under the circumstances of a 

64


Figure 18 

Figure 19 

65


moderate and aggressive tax credit and no tax credit at all. To add an additional 

layer of change, the first graph represents a scenario with no carbon tax, and the 

second a scenario with a $13.70 carbon tax. 28 

As a whole, there is a steady decline in the retail allocation as the renewable 

tax credit is increased. Again, the point of interest is where the economic burden, 

this time on the government, justifies the social benefit of more renewable energy. 

As opposed to the carbon tax, which encumbers consumers with higher prices, the 

tax credit diminishes the government’s spending power because each claimed tax 

credit represents a loss of tax revenue that the government would otherwise collect. 

A high tax credit for renewable energy could deplete tax revenue to the point that 

cutbacks are made to other programs. Hence, there is a need to reconcile the 

conflicting aims of conserving finances and encouraging investment in renewable 

energy technology. Chapter 4 will quantify this problem from the perspective of 

society as a whole. 

As a side note, Figure 18 shows a 22% allocation to wind electricity under a 

30% tax credit, which suggests that the U.S. government should be able to meet its 

goal of “25% Wind Energy by 2030” by continuing current practices. Given enough 

time to respond to the historically low prices in the wind industry right now, 

consumers in the market should reach the optimal electricity mix in the long term. 

Over the next decade, wind electricity prices are projected to decline another 11%, 

catalyzing an increase in the wind allocation and bringing it near the target 25%. 

28 $13.70 comes from President Obama’s proposed cap-‐and-‐trade scheme, which has yet to be 

approved. Analysts have predicted that the carbon allowances (i.e., the right to emit one ton of 

carbon dioxide) would be traded at a price of $13.70 by 2012 under the scheme [66]. 

66


3.3 The Impact of Government Incentives on Electricity Prices 

While it is important to understand how government intervention will 

impact the national electricity mix, it is equally important to determine how 

electricity prices change as a result of government intervention. Both the electricity 

mix and electricity prices must be considered in order to arrive at a prudent 

renewable energy policy. 

3.3.1 Background on the Electricity Price-‐Carbon Tax Relationship 

Unfortunately, existing scholarly work does not typically account for the 

subtleties in average electricity prices’ response to a carbon tax. For example, in a 

presentation given as part of the Science, Technology, and Environmental Policy 

(STEP) Seminar Series at Princeton University, the relationship between the U.S. 

average electricity generation price and the CO2 emissions price (i.e., the “cost of 

carbon”) was assumed to be linear. Figure 20 duplicates the illustration used in the 

presentation, “Alternative Approaches to CO2 Capture and Storage at Existing Coal 

Power Plant Sites” [1]. 2930 

29 The legend in Figure 20 contains two other lines that are not relevant to the discussion at hand, 

but for the reader’s reference, “Written-‐off PC-‐V plant” refers to a vented plant that produces 

pulverized coal, and “PC-‐CCS retrofit” refers to a coal plant retrofitted with CO2 capture and storage 

technology. 

30 Note that Figure 20 plots the average electricity generation price, which only accounts for 68% of 

the U.S. average retail electricity price according to the Energy Information Administration [11]. The 

other components of the electricity price are distribution (24%) and transmission (7%) of electricity 

[11]. Following those calculations, the U.S. average retail electricity price would be $0.09 per 

kilowatt-‐hour based on the $60/MWh generation cost in Figure 20. This average price, while lower 

than the $0.11/kWh average price used thus far, is entirely reasonable depending on the year of the 

data used to create the graph. 

67


The assumption of linearity is a faulty one because it neglects the presence of 

renewable technology. A linear electricity price-‐carbon tax relationship implies that 

the electricity mix in the U.S. is static and that no consumers switch to carbon-‐free 

renewables as the price of retail electricity rises. Of course, that assumption is 

erroneous, especially in an age when renewable energy is gaining traction in the 

marketplace. 

Figure 20. Graph used in STEP Seminar [1] 

3.3.2 Improvement upon Linearity in the Electricity-‐Carbon Tax Relationship 

The plot in Figure 20 is in need of a model predicting how electricity 

portfolio allocations change in response to a carbon tax. A dynamic electricity 

portfolio is crucial in order to show how the average electricity price changes under 

different circumstances. Conveniently, one need only apply the data compiled thus 

far in order to improve the average electricity price curve in Figure 20. Rather than 

increasing linearly, a more realistic electricity price curve will show that prices level 

68


Figure 21 

Figure 22 

69


off as the carbon tax increases and as consumers rely more heavily on renewables 

instead of conventional retail electricity. 

Figures 21-‐23 display more refined electricity price curves than the one used 

in the STEP presentation. All three plot the U.S. average electricity price in relation 

to a carbon tax, or, equivalently, a “greenhouse gas emissions price,” as it was 

expressed in Figure 20. Figure 21 treats the renewable tax credit as a single value 

(so β solar = β wind ), whereas Figure 22 and 23 shows how varying the solar and wind 

tax credits, respectively, while keeping the other credit constant can influence the 

price curve. Figures 21 and 22 reveal a few interesting characteristics of the 

electricity price curve, namely 

Figure 23 

70


• The carbon tax exerts a diminishing marginal impact on electricity prices. 

The price curves extending outward from the initial value of c carbon = 0 

appear to be linear, but their slopes gradually taper off as the carbon tax 

€ 

increases. This result illustrates that as the carbon tax rises, more and more 

people rely on renewable energy. An increased allocation to non-‐carbon 

renewables leads to an average electricity price that is more “immune” to a 

carbon tax. Theoretically, if the carbon tax were high enough, the slope of 

the electricity price curve would eventually become zero. 

• The nonlinearity of the price curve becomes more pronounced as the tax 

credit increases. Figures 21-‐23 illustrate that a higher tax credit for one or 

both renewables accelerates the tapering off of the price curve, which is a 

natural consequence of more consumers choosing to rely on either wind or 

solar or both. 

• The electricity price curves representing different tax credits splay outward 

as the carbon tax increases, demonstrating that a tax credit and a carbon tax 

acting in concert can have a marked effect on the price of electricity. 

• The carbon tax may be considered a futile burden at a certain level. This 

effect is most clearly seen in the turquoise and purple lines in Figure 22, but 

it applies to all scenarios in principle. Once the price curve flattens to a 

near-‐zero slope, increasing the carbon tax no longer produces a significant 

change in allocation, but it penalizes consumers who continue to use retail 

electricity. 

71


• The price curves in Figure 23 diverge slightly more than the prices curves in 

Figure 22, suggesting that the wind credit exerts greater influence over the 

price curve than the solar credit. This is consistent with the finding that for 

most consumers, it more economical to invest in wind power before solar 

power. 

3.4 Laying the Groundwork for Policy Optimization 

This chapter sought to visually demonstrate the effects of government 

intervention on the electricity mix and average electricity price in the United States. 

What the graphs reveal in totality is the very wide spectrum of outcomes that could 

result from government intervention: depending on the nature of the implemented 

policy, the U.S. electricity market could undergo drastic change, maintain the status 

quo, or even fall backward if the current Residential Renewable Energy Tax Credit is 

rescinded or reduced. Even relatively minor changes—like instituting a carbon tax 

of $5, or increasing the tax credit to 35%—could lead hundreds of thousands, if not 

millions, of consumers to acquaint themselves with renewable technology. 

Having developed a model to predict the optimal electricity mix under 

different scenarios, the next step is to complete a more rigorous analysis of the costs 

and benefits associated with any given set of carbon tax and tax credit policies. The 

improved electricity price curves presented in this chapter will fine-‐tune the cost 

estimation to American consumers of higher electricity prices. Likewise, the 

projected electricity mixes will facilitate the quantification of social benefits of a 

change in the electricity mix, namely reduction in long-‐term damage caused by CO2 

72


in the atmosphere. The interplay of the positive and negative consequences of 

change in the electricity mix will drive the optimal policy solution. 

73

4. Optimizing Environmental Tax Policy 

Chapter 3 explored the degree to which the U.S. residential electricity 

market would respond to carbon taxes and investment tax credits for 

renewable technology based on economic considerations alone. This chapter aims 

to place that analysis in a broader context, showing how a carbon tax and tax credits 

will affect the proverbial “bottom line,” which is, in this case, the benefit or cost— 

the profit or loss, so to speak—to the whole of society. The goal is to determine the 

carbon tax and tax credit policies that maximize the overall benefit to society, which, 

if formulated suitably, will strike a balance between encouragement of clean energy 

and spending restraint.

Optimizing Environmental Tax Policy 

The method to maximize the benefit to society draws upon foundations in 

environmental economics. As environmental economist Dan Phaneuf writes, “Cost-‐ 

benefit analysis provides an organizational framework for identifying, quantifying, 

and comparing the costs and benefits of a proposed policy action” [69]. While the 

costs of the proposed policy are usually easily quantifiable in dollar value, the 

benefits are less so: there is significant debate as to how, and whether, to place a 

dollar value on improved air and water quality and other such “priceless” benefits 

arising from environmental policies. Yet the environmental economist is “tasked 

with recommending policies that reflect scarcity” of available funds in society, 

eradicating the possibility of pursuing “zero pollution objectives” [69]. Instead, 

utilizing a cost-‐benefit framework, as environmental economists often do, will 

provide practical solutions in the policy arena. 

4.1 Structure of the Cost-‐Benefit Analysis in One Time Period 

In order to translate the benefit of reduced pollution into dollar form, the 

benefit to society is defined as the net savings accrued over time from the energy 

policy in place. (Even though the absolute price of electricity will rise in response to 

a carbon tax, consumers will also save a certain amount, depending on the social 

cost of carbon, for having averted environmental damage by emitting less carbon 

dioxide.) Accordingly, if the energy policy were to do more harm than good, the cost 

to society would be defined as the net losses accrued over time. 

There are three major components of the cost-‐benefit analysis: Government 

Net Revenue, Consumer Net Revenue, and Social Benefit from CO2 Reduction. The 

75

€ 

€ 


sum of these three components is the net benefit to society of a proposed 

environmental tax policy consisting of a carbon tax, renewable tax credits, or both. 

Because the burden of the social cost of carbon is not borne by either the 

government or the consumers exclusively, but rather by the whole of society, it is 

separated from the first two terms. 

The cost-‐benefit analysis is presented here in one time period for the sake of 

clarity in explanation. In later sections a time component will be added, projecting 

policies out forty years to get a sense for their long-‐term impact on society. 

4.1.1 Government Net Revenue 

A policy consisting of a carbon tax and investment tax credit produces two 

effects on the government cash flow: a carbon tax serves as a stream of incoming 

revenue over a period of time, and the tax credit represents a one-‐time outflow of 

cash from the government to a consumer who installs solar or wind technology. 

In time period t, government spending on tax credits for residential wind 

energy installations is represented by the one-time subsidy cost 

where 

wind 

βt and 

β t 

51 

wind wind 

C t,install,i 

∑ h i (µ t,i 

i=1 

wind wind 

− µ0,i ) 

€ 

cost of wind turbines, respectively, in state i at time t. The remnant of the term, 

€ 

wind 

hi(µ t,i − µ0,i 

wind 

C t,install,i 

are the tax credit for wind installations and the installation 

wind ), is the number of new households installing wind turbines in state i 

at time t; it excludes households who have installed wind turbines previously. 31 

31 Appendix A-‐7 contains a breakdown electricity generation resource mixes for all states. This data 

from the Environmental Protection Agency provides the 

benefit calculations. 

€ 

wind solar retail 

µ 0,i , µ0,i , µ0,i constants used in the cost-‐ 

76


Likewise, government spending on tax credits for residential solar energy 

installations is represented by 

€ 

the government of tax credits in time period t is 

β t 

51 

solar solar 

C t,install,i 

∑ h i(µ t,i 

i=1 

solar solar 

− µ0,i ) 

where all variables are defined for solar PV installations. Together, the total cost to 

gov 

Ct,tax credit 

= β t 

51 

wind wind 

C t,install,i 


i=1 

51 

wind wind solar solar 

− µ0,i ) + βt C t,install,i 


€ 

electricity source to power their homes for the duration of the technology’s lifetime. 

€ 

€ 

€ 

i=1 

solar solar 

− µ0,i ) 

Consumers who take advantage of the tax credit will have a renewable 

Therefore, the government’s one-‐time payments to consumers who install 

renewable technology in time t are effectively spread out over twenty years. A 

comparable measure of revenue, then, must also be viewed over the lifetime of the 

renewable installations. For twenty years following time t, the government will 

collect a carbon tax from the consumers who fail to install renewable technology in 

time period t. The present value of this stream of income over time is represented by 

where 

gov 

Rt,carbon tax 

€ 

c carbon = carbon tax ($/ton CO2) 

= c carbon retail CO2 µ t 

mt 1 

1− 

r (1+ r) −n 

⎡⎡ ⎤⎤ 

⎢⎢ ⎥⎥ 

⎣⎣ ⎦⎦ 

retail 

µ t = national allocation to retail electricity in time t 

CO2 mt = carbon dioxide emissions from the residential sector from electricity 

use in time t (metric tons CO2) 

r = the discount rate (2%) 

77

n = the number of time periods the tax is collected (20 years) 


The complete expression for government net revenue is dictated by the 

decision variables 

wind 

βt , 

wind 

βt , and 

c carbon embedded in the revenue and cost 

functions. Government net revenue in time period t is simply the future stream of 

€ € 

carbon tax income from retail 

€ 

electricity users less one-‐time tax credits to adopters 

of renewable technology: 

overall cost-‐benefit analysis. 

€ 

gov gov 

gov 

Rnet = Rt,carbon 

tax − Ct,tax credit 

The government net revenue function is one of three main components of the 

4.1.2 Consumer Net Revenue 

The structure of cash flow in time t from the consumer’s perspective is a little 

more elaborate than that of government cash flow. Consumers incur one-‐time 

installation costs for wind and solar technology, which are subsidized by the tax 

credit from the government. The installation costs provide a source of electricity for 

twenty years. However, three more line items must be factored into the consumer 

net revenue calculation: the present value of the change in spending on retail 

electricity, the present value of the change in spending on wind turbine 

maintenance, and the present value of the change in spending on solar module 

maintenance. These last three lines account for the future costs that are incurred or 

eliminated based on the decision—to install or not to install renewable 

technology—made in time t. Like carbon tax revenue, future revenue or costs 

incurred by consumers are discounted to the present. 

78


In time period t, the one-time wind installation cost incurred by consumers in 

aggregate is represented by 

€ 

51 

wind 

C t,install,i 


i=1 

wind wind 

− µ0,i ) 

Likewise, the one-time solar installation cost incurred by consumers in aggregate is 

represented by 

€ 51 

wind 

= C t,install,i 

51 

solar 

C t,install,i 


i=1 

solar solar 

− µ0,i ) 

The sum of the one-‐time installation costs incurred in time period t is then 

con 

Ct,install ∑ h i (µ t,i 

i=1 

wind − µ0,i 

wind solar 

) + C t,install,i 

€ 

other hand, the tax credits are inflows of cash from the consumer perspective. That 

51 

∑ h i (µ t,i 

i=1 

solar solar 

− µ0,i ) 

The installations costs are outflows of cash from the consumer perspective. On the 

is, the government’s loss is the consumer’s gain: 

gov 

Ct,tax credit 

con 

= Rt,tax credit 

In other words, from the perspective of society, the inflow of the tax credit cash to 

consumers neutralizes the 

€ 

outflow of tax credit cash from government; the tax 

credit is simply a redistribution of income. 

A carbon tax and tax credit policy implemented at the beginning of time 

period t will influence cash flows not only during time t, but also after time t. For 

example, consider what would happen if the government began to enforce a carbon 

tax of $10 per ton. The tax might induce some percentage of consumers to invest in 

renewable energy, leaving everyone else with higher retail electricity bills. 

Consumers who do choose to invest in renewable technology will incur 

79

€ 

€ 

€ 


maintenance expenses over time. Hence, the incremental increases or decreases in 

spending originating from the tax policy in time t must be included in the consumer 

net revenue calculation. 

is given by 

where 

The present value of the incremental spending on retail electricity over time 

con 

Ct,elec = 

51 

retail elec retail 

∑365 p 0,i d i 

hi µ 0,i − 365 p t,i 

i=1 

r 

51 


∑ d i 

hi µ t,i 

i=1 

retail 

p t,i = the price of retail electricity at time t ($/kWh) 

1 

1− 

(1+ r) −n 

⎡⎡ ⎤⎤ 

⎢⎢ ⎥⎥ 

⎣⎣ ⎦⎦ 

elec 

d i = the average daily electricity consumption of a single-‐family home in 

state i (kWh) 

h i = the number of single-‐family detached homes in state i 

As before, the discount rate is 2% and the incremental change in spending is 

€ 

discounted over twenty years. The payment 

51 


∑365 p 0,i d i 

hi µ 0,i − 365 p t,i 

i=1 

51 


∑ d i 

hi µ t,i 

i=1 

is calculated as such in order to isolate the incremental spending on retail electricity 

€ 

that arises from the tax policy. Hence, the spending on retail electricity at time t is 

subtracted from the spending on retail electricity at time 0 (i.e., before the policy is 

implemented). 

given by 

The present value of the incremental change in wind maintenance costs is 

80

€ 

€ 

Because 

wind 

C 0,mntc,i 

con 

Ct,windmntc 51 

wind wind 

= ∑µ 0,i 

hi C 0,mntc,i − ∑µ 

t,i 

i=1 


wind wind 

hi C t,mntc,i 

is already defined as a present value, the present value of the 

€ 

incremental change can be simply expressed as a difference between 

€ 

and t = t. In the same way, the present value of the incremental change in solar 

maintenance costs is given by 

con 

Ct,solarmntc € 

is summarized by the equation 

51 

51 

i=1 

solar solar 

= ∑µ 0,i 

hi C 0,mntc,i − ∑µ 

t,i 

i=1 

51 

i=1 

€ 

solar solar 

hi C t,mntc,i 

wind 

C 0,mntc,i at t = 0 

Finally, the impact of the carbon tax and tax credit on consumer net revenue 

con con 

con con con 

con 

Rnet = Rt,tax 

credit − Ct,install + Ct,elec + Ct,wind 

mntc + Ct,solar mntc 

The last three cost terms are added, rather than subtracted, because of the 

way the 

€ 

terms are defined, but there is no inconsistency among the cost variables. 32 

For the consumer, the only source of revenue arising out of the tax policy is the tax 

credit from the government. Absent a decline in the cost of renewable technology, 

individual consumers will not benefit financially from a tax policy designed to 

reduce pollution; they will, however, benefit as a society from scaled back CO2 

emissions. 

32 

con 

Ct,install Ct,elec term. 

is defined as the difference between installation costs at t=0 and t=t, where t=t is the first 

con con 

, Ct,wind 

mntc 

where t=0 is the first term. 

con 

, Ct,solar mntc 

are defined as incremental changes in cost between t=0 and t=t, 

81

4.1.3 Net Social Benefit 


With no direct recipient besides the entirety of society, the social benefit of 

environmental tax policy is an important, and too often neglected, component of 

cost-‐benefit analysis. The benefit to society from the tax policy is quantified as 

B society = c SCC CO2 CO2 (m0 − mt ) 

where c SCC is the social cost of carbon ($/ton CO2) and 

CO2 mt is carbon dioxide 

€ 

emissions from the residential sector from electricity use in time t (metric tons 

€ 

CO2). € 

33 If the policy achieves its desired effect (i.e., to reduce consumption of fossil 

fuels), then 

€ 

CO2 CO2 m0 ≥ mt and 

4.1.4 Summary Table 

B society will be positive. 

€ 

In its most condensed form, the benefit to society calculation is given by 

gov con society 

Rnet + Rnet + B 

This result, along with the foundational calculations and methods presented in 

Chapters 2, 3, and 4, are€ encapsulated in Table 10. This summary table contains the 

major decisions, assumptions, and cost-‐benefit line items that ultimately lead to a 

quantification of the net benefit (or cost) to society as a result of the tax policy. Of 

course, the final net benefit figure is the product of numerous underlying 

assumptions, including the social cost of carbon, consumer behavior patterns, and 

the current cost of installing renewable technology, to name only a few. A more 

thorough discussion of these assumptions follows. 

33 Using data from the Department of Energy: the U.S. residential sector emitted 1,261,000,000 

metric tons of carbon dioxide in 2008. 80% of those emissions, or 1,008,800,000 were emitted by 

single-‐family detached homes. Roughly 60% of emissions were generated for electricity 

consumption, so the final figure comes to 605,280,000 metric tons of carbon dioxide for electricity 

generation in single-‐family detached homes. 

82

4.2 Calculating the Social Cost of Carbon 


Climate change legislation in the United States and abroad often leads to 

contentious political debate due to the fact that long-‐term environmental damage is 

very difficult to quantify. While almost everyone agrees that releasing carbon 

dioxide into the atmosphere causes harm to the planet, there is little consensus in 

the academic community as to the precise value of the social cost of carbon, which is 

formally defined as the marginal cost of emitting an additional ton of carbon. That 

one input can wield such influence over the direction of legislation underscores the 

importance of using a credible estimate. 

Table 10 

An interagency working group within the U.S. government issued a report, 

Social Cost of Carbon for Regulatory Impact Analysis Under Executive Order 12866, to 

83


standardize the estimates of the SCC used in all federal offices. For 2010, the EPA 

selected four SCC estimates for its use in regulatory analyses: $5, $21, $35, and $65 

per ton, as shown in Table 11 [36]. The first three values are based on SCC models 

using 5%, 3%, and 2.5% discount rates, respectively. The fourth value, $65, 

represents an upper-‐tail estimate at the 95 th percentile using a 3% discount rate; 

such an estimate acknowledges the risk discussed in SCC literature that the 

expected welfare loss might be unbounded due to uncertainty about climate change 

[36] [5]. 

Table 11. Estimated Social Cost of CO2, 

2010-‐2050 (in 2007 dollars) [36] 

While the carbon tax is a decision variable in this model, the social cost of 

carbon is not. Following the U.S. government’s lead, the adopted value for the social 

cost of carbon is $35 per ton—the interagency working group’s SCC estimate that is 

most in line with other SCC estimates from literature in the field. 

84

4.3 Modeling Consumer Behavior 


One of the biggest challenges of modeling the impact of a carbon tax and tax 

credit over time is predicting how market agents will respond to new policies. If the 

government suddenly instituted a $30 carbon tax, not all consumers would invest in 

renewable technology at the same time: some would switch to an alternative energy 

source right away, others would switch after a few years’ time, and still others 

would probably prefer to stick with retail electricity despite the higher prices. 

Consumer behavior depends on many factors, two of which will be given special 

consideration here: the economic incentive to switch, and time. 

4.3.1 Inducement to Change Threshold 

Chapter 3 assumed that consumers would adopt whichever electricity source 

is cheapest in their state, whether that is a renewable or non-‐renewable source. The 

optimal portfolio allocations presented in Chapter 3 presuppose that, over time, 

rational market participants will always select the electricity source that is the least 

expensive, even if only marginally so. 

Yet the real world operates a bit differently, especially in the short term. 

There are inconveniences associated with installing a wind or solar system that may 

prevent consumers from switching electricity sources, even if their retail electricity 

rates are rising. Therefore, consumers will only switch away from retail electricity if 

the benefit of doing so is “worth it” to them; there must be sufficient expected 

financial gain from switching in order to pursue a residential renewable installation 

project. (Alternatively, consumers with an environmentalist bent might view 

protecting the environment as sufficient compensation for switching.) To get an 

85


idea of how much compensation consumers require for the inconvenience of 

switching to a new and somewhat less reliable source of energy, it is helpful to look 

at consumer behavior in the United States today. 

Hawaiians currently pay the highest retail electricity rates in the nation. At 

$0.24 per kilowatt-‐hour, retail electricity in Hawaii is about four times as expensive 

as in Idaho, where residential consumers pay only $0.06 per kilowatt-‐hour. This is 

due in large part to Hawaii’s reliance on petroleum oil, which is more expensive 

than coal or natural gas. 34 Figure 24 shows the rise in the price of petroleum liquids 

just in the past year. 

Figure 24. Electric Power Industry Fuel Costs, 

January 2009 through December 2009 [71] 

Yet despite Hawaii’s lofty retail prices, only 6.5% of Hawaii’s electricity 

comes from renewable energy sources. This would be far less remarkable if it were 

not for Hawaii’s exceptional potential for solar energy. In Chapter 2, Hawaii ranked 

34 Hawaii gets 77.3% of its electricity from petroleum, 13.7% from coal, 6.5% from renewables 

excluding hydroelectric power, 1% from hydroelectric power, and 0.8% from other gases [72]. 

86


as the fifth cheapest state for residential solar electricity, with a price of $0.18 per 

kilowatt-‐hour. Even without government incentives, solar electricity is cheaper 

than retail electricity in Hawaii! Purely on the basis of cost comparison, Hawaiians 

should be allocating much more than 6.5% of their electricity to renewable sources. 

Clearly, there exists some resistance to increasing the renewable energy 

allocation that is unaccounted for in retail and solar electricity prices. Based on the 

calculations in Chapter 2, the solar electricity price in Hawaii represents a 26.6% 

potential savings from the retail electricity price in 2008. Ostensibly, there is a 

certain threshold for the savings percentage over which Hawaiians would begin to 

switch to renewable sources in greater numbers. 

While the discrepancy between retail and solar electricity prices in Hawaii is 

the greatest wonder of all, the same behavioral phenomenon is observed in other 

states, most notably in California, where wind electricity is 14.2% cheaper than 

retail electricity, and in Rhode Island, where wind electricity is 11.9% cheaper than 

retail electricity. To a lesser degree, wind electricity is also more economical in 

Alaska, Nevada, and New Hampshire before government incentives. Even so, all of 

these states continue to allocate only a small fraction of their electricity to the wind 

resource. 

However, determining the precise value of the savings threshold required to 

motivate consumers to consider renewable energy is outside the scope of this thesis. 

Rather, this model attempts to incorporate the consumer behavior observed in 

Hawaii and other states, but not to fixate on the level of the threshold, which will 

henceforth be called the “inducement to change” threshold. 

87


Applying the consumer behavior observed in these states to the framework 

presented here, an inducement to change threshold of 27% is built into the model. 

The assumption is that consumers will not be willing to embark on researching, 

purchasing, and installing residential renewable systems unless they are 

compensated by a 27% savings rate compared to retail electricity prices. The 27% 

figure comes from the current 26.6% price discrepancy in Hawaii; despite the fact 

that 27% appears to be too low an inducement threshold for Hawaii, the model 

assumes that consumers in other states would find 27% savings sufficiently enticing 

to shift into the renewable electricity market. The anomalous resistance to solar 

energy in Hawaii is likely to diminish over time as solar PVs enter the mainstream 

market. 

4.3.2 Renewable Adoption Rate, or Switchover Rate 

The second component of modeling consumer behavior is tracking consumer 

response to renewable technology over time. Even if the potential savings from 

renewable electricity exceed the inducement to change threshold, it is unlikely that 

all consumers will immediately flood the renewable energy markets. Realistically, 

adoption of renewable energy technology will be staggered. When, and under what 

circumstances, a consumer adopts the technology will depend on the consumption 

style of the individual. 

Sociologist Everett Rogers first introduced the theory of diffusions of 

innovations in 1962. Rogers proposed that consumers in the marketplace fall into 

five distinct categories: innovators, early adopters, early majority, late majority, and 

laggards. Each consumer’s classification drives the timing of his or her adoption of a 

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new technology, as represented in the bell curve of Figure 25. Innovators and early 

adopters, who are typically regarded as the technology enthusiasts in a society, 

comprise only a small portion of the market. They are often characterized by self-‐ 

sufficiency, a willingness to take risks, an interest in technology, and a visionary 

quality [73]. In contrast, the early majority tends to be more pragmatic, risk averse, 

and unwilling to invest in unproven applications [73]. Consumers in the late 

majority tend to be even more cautious when evaluating innovations, “taking more 

time than average to adopt them, and often at the pressure of peers” [74]. Finally, 

laggards are consumers that tend to be “anchored in the past, are suspicious of the 

new,” and often belong to older generations [74]. 

Figure 25. Technology Adoption Bell Curve [70] 

In his book Crossing the Chasm, Silicon Valley consultant Geoffrey Moore 

posits that a chasm exists between early adopters and the early majority, making it 

difficult for new and unfamiliar high tech products to enter mainstream markets. 

(This is certainly true of solar PVs and wind turbines, both of which have already 

established a foothold among technology enthusiasts.) Moore asserts that most high 

89


tech ventures struggle to cross this chasm successfully [75]. To do so requires a 

shrewd marketing technique, strategic control over prices and distribution, or some 

other means of attracting the interest of more orthodox consumers. In the context 

of solar and wind energy, the carbon tax and renewable tax credit are two of the 

most powerful means of crossing the chasm aside from an overall drop in renewable 

technology prices. 

The technology adoption curve—essentially a probability density 

distribution 35 —is considered the gold standard in the high tech venture industry 

today. Its cumulative density forms an S-‐curve like that in Figure 26. The S-‐curve is 

an appropriate model for consumer behavior because it captures the three standard 

phases of a technology’s market share expansion: stalled adoption, rapid adoption, 

and mass adoption. It could be argued that wind and solar technology are currently 

situated at the inflection point between Phase I and Phase 2 on the S-‐curve, on the 

brink of rapid adoption. According to Aghion, Hemous, and Veugelers, “There are 

Figure 26. Phases of Technology Adoption [76] 

35 Rogers provided the following breakdown of the consumer population: 2.5% innovators, 13.5% 

early adopters, 34% early majority, 34% late majority, and 16% laggards, for a total of 100%. 

90


some signs, particularly from the venture capital market, that private green 

innovation machine might be ready to take off” and ascend the steep slope of Phase 

II [41]. 

The background on Moore and Rogers’ work serves to prove the point that 

consumers cannot be treated as uniformly rational automatons, but rather as 

individuals with differing preferences and tolerances for risk. Besides having 

dissimilar consumption habits, consumers will adopt technology at different rates 

due to inertia; the general inconvenience associated with installing a new electric 

system will slow down the rate of adoption. Most homeowners are so preoccupied 

with their jobs, children, and other responsibilities that installing renewable 

technology may be an afterthought even if it would reduce electrical bills. 

To incorporate these ideas into the policy optimization model, Rogers’ 

adoption bell curve was translated into the cumulative density function in Figure 27. 

The consumer behavior schedule in Table 12 sets benchmarks for the proportion of 

consumers that are expected to adopt renewable technology over time according to 

Rogers’ model. The cost savings of renewable electricity compared to retail 

electricity are projected alongside the market adoption rate. Obviously, the 

cumulative market penetration will increase as the savings from adopting 

renewable technology grow over time. The consumer behavior schedule of Table 12 

(with slight modifications 36 ) was built into the model to garner a more realistic 

prediction of consumer response to tax policy over time. 

36 Due to inertia and the fact that renewable technology may not be effective in all states, Rogers’ 

model was adapted such that renewable energy technology reaches a maximum adoption of 80%, 

91

Market 

Adoption 

Rate 

Table 12. Consumer Behavior Schedule 

Absolute 

Savings % 

(Projected) 

Inducement 

Threshold 


Savings in 

Excess of 

Inducement 

0.0% 0% 27% 0% 

0.4% 5% 27% 0% 

1.0% 10% 27% 0% 

1.8% 15% 27% 0% 

2.5% 20% 27% 0% 

4.0% 25% 27% 0% 

6.0% 30% 27% 3% 

10.0% 35% 27% 8% 

16.0% 40% 27% 13% 

22.0% 45% 27% 18% 

30.0% 50% 27% 23% 

37.0% 55% 27% 28% 

50.0% 60% 27% 33% 

63.0% 65% 27% 38% 

72.0% 70% 27% 43% 

78.0% 75% 27% 48% 

84.0% 80% 27% 53% 

90.0% 85% 27% 58% 

94.0% 90% 27% 63% 

98.0% 95% 27% 68% 

100.0% 100% 27% 73% 

Figure 27 

even after laggards have adopted. This presupposes that some consumers will never adopt 

renewable energy technology. 

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4.4 Declining Costs of Renewable Technology Over Time 


Technological progress is another crucial dimension of assessing the impact 

of a tax policy over time. Fortunately for the green energy movement, most industry 

analysts project that the price of renewable electricity will fall significantly in the 

coming years as renewable technology is brought to scale. Still, there is appreciable 

uncertainty regarding the future prices of solar and wind electricity, so a well-‐ 

designed, robust policy should allow for a range of prices. 

4.4.1 Solar Photovoltaic Cost Trends 

Between 1995 and 2005, the average installation cost of solar PVs declined 

by 4.8% per year in real dollars [77]. But for a two-‐year period until 2007, 

installation costs remained flat due to the fact that, starting in 2005, “U.S. and global 

PV markets expanded significantly, creating shortages in the supply of silicon for PV 

module production and putting upward pressure on PV module prices” [77]. Since 

then, PV module designers and producers have reacted to the silicon shortage, and 

PV technology has recommenced its movement down the price curve, falling 4% in 

2008 and a further 27% in 2009 alone [81] [33]. Two recent developments made 

this possible: producers ramped up polysilicon production following the 2005 

shortage, and PV innovations (like polycrystalline thin film technology) required 

less silicon than earlier generations of PV technology [80]. 

A further decline in PV costs is all but imminent. Clean Edge, a research firm 

devoted to the clean-‐tech sector, predicted that the installed cost for solar PV will 

drop another 60% within the next decade to well under $3,000 per kilowatt [33]. 

Such a decline would put solar power at grid parity with fossil fuels, ushering in a 

93


new age of cost competitive renewable electricity. Figure 28 extrapolates future 

price declines of PV technology according to cumulative production, not years: by 

the time worldwide PV cumulative production grows by two orders of magnitude, 

the price per kilowatt-‐hour of solar electricity will fall below that of wholesale coal 

electricity. 

Figure 28. Projected costs of solar PV technology as 

cumulative production increases [34] 

A number of catalysts are accelerating the movement toward grid parity. In 

green tech hotbeds like Silicon Valley, venture capitalists are investing huge sums in 

the research and development of photovoltaic technology. As a percent of U.S.-‐ 

based venture capital investments, green energy rose from 11.4% in 2008 to 12.5% 

in 2009, the highest historical share in the history of green-‐tech as an asset class 

94


[33]. The true impact of this funding will not manifest itself for years, but promising 

sprouts are already emerging: Argonne National Lab, for example, is developing a 

“solar paint” that forms interconnected solar cells like those on PV panels when it 

dries [83]. It can be applied to almost any surface, including walls, roof, and 

windows. Meanwhile, engineers at Princeton University have developed a 

technique for producing electricity-‐conducting plastics that could “slash the cost of 

solar panels” if commercialized [82]. These and other research projects are likely to 

transform the solar power landscape before the decade is over. 

4.4.2 Wind Turbine Cost Trends 

Due to its historical cost advantage, wind energy has been scaled up much 

more quickly than solar energy. The difference is certainly huge: global wind power 

capacity reached 157.9 gigawatts at the end of 2009, compared to global solar 

power capacity of 

6.43 gigawatts [78] 

[85]. As Figure 29 

illustrates, installed 

wind capacity is 

expected to swell in 

coming years, which 

will likely have the 

effect of further 

depressing installed 

Figure 29 

95

wind costs. 


Having reached grid parity with fossil fuels in some states, wind turbine 

prices are already stabilizing. Today, residential wind turbines can be installed for 

approximately $4,000 per kilowatt before incentives, and the installation cost for 

large-‐scale wind farms can dip as low as $1,690 per kilowatt [33]. Twenty-‐five 

years ago, the installation cost was six times what it is today [84]. 

Yet even though wind turbine prices have dropped precipitously since the 

1980s, Clean Edge research projects that they will drop another 11% in the coming 

decade [33]. Roughly speaking, the cost of wind energy “has dropped by 

approximately 15% with each doubling of installed capacity worldwide” [84]. If that 

trend continues, billowing winds could soon eclipse coal as the most economical 

source of electricity. 

96

5. Results of the Mathematical Model 

The cost-‐benefit framework presented in Chapter 4 serves as a 

springboard for tax policy analysis and optimization. In this chapter, 

the framework will be applied to numerous hypothetical tax policies in an endeavor 

to pinpoint the combination of carbon tax and investment tax credit that best serves 

the interests of society. Because the model in Chapter 4 encapsulates both private 

and social costs, the optimal tax policy will minimize the holistic “cost to society.” 

Resting on a model fine-‐tuned for consumer behavior, the social cost of 

carbon, and declining technology prices over time, the forthcoming analysis aims to 

present a meaningful and accurate portrayal of the economic consequences of 

various tax policies, both in the short term and in the long term.

5.1 Net Savings to Society for One Time Period 

Results of the Mathematical Model 

For now, the cost-‐benefit analysis is limited to one time period in order to 

gain an understanding of the short-‐term costs and benefits of various tax policies. 

Because the model is designed to calculate cost to society annually, the time period 

examined is the first year following the implementation of the tax policy. Recall that 

the one-‐period cost or benefit to society is measured as the change in the present 

value of the future costs or benefits to society that directly result from consumer 

decisions in the first year of the new tax policy. Because those decisions carry 

financial implications through the entire lifetime of the renewable energy system, 

the future costs and benefits related to the consumer decision must be discounted 

back to the first year in order to fully reflect the one-‐period cost or benefit to society 

of the tax policy. 

5.1.1 Net Savings with Lockstep Technology Improvement 

On the following pages, Figures 30-‐35 plot the net savings or net cost to 

society in year one as a function of the carbon tax and federal tax credit. Each point 

on the surface represents a different combination of the carbon tax and federal 

investment tax credit (ITC). On these graphs, the color red reflects the most positive 

part of the surface (i.e., the greatest net savings to society), and the rest of the color 

spectrum reflects a descending surface, where blue marks the tax policies with the 

highest net cost to society (or least net savings, as the case may be). 

Each of the six graphs plots the cost-‐benefit function with a different 

underlying assumption about the state of technological improvement. For instance, 

Figure 30, which assumes a 0% decline in renewable technology costs, portrays the 

98

Figure 30 

Figure 31 


99

Figure 32 

Figure 33 


100

Figure 34 

Figure 35 


101


cost-‐benefit analysis of tax policies implemented today. Figures 31-‐35, however, 

plot the cost-‐benefit function assuming 10%, 30%, 50%, 70%, and 90% declines in 

renewable technology costs, respectively, at the starting point of the time period. 

For these graphs, the time period represented is not today, but rather some point in 

the future—specifically, the first year in which technology costs decline to the level 

indicated on the graph. 

Figures 30-‐35 assume that costs of wind and solar technology decline in 

lockstep, whereby wind turbines and PV panels are clumped together as “renewable 

technology.” Such a simplification allows one to interpret how technological 

progress will affect the overall cost-‐benefit analysis without getting bogged down in 

forecasted rates of technology improvement. In the next section, cost declines of 

solar and wind technology are considered separately. 

As a whole, this set of graphs lends itself to an interesting analysis. 37 The 

interplay between the carbon tax, the federal tax credit, and the net cost to society 

evolves considerably as renewable energy becomes cheaper. In a scenario with no 

or little decline in the cost of renewable technology (Figures 30 and 31), the net cost 

to society soars after the federal tax credit crosses 50%. While a higher tax credit 

would benefit consumers, the onus of paying for the installations would shift to 

government. Yet consumers retain the power to decide whether to install 

renewable technology, and because the installation costs are so artificially 

depressed, consumers will choose to switch to renewable technology before it is 

37 It is important to bear in mind that the scale of the z-‐axis on each graph is different. Adjusting the 

z-‐axis scale was necessary in order to show the curvature of each surface. As a warning, comparing 

the graphs side by side is misleading unless scale is taken into account. 

102


economical to do so. This leads to an unsustainable burden on the government to 

heavily subsidize installations at the whim of the consumer. 

As renewable technology declines 30% from its initial cost (Figures 32), the 

net cost to society of tax policies becomes less negative across the board; in fact, 

with some moderate tax policies, society actually incurs net savings. Although the 

curvature of the surfaces in Figures 30-‐32 is consistent, the lower bound of the z-‐ 

axis changes such that tax credits in Figure 32 are significantly less costly to society 

than tax credits in Figure 30, the base case today. 

In Figure 33, which depicts the cost-‐benefit of policies with a 50% decline in 

renewable technology costs, implementing environmental tax incentives becomes 

categorically beneficial to society: at no point on the surface does a tax policy return 

a net cost to society. Indeed, the scenario in Figure 33 marks a turning point in the 

cost-‐benefit calculations. The sudden attractiveness of the tax policies can be 

explained by the fact that, with 50% cost declines, renewable technology finally 

becomes a genuinely economical investment across the country. By shifting to 

renewable energy, savings from carbon taxes and the social cost outweigh the net 

cost to government of subsidizing renewable installations. Overall, society benefits 

from every tax policy on the surface, though some policies generate more savings 

than others, as evidenced by the prominent peak at the 50% tax credit, $0 carbon 

tax point. 

Figures 34 and 35 present even more optimistic outcomes of the cost-‐benefit 

analysis. In these scenarios, the slope of the surface has essentially rotated ninety 

degrees from its starting slope in Figures 30-‐32. Not only does the carbon tax cease 

103


to burden society in these scenarios, the most extreme tax policy on the surface 

(100% tax credit, $100 carbon tax) generates the maximum net savings to society in 

both Figures 34 and 35. 

While that tax policy might seem an unlikely candidate for an optimum, there 

are a few explanations for this result. The consumer behavior model in Chapter 4 

predicts that there are some laggards in society who resist adopting renewable 

energy technology even when the savings from doing so exceed the inducement 

threshold by a large margin. Skepticism, discomfort with new technology, and 

firmly ingrained habit may all contribute to this behavior. In theory, some laggards 

may continue to use retail electricity even after the government imposes a carbon 

tax as high as $100. The government, then, collects large premiums from laggards 

who prefer not to switch to wind or solar energy. Meanwhile, the rest of society will 

have adopted solar and wind technology, reducing the social cost of carbon to all of 

society. With 70% and 90% cost declines, renewable technology is so cheap that the 

optimal action is for the government to encourage as many people to switch as 

possible (hence, implementing the 100% tax credit). 

5.1.2 Optimal Policies in the One Period Model 

In Figures 30-‐32, the scale of the z-‐axes prohibits the viewer from 

determining the optimal policy by sight. Figure 36 remedies this problem, providing 

a zoomed in view of Figure 30. In this scenario, which represents a one-‐year time 

period starting today, the optimal policy is a 50% tax credit combined with a $0 

carbon tax. The fact that a policy with no carbon tax is optimal suggests that now is 

an inopportune time to implement a carbon tax, despite many politicians’ insistence 

104

Figure 36. Close-‐up of Figure 30 


on doing so. It is apparent that a carbon tax would result in a total cost to 

consumers that is greater in magnitude than the benefit of reducing pollution, as 

quantified by the social cost of carbon. To put it plainly, the cost-‐benefit analysis in 

one time period indicates that society simply would not benefit from a carbon tax, 

be it explicit or implicit in a cap-‐and-‐trade system. 

Of course, the suitability of a given tax policy changes for every scenario. 

Even though the carbon tax inflicts more harm than good today, it may be an 

important component of the environmental tax policy in a future scenario with 

improved technological capabilities. Table 13 provides a summary of the optimal 

tax policies and corresponding net savings to society associated with each 

scenario. 38 There is no timeless policy, as the table shows; the policy that delivers 

38 While it may seem ironic that a tax policy would generate savings, recall that the cost-‐benefit 

calculation is designed for neither the consumers nor the government. Rather, “net benefit” or “net 

savings” refers to the benefit accruing to society as a whole. Because the externality of carbon 

105


the greatest benefit to society depends entirely on the technological development of 

renewable technology at each stage. 

According to the cost-‐benefit analysis of independent scenarios depicted in 

Figures 30-‐35, the optimal tax policy hovers around a 50% tax credit and $0 carbon 

tax for all scenarios until renewable technology costs decline by more than 50%. 

For scenarios in which renewable technology installation expense is 60% to 90% 

reduced from its level today, the optimal single-‐time period tax policy suddenly 

leaps to a 100% tax credit and a $100 carbon tax. 

Of course, it is worthwhile to keep in mind that the latter scenarios 

sensationalize the benefit of environmental tax policy to a degree. It is dubious 

whether the costs of both solar and wind technology will ever jointly decline so far 

Renewable 

Tech Cost 

Decline 

Table 13 

Optimal Tax Policy by Scenario 

Carbon Tax 

($/ton) 

Federal 

Tax Credit 

Net Savings 

to Society 

(billions) 

0% 0 50% 4.7 

10% 0 60% 14.4 

20% 0 50% 26.0 

30% 0 50% 41.9 

40% 0 50% 61.5 

50% 0 50% 110.7 

60% 100 100% 305.6 

70% 100 100% 545.6 

80% 100 100% 795.7 

90% 100 100% 1,055.8 

dioxide emissions is quantified and incorporated into the cost-‐benefit analysis, any tax policy under 

consideration for implementation should return positive net savings. Otherwise, it is not worth 

pursuing. 

106


as 80%, for example. The discussion in Chapter 4 testified that such declines are 

entirely plausible for solar PVs, but the costs of wind turbines have already begun to 

plateau. The difference in maturity of the wind and solar PV markets necessitates 

the separation of the “decline in renewable technology” into two distinct variables: 

the decline in cost of wind turbines, and the decline in cost of solar PVs. 

5.1.3 Delinking Wind and Solar Technology Improvement Variables 

The symmetry of solar and wind technological improvements is the biggest 

drawback in the one time period cost-‐benefit analysis. In recognition of this 

shortcoming, Figures 37-‐41 on pages 109-‐110 were created to give greater context 

to the cost-‐benefit outcomes. Each graph represents a different underlying policy 

with a tax credit growing in increments of 20%. The most important insights 

gleaned from these surfaces are: 

• A substantial decline in the cost of either wind or solar technology will lead 

to greater net savings to society than a moderate decline in the costs of both 

wind and solar technology. 

• As solar technology costs decline, the net benefit to society is preceded by a 

small dip into net cost territory. This occurs because the government, 

through tax credits, artificially lowers the cost of solar PVs to the point that 

more consumers choose to install solar technology than is economical. The 

cost of installations outweighs the benefit from reduced pollution at the dip. 

This is easiest to see in Figure 40. 

• As wind technology costs decline, the net benefit to society increases 

everywhere on the curve. Even large tax credits do not lead consumers to 

107


switch before it is advantageous to do so. This result is consistent with the 

relatively mature wind turbine market; because wind electricity prices have 

already fallen to grid parity levels in many states, a further decline in wind 

turbine costs will only benefit consumers. 

• Interestingly, society benefits more from large declines in solar technology 

costs than from large declines in wind technology costs. Again, this finding is 

consistent with the relative maturities of these markets: the solar PV market 

is much less mature than the wind turbine market, so advances in the former 

technology will have a greater impact on society than advances in the latter 

market. In other words, the “Solar Tech Cost Decline” axis reflects 

reductions from a larger base cost; therefore, the same percentage decrease 

in costs is more notable for solar than for wind technology. 

• The concavity of the surface shows that the marginal change in net benefit to 

society rises as technology improves. That is, when solar PVs are reduced 

from 60% to 70% off their original price, the incremental rise in the net 

benefit to society will be greater than when solar PVs decline from 10% to 

20%. This finding alludes to the consumer behavior model in Chapter 4: 

steep reductions in cost will open up the renewable technology market to 

the early majority, then the late majority, and eventually the laggards. Prior 

to the steep reductions in cost (for solar PV especially), only innovators and 

early adopters will utilize the renewable energy technology, limiting the 

marginal impact on the net benefit to society. 

108


• Intuitively, society incurs the greatest net savings when cost declines for 

wind and solar technology both approach 100%. 

The main takeaway from the graphs is that technological improvement is 

unequivocally a good thing for society. In the case of solar power, the tax credit 

should be implemented with discretion due to potential for distortion of incentives. 

Figure 37 

Figure 38 

109

Figure 39 

Figure 40 

Figure 41 


110

5.2 Net Savings to Society Over Time 


Section 5.1 graphically illustrated the cost-‐benefit analysis of numerous tax 

policies in one time period. The ideas derived from the single period analysis are 

integral to evaluating tax policy, and they naturally lead to a more expansive 

discussion of the longer term trade-‐offs inherent in carbon taxes and investment tax 

credits. An essential dimension of that discussion, of course, is time. Time 

considerations were excluded until this point in order to establish a firm grounding 

in the cost-‐benefit framework. But now, the cost-‐benefit analysis is conducted over 

forty years to get a sense for the long-‐term reverberations of environmental tax 

policies for wind and solar technology. 

5.2.1 Net Cost to Society with Variable Rates of Technology Improvement 

By virtue of representing one time period each, Figures 30-‐35 were forced to 

assume a flat decline in the cost of technology. In a multi-‐period model, building in a 

gradual rate of technology improvement over time adds realism to the cost-‐benefit 

analysis. Using industry experts’ projections, the following assumptions are built 

into the time progression model: 

• Solar PVs will decline in cost 60% in the next ten years and 80% in the next 

twenty years. After twenty years, the cost stabilizes, having reached (or 

come close to) its steady state price. 

• Wind turbines will decline in cost 11% in the next ten years and 22% in the 

next twenty years. After twenty years, the cost stabilizes, having reached (or 

come close to) its steady state price. 

111


Hence, the multi-‐period model sidesteps the solar-‐wind linkage problem 

encountered in the single-‐period model. 

A second major difference between the single-‐ and multi-‐period models is 

the object of the calculation. The single-‐period cost-‐benefit analysis calculated the 

present value of the change in electricity-‐related costs to society as a result of the 

first year of the tax policy. In contrast, the multi-‐period model calculates the 

present value of the total cost to society of all electricity-‐related expenses for the 

next forty years. Figures 42 and 43 39 —the same graph from two different 

viewpoints—show how different tax policies affect the present value of the cost to 

society over forty years. 

In the single-‐period graphs, higher surfaces indicated greater net savings. 

But here, the lower the surface, the lower the present value of the cost to society. 

Therefore, the optimal tax policy over time corresponds to the lowest point on the 

graph, which is an 80% tax credit combined with a $0 carbon tax. The tax policy 

that results in the highest net cost to society is, essentially, no tax policy at all—a 0% 

tax credit combined with a $0 carbon tax. 

Obviously, this optimal policy result is slightly different from that in the 

single-‐period analysis. The disagreement is explained by the different assumptions 

in each model: the single-‐period model assumes an instant decline in technology 

costs, whereas the multi-‐period model assumes a gradual rate of decline in 

technology costs over time. Hence, the optimal policy outcomes from the two 

models are not 

39 Appendix A-‐10 contains the code used to generate these graphs. 

112


Figure 42. Front View: Present Value of Cost to Society Over 40 Years 

Figure 43. Back View: Present Value of Cost to Society Over 40 Years 

113


comparable. The single-‐period model returns the optimal policy for one year 

depending on current technology costs, but because technology costs are always 

changing, society is better served by a policy optimized over time, as in the multi-‐ 

period model. 40 

Figures 42 and 43 beg the question, why is such a high investment tax credit 

optimal? Along the tax credit axis, the present value of the cost to society 

continuously decreases until the tax credit reaches 80%. The answer relates to the 

current state of wind and solar technology. Despite the fact that wind technology 

has come down to a cost competitive level in some states, in most states it has not; 

the same is true for solar power everywhere. Until renewable energy technology 

becomes truly cost competitive, society is made better off by federal tax credits that 

will encourage renewable energy installations. 

Because experts project that the cost of solar technology will decline rapidly 

this decade, the annual cost of the tax credit to government will become increasingly 

cheaper. On the other hand, society will accumulate more and more savings from 

averted social costs of carbon. The present value of the benefits of installing 

renewable technology in the short term greatly outweigh the installation costs. 

In fact, it is probable that the model actually understates the negative 

economic consequences of the carbon tax. Instituting a carbon tax will lead to job 

loss and unemployment as companies are forced to find ways to cut costs. And 

because carbon is an input in the manufacturing process of virtually any product on 

40 Assuming that the government is unwilling to adapt the policy annually. 

114


the marketplace, a carbon tax will raise prices of goods across the board. In 

quantifying the negative impact on society of rising electricity costs, the model does 

not fully capture the indirect ramifications of a carbon tax. 

5.2.2 Optimal Policies in the Time Lapse Model 

Optimal or not, most American politicians today would balk at the idea of an 

80% investment tax credit. Faced with pressure to balance the budget, policy 

makers usually seek to find streams of revenue in bills they propose that require 

spending. As such, it is unlikely that Congress would approve an investment tax 

credit higher than 30% without some level of a carbon tax. Acknowledging this 

reality, Table 14 provides a summary of the optimal tax credits according to carbon 

tax level. 

Optimal Tax Credit by Carbon Tax 

Carbon Tax 

($/ton) 

Table 14 

Federal 

Tax Credit 

Cost to 

Society 

(billions) 

0 80% 1,477.8 

10 80% 1,486.8 

20 70% 1,496.6 

30 70% 1,494.0 

40 70% 1,498.6 

50 60% 1,503.4 

60 60% 1,506.9 

70 60% 1,510.5 

80 60% 1,513.6 

90 90% 1,515.3 

100 90% 1,516.7 

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If the federal government were to impose no carbon tax at all, the cost-‐ 

benefit model indicates that it could minimize the cost to society by implementing 

an 80% tax credit for renewable energy installations. Such a policy would reduce 

the cost to society by $330 billion compared to a scenario without any government 

intervention, which has a $1.808 trillion cost to society over the next forty years. 

In essence, the government faces the same decision as the individual 

homeowner considering an investment in wind or solar technology. That is, the 

government must weigh sacrificing money in the short term with reaping benefits in 

the long term. Like consumers, the government must also decide how to adjust its 

budget according to its investment decisions. In practice, the government is likely to 

impose a sub-‐optimal carbon tax in order to balance its own budget, shifting the 

higher cost to the taxpayer. 

The tax policies in Table 14 may be as implausible as they are idealistic. Yet 

if there is one thing the cost-‐benefit analysis makes clear, it is that the government 

can do no worse than to do nothing. Even if political tensions prohibit it from 

ratifying an optimal tax policy, implementing incentives at any level is a move in the 

right direction. 

116

6. Summary and Conclusion 

The twenty-‐first century will see dramatic changes in the way that societies 

harness and distribute power. Right now, the developed world is at the brink of a 

clean tech revolution: the rapid advancement of solar technology and the 

exponential growth in wind power capacity worldwide are testaments to the 

promise of fossil fuel alternatives. The fervor surrounding the renewable energy 

industry is fueled, at least in part, by the threat of scarce resources. If renewable 

energy technology is widely adopted all over the world, the perils imposed by fossil 

fuels—economic, environmental, and political—will diminish. The question at 

present is if, and when, that will happen. 

6.1 Summary of the Thesis 

This thesis sought to explore how public policy can be designed to encourage 

residential investment in solar and wind technology. Confronted with a dearth of

Summary and Conclusion 

solar and wind electricity price data, the first task was to build a data set “from the 

ground up.” This required compiling state-‐level data on wind and solar resources, 

electricity consumption, population distribution, retail electricity prices, running 

rates for solar PV and wind turbine installation, and other contributors to local 

electricity prices. After coming up with a comparative price per kilowatt-‐hour of 

electricity for each of the three sources in all fifty states plus D.C., the data was 

applied to a cost function with government decision variables as inputs. Minimizing 

the cost function dictated the optimal electricity mix and prices in each state based 

on varying levels of government intervention. Subsequently, single-‐period and 

multi-‐period cost-‐benefit analyses were developed to predict the economic 

consequences of the different tax policies. 

The upshot of the cost-‐benefit analysis is that society benefits most from a 

substantial investment tax credit for renewable energy. Even though a carbon tax 

also encourages consumers to switch to renewable energy, it does so at a greater 

cost to society than the investment tax credit. The optimal tax policy was an 80% 

tax credit and no carbon tax. If this policy were implemented today, the projected 

electricity mix in the United States in twenty years shows solar as the leading source 

of electricity, followed by retail and wind electricity. Obviously, this result, which 

rests on optimistic assumptions about the rate of decline in PV costs, paints a 

drastically different picture from the reality today. 

118

6.2 Limitations of this Model 


Any economic model must stand on assumptions that, at least to some extent, 

depart from reality. The following idealizations in this model limit the credibility of 

the results: 

• Households must choose between retail, solar, and wind electricity. To 

simplify the analysis, this model ignored the options of nuclear power, 

often cited as a clean and relatively cheap alternative to fossil fuels. 

• Retail, solar, and wind electricity are treated as perfect substitutes. In 

actuality, wind and solar energy suffer from more than just cost 

disadvantages; engineers and innovators are still trying to develop ways to 

ensure that solar and wind resources provide consistent power like fossil 

fuels. The unreliability of solar and wind power is a major roadblock to its 

commercialization. 

• The technology adoption paradigm used to model consumer behavior is 

based on past technologies’ patterns of market penetration. Whether 

renewable energy technology follows or deviates from this paradigm 

remains to be seen. 

• Rates of technological improvement are highly uncertain. There is no 

guaranteed timeline for how long it will take for a breakthrough to occur. 

Furthermore, the progress of solar PV technology and, to a lesser extent, 

wind turbines is subject to private and public funding, which are largely 

contingent on the economy. 

119


• The cost-‐benefit analysis in this model does not fully account for the 

economic repercussions of a carbon tax. The cost to society is captured by 

the marginal change in retail electricity prices caused by the carbon tax, but 

the model does not consider other side effects, like job loss, reduced 

competitiveness of American companies, and inflation that is caused by 

companies’ passing higher cost of goods sold onto consumers. 

• Another limitation of the model used to predict the price of retail electricity 

under different carbon tax regimes is the omission of any forecasting of the 

change in retail prices due to shrinkage of the rate base. As consumers 

switch to wind and solar, the power plants will be selling fewer kWh of 

electricity, but the fixed costs of running the plant will remain virtually the 

same. Those costs will need to be spread over fewer customers, putting 

even more upward pressure on retail electricity prices beyond the carbon 

tax pass-‐through. A step-‐variable cost structure will exist where a plant 

cannot be closed down until enough customers switch to justify closing the 

whole plant. During the transition period, prices will be higher until 

the electricity demand shrinks enough to enable closure of a power plant. 

This factor has not been accounted for in the model. 

In spite of these limitations, the methodology and results presented in this 

thesis are intended to serve as a springboard for related analyses pertaining to tax 

policies in the renewable energy space. 

120

6.3 Areas for Further Investigation 


Environmental tax policy and, more generally, renewable energy incentives 

present many directions for further research. It may be advantageous to learn more 

about the consumer response, both real and perceived, to renewable energy 

technology. It would be particularly helpful to identify what steps might be taken to 

lower the “inducement to change” threshold in states like Hawaii. Additionally, it 

would be worth researching whether consumers will respond to renewable energy 

in the same way that they responded to personal computers, cell phones, and iPods, 

or whether renewable energy will depart from standard patterns of technology 

adoption. 

This analysis might be refined by breaking down the United States by county 

rather than by state. Some liberties are taken when one is forced to classify an 

entire state’s wind resource. A more robust analysis would divide the United States 

into smaller territories, though the paucity of data at such levels makes this 

challenging. 

The renewable portfolio standard (RPS) implemented in some states is 

another form of government regulation that deserves attention. The RPS is “a policy 

that seeks to increase the proportion of renewable electricity used by retail 

customers” by requiring electric utilities to provide a certain percentage of 

electricity from renewable sources, including wind, solar, biomass, and geothermal. 

[87]. Thus far, twenty-‐seven states have approved such a standard. If successful, 

the RPS policy will dramatically increase the proportion of retail electricity derived 

from renewable sources, effectively nullifying the treatment of retail electricity as a 

121


proxy for fossil fuels in this thesis. A full list of the thirty-‐seven states and their 

respective renewable portfolio standards is included in Appendix A-‐11. 

6.4 Final Thoughts 

The energy problem facing the world today is one of trade-‐offs. From a 

consumer’s perspective, the less environmentally friendly choice is often the less 

expensive choice. From the government’s perspective, the opportunity cost of a 

dollar spent on green energy is a dollar that could have gone to public schools, 

Medicare, Social Security, or a host of other federally funded programs. With so 

many interconnected, conflicting objectives at play, the “optimal” policy solution is 

as dependent on judgment and preferences as it is on quantifiable parameters. 

Going forward, educating the public about the country’s troublesome 

dependence on fossil fuels will be as important as designing policies to remedy it. 

The energy problem is at risk of going unaddressed if there is not strong public 

support behind finding alternatives to fossil fuels. In a recent Gallup poll, a slight 

majority of Americans said that U.S. should prioritize development of energy 

supplies (defined in the question as oil, gas, and coal) over protection of the 

environment [89]. This year marked the first time in the question’s ten-‐year history 

that Americans indicated a preference for energy over environment. 

It is the nature of the American political system to give voters the loudest 

voice of all. Unless Americans begin to prioritize environmental concerns ahead of 

economic worries, the government will act as a barrier, rather than a facilitator, of 

the inevitable movement toward renewable energy. 

122

Appendix 

A-1. Solar Appendix: Excel worksheet for Solar Calculations 

State 

Average 

peak 

sun 

hours 

per day 

Avg 

daily 

elec 

consmpt 

(kWh) 

Solar 

panel 

required 

(kW) 

Avg 

install. 

cost 

($) 

Pres 

value of 

maint. 

cost ($) 

Total cost 

(inst + 

main) of 

module 

($) 

Total output 

of 

electricity 

of module 

(kWh) 

Cost per 

kWh over 

lifespan 

($/kWh) 

.Alabama 4.23 43 11.63 81,427 24,100 105,527 404,095 0.26 

.Alaska 3.77 22 6.64 46,486 13,759 60,245 205,609 0.29 

.Arizona 6.50 37 6.62 46,371 13,725 60,096 353,622 0.17 

.Arkansas 4.25 37 9.92 69,430 20,549 89,980 346,191 0.26 

.California 5.74 19 3.81 26,669 7,893 34,563 179,598 0.19 

.Colorado 5.37 23 4.99 34,896 10,328 45,225 219,853 0.21 

.Connecticut 3.73 25 7.72 54,061 16,000 70,061 236,574 0.30 

.Delaware 3.63 31 9.97 69,801 20,659 90,460 297,266 0.30 

DC 4.23 25 6.89 48,232 14,275 62,507 239,361 0.26 

.Florida 5.41 38 8.11 56,739 16,793 73,532 360,125 0.20 

.Georgia 4.87 38 9.07 63,463 18,783 82,247 362,602 0.23 

.Hawaii 6.02 21 4.10 28,717 8,499 37,217 202,822 0.18 

.Idaho 4.81 35 8.45 59,152 17,507 76,659 333,804 0.23 

.Illinois 3.14 26 9.49 66,404 19,654 86,058 244,625 0.35 

.Indiana 4.21 35 9.48 66,328 19,631 85,960 327,611 0.26 

.Iowa 4.40 29 7.59 53,147 15,730 68,877 274,351 0.25 

.Kansas 5.18 30 6.70 46,876 13,874 60,751 284,880 0.21 

.Kentucky 4.94 40 9.29 65,022 19,245 84,267 376,846 0.22 

.Louisiana 4.83 42 9.96 69,727 20,637 90,364 395,115 0.23 

.Maine 4.35 17 4.59 32,158 9,518 41,675 164,115 0.25 

.Maryland 4.47 36 9.16 64,124 18,979 83,103 336,282 0.25 

.Massachusetts 3.95 21 6.06 42,430 12,558 54,988 196,629 0.28 

.Michigan 4.10 22 6.31 44,161 13,070 57,231 212,421 0.27 

.Minnesota 4.53 27 6.93 48,475 14,347 62,823 257,630 0.24 

.Mississippi 4.43 41 10.73 75,129 22,236 97,365 390,471 0.25 

.Missouri 4.56 37 9.27 64,884 19,204 84,088 347,119 0.24 

.Montana 4.69 27 6.62 46,371 13,725 60,096 255,153 0.24 

.Nebraska 5.01 34 7.74 54,157 16,029 70,185 318,322 0.22 

.Nevada 6.20 32 6.00 41,974 12,423 54,397 305,317 0.18 

.New Hamp 3.40 21 7.01 49,061 14,521 63,581 195,700 0.32 

.New Jersey 4.21 24 6.54 45,765 13,545 59,311 226,046 0.26 

.New Mexico 6.77 21 3.56 24,951 7,385 32,336 198,177 0.16 

.New York 3.58 20 6.36 44,530 13,180 57,709 187,030 0.31 

.North Carolina 5.01 37 8.60 60,215 17,822 78,037 353,932 0.22 

.North Dakota 5.01 35 8.11 56,791 16,808 73,599 333,804 0.22 

.Ohio 4.05 30 8.62 60,346 17,861 78,207 286,737 0.27 

.Oklahoma 5.29 36 7.84 54,882 16,244 71,126 340,617 0.21 

.Oregon 4.09 33 9.30 65,112 19,272 84,384 312,439 0.27 

.Pennsylvania 3.60 29 9.15 64,077 18,965 83,043 270,636 0.31 

.Rhode Island 4.23 20 5.42 37,937 11,228 49,165 188,268 0.26 

.South Carolina 5.06 40 9.02 63,115 18,680 81,795 374,678 0.22 

.South Dakota 5.23 32 7.14 50,011 14,802 64,813 306,865 0.21 

.Tennessee 4.41 44 11.49 80,437 23,807 104,244 416,172 0.25 

.Texas 5.64 37 7.59 53,161 15,734 68,896 351,764 0.20 

.Utah 5.55 26 5.45 38,140 11,288 49,428 248,341 0.20 

.Vermont 2.95 19 7.57 52,966 15,676 68,642 183,314 0.37 

.Virginia 4.13 40 11.02 77,135 22,830 99,965 373,750 0.27 

.Washington 4.45 35 9.09 63,641 18,836 82,477 332,256 0.25 

.West Virginia 3.65 37 11.76 82,290 24,356 106,645 352,384 0.30 

.Wisconsin 4.29 24 6.37 44,604 13,202 57,806 224,497 0.26 

.Wyoming 6.06 29 5.42 37,935 11,228 49,163 269,707 0.18

A-2. Retail Electricity Prices in the United States, 2008 [56] 

Appendix 

State 

Proportion of 

U.S. Pop'n 

Avg retail elec 

price ($/kWh) 

State 

Proportion of 

U.S. Pop'n 

Avg retail elec 

price ($/kWh) 

.Alabama 1.5% 0.0932 .Montana 0.3% 0.0877 

.Alaska 0.2% 0.1518 .Nebraska 0.6% 0.0759 

.Arizona 2.1% 0.0966 .Nevada 0.9% 0.1182 

.Arkansas 0.9% 0.0873 .New Hampsh 0.4% 0.1488 

.California 12.0% 0.1442 .New Jersey 2.8% 0.1414 

.Colorado 1.6% 0.0925 .New Mexico 0.7% 0.0912 

.Connecticut 1.1% 0.1911 .New York 6.4% 0.1710 

.Delaware 0.3% 0.1316 .N Carolina 3.1% 0.0940 

.DC 0.2% 0.1118 .North Dakota 0.2% 0.0730 

.Florida 6.0% 0.1122 .Ohio 3.8% 0.0957 

.Georgia 3.2% 0.0910 .Oklahoma 1.2% 0.0858 

.Hawaii 0.4% 0.2412 .Oregon 1.2% 0.0819 

.Idaho 0.5% 0.0636 .Pennsylvania 4.1% 0.1095 

.Illinois 4.2% 0.1012 .Rhode Island 0.3% 0.1405 

.Indiana 2.1% 0.0826 .S Carolina 1.5% 0.0919 

.Iowa 1.0% 0.0945 .S Dakota 0.3% 0.0807 

.Kansas 0.9% 0.0819 .Tennessee 2.1% 0.0784 

.Kentucky 1.4% 0.0734 .Texas 8.1% 0.1234 

.Louisiana 1.5% 0.0937 .Utah 0.9% 0.0815 

.Maine 0.4% 0.1652 .Vermont 0.2% 0.1415 

.Maryland 1.9% 0.1189 .Virginia 2.6% 0.0874 

.Massachusetts 2.1% 0.1623 .Washington 2.2% 0.0726 

.Michigan 3.2% 0.1021 .West Virginia 0.6% 0.0673 

.Minnesota 1.7% 0.0918 .Wisconsin 1.8% 0.1087 

.Mississippi 1.0% 0.0936 .Wyoming 0.2% 0.0775 

.Missouri 2.0% 0.0769 

124

A-3. Wind Appendix: Excel worksheet for Wind Calculations 

State 

Avg 

Elec 

Cons 

per Year 

(kWh) 

Wind 

Class 

(1-7) 

Annual 

avg 

wind 

speed 

(m/s) 

Rotor 

diam. 

req 

(m) 

Pwr 

rating 

req 

(kW) 

Avg 

install. 

cost ($) 

Pres 

value of 

maint. 

cost ($) 

Total 

cost of 

turbine 

($) 

Annual 

output 

of 

turbine 

(kWh) 

Appendix 

Cost per 

kWh 

over 

turbine 

life 

($/kWh) 

.Alabama 15,660 1 2.20 32.0 126 502,749 164,413 667,162 15,740 2.12 

.Alaska 7,968 3 5.35 6.0 4 17,675 5,780 23,455 8,150 0.15 

.Arizona 13,704 1 2.20 30.0 110 441,869 144,504 586,373 13,840 2.12 

.Arkansas 13,416 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.20 

.California 6,960 3 5.35 5.5 4 14,852 4,857 19,709 6,850 0.12 

.Colorado 8,520 5 6.20 5.5 4 14,852 4,857 19,709 9,310 0.12 

.Connecticut 9,168 2 4.75 7.5 7 27,617 9,031 36,648 9,510 0.20 

.Delaware 11,520 2 4.75 8.0 8 31,422 10,276 41,698 10,820 0.20 

.DC 9,276 2 4.75 7.5 7 27,617 9,031 36,648 9,510 0.20 

.Florida 13,956 1 2.20 30.0 110 441,869 144,504 586,373 13,840 2.12 

.Georgia 14,052 1 2.20 30.0 110 441,869 144,504 586,373 13,840 2.05 

.Hawaii 7,860 1 2.20 22.5 62 248,551 81,283 329,835 7,780 2.03 

.Idaho 12,936 5 6.20 6.5 5 20,743 6,784 27,527 13,000 0.11 

.Illinois 9,480 2 4.75 7.5 7 27,617 9,031 36,648 9,510 0.20 

.Indiana 12,696 2 4.75 8.5 9 35,472 11,600 47,073 12,210 0.18 

.Iowa 10,632 3 5.35 7.0 6 24,057 7,867 31,925 11,100 0.14 

.Kansas 11,040 3 5.35 7.0 6 24,057 7,867 31,925 11,100 0.14 

.Kentucky 14,604 1 2.20 31.0 118 471,818 154,298 626,116 14,780 2.12 

.Louisiana 15,312 1 2.20 31.5 122 487,161 159,316 646,476 15,260 2.12 

.Maine 6,360 2 4.75 6.0 4 17,675 5,780 23,455 6,080 0.18 

.Maryland 13,032 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.20 

.Massach 7,620 2 4.75 6.5 5 20,743 6,784 27,527 7,140 0.18 

.Michigan 8,232 2 4.75 7.0 6 24,057 7,867 31,925 8,280 0.21 

.Minnesota 9,984 3 5.35 6.5 5 20,743 6,784 27,527 9,570 0.15 

.Mississippi 15,132 1 2.20 31.5 122 487,161 159,316 646,476 15,260 2.12 

.Missouri 13,452 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.20 

.Montana 9,888 5 6.20 5.5 4 14,852 4,857 19,709 9,310 0.10 

.Nebraska 12,336 3 5.35 7.5 7 27,617 9,031 36,648 12,740 0.14 

.Nevada 11,832 4 5.80 6.5 5 20,743 6,784 27,527 11,270 0.12 

.New Hamp 7,584 3 5.35 6.0 4 17,675 5,780 23,455 8,150 0.15 

.New Jersey 8,760 2 4.75 7.0 6 24,057 7,867 31,925 8,280 0.18 

.New Mex 7,680 3 5.35 6.0 4 17,675 5,780 23,455 8,150 0.15 

.New York 7,248 2 4.75 6.5 5 20,743 6,784 27,527 7,140 0.18 

.N Carolina 13,716 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.20 

.N Dakota 12,936 4 5.80 7.0 6 24,057 7,867 31,925 13,070 0.12 

.Ohio 11,112 2 4.75 8.0 8 31,422 10,276 41,698 10,820 0.18 

.Oklahoma 13,200 3 5.35 7.5 7 27,617 9,031 36,648 12,740 0.14 

.Oregon 12,108 4 5.80 6.5 5 20,743 6,784 27,527 11,270 0.12 

.Pennsyl 10,488 3 5.35 7.0 6 24,057 7,867 31,925 11,100 0.14 

.Rhode Isl 7,296 3 5.35 5.5 4 14,852 4,857 19,709 6,850 0.12 

.S Carolina 14,520 1 2.20 30.5 114 456,721 149,361 606,082 14,300 2.05 

.S Dakota 11,892 4 5.80 6.5 5 20,743 6,784 27,527 11,270 0.12 

.Tennessee 16,128 2 4.75 9.5 11 44,310 14,491 58,800 15,250 0.18 

.Texas 13,632 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.20 

.Utah 9,624 3 5.35 6.5 5 20,743 6,784 27,527 9,570 0.15 

.Vermont 7,104 3 5.35 5.5 4 14,852 4,857 19,709 6,850 0.15 

.Virginia 14,484 2 4.75 9.0 10 39,768 13,005 52,774 13,690 0.18 

.Washington 12,876 4 5.80 7.0 6 24,057 7,867 31,925 13,070 0.12 

.W Virginia 13,656 3 5.35 7.5 7 27,617 9,031 36,648 12,740 0.12 

.Wisconsin 8,700 2 4.75 7.0 6 24,057 7,867 31,925 8,280 0.18 

.Wyoming 10,452 5 6.20 6.0 4 17,675 5,780 23,455 11,070 0.12 

125

A-4. Weibull modeling for wind calculations – MATLAB file 

%Weibull wind2.m file 

Appendix 

Scale = [2.2 5.4 2.2 4.8 5.4 6.2 4.8 4.8 4.8 2.2 2.2 2.2 6.2 4.8 4.8 5.4 

5.4 2.2 2.2 4.8 4.8 4.8 4.8 5.4 2.2 4.8 6.2 5.4 5.8 5.4 4.8 5.4 4.8 4.8 5.8 

4.8 5.4 5.8 5.4 5.4 2.2 5.8 4.8 4.8 5.4 5.4 4.8 5.8 5.4 4.8 6.2]; 

Shape = 2; 

SCALE = zeros(1000,51); 

for i = 1:1000 

for j = 1:51 

SCALE(i,j)=Scale(j); 

end 

end 

windspeed = wblrnd(SCALE,Shape,1000,51); 

%PDF of wind speeds in Alabama 

WblPDFAL = wblpdf(windspeed(1:1000,1),Scale(1),Shape); 

%PDF of wind speeds in Montana 

WblPDFMT = wblpdf(windspeed(1:1000,27),Scale(27),Shape); 

%PDF of wind speeds in N. Dakota 

WblPDFND = wblpdf(windspeed(1:1000,35),Scale(35),Shape); 

%figure 1 - Alabama 

plot(windspeed(1:1000,1),WblPDFAL,'d') 

xlabel('Wind speed V (m/s)') 

ylabel('Probability Density') 

title('Weibull PDF Modeling Wind Speeds in Alabama') 

%figure 2 - Montana 

plot(windspeed(1:1000,27),WblPDFMT,'d') 



title('Weibull PDF Modeling Wind Speeds in Montana') 

%figure 3 - North Dakota 

plot(windspeed(1:1000,35),WblPDFMT,'d') 



title('Weibull PDF Modeling Wind Speeds in North Dakota') 

syms V; 

%Power produced by the wind turbine (Montana example) 

rho = 1.225; %air density (kg/m^3) 

Cp = .35; %coefficient of performance (.35 is Cp for a good 

design) 

Ng = .80; %generator efficiency (.80 is standard for a gridconnected 

induction generator or a permanent magnet generator) 

Nb = .95; %gearbox/bearings efficiency 

AforMT = 23.76; %rotor swept area (23.76 m^2 for 5.5-m diameter in MT) 

AforND = 38.48; %rotor swept area (38.48 m^2 for 7-m diameter in ND) 

WMT = 0.5.*rho.*AforMT.*Cp.*windspeed(1:1000,27).^3.*Ng.*Nb/1000; 

%returns wind turbine power in kW based on wind speed WblPDF 

WND = 0.5.*rho.*AforND.*Cp.*windspeed(1:1000,35).^3.*Ng.*Nb/1000; 

%returns wind turbine power in kW based on wind speed WblPDF 

%Use this T value to plot figure 3 - Montana and ND only 

TMT = WblPDFMT.*8760; %# of hours/yr during which wind blows with speed V 

TND = WblPDFND.*8760; %# of hours/yr during which wind blows with speed V 

126

%figure 4 - Montana - illustration of integral 

plot(windspeed(1:1000,27),WMT.*TMT,'d') 


ylabel('Annual Energy Produced as a Function of Wind Speed V (kWh)') 

title('W(V)*T(V): Annual Energy Produced in Montana as a Function of V 

(kWh)') 

Appendix 

%figure 5 - N. Dakota - illustration of integral 

plot(windspeed(1:1000,35),WND.*TND,'d') 


ylabel('Annual Energy Produced as a Function of Wind Speed V (kWh)') 

title('W(V)*T(V): Annual Energy Produced in North Dakota as a Function of V 

(kWh)') 

%Definining P(V), T(V), W(V) in Hasan paper 

PofVmt = (Shape/Scale(27))*(V/Scale(27))*(exp(-V/Scale(27))^Shape); %pdf 

of Weibull distribution 

TofVmt = PofVmt*8760; %# of hours/yr when wind blows with speed V (hours) 

WofVmt = 0.5*rho*AforMT*Cp*V^3*Ng*Nb/1000; %power output in MONTANA of 

wind turbine as a function of wind speed V (kW) 

PofVnd = (Shape/Scale(35))*(V/Scale(35))*(exp(-V/Scale(35))^Shape); %pdf 

of Weibull distribution 

TofVnd = PofVnd*8760; %# of hours/yr when wind blows with speed V (hours) 

WofVnd = 0.5*rho*AforND*Cp*V^3*Ng*Nb/1000; %power output in MONTANA of 

wind turbine as a function of wind speed V (kW) 

%V1 and V2 speeds 

cutin = 3; %cut-in speed is 3 m/s 

cutout = 20; %cut-out speed is 20 m/s 

%Calculates integral of total energy production PER YEAR 

EnergyPerYearMT = int(WofVmt*TofVmt,cutin,cutout) %%Montana 

EnergyPerYearND = int(WofVnd*TofVnd,cutin,cutout) %%North Dakota 

%Code below is to calculate what rotor diameter should be for every state 

in order to produce enough electricity to meet household need. Must adjust 

PofV values for every state because states have different scale parameters. 

Rotor = 1:0.5:33; %rotor diameter in m 

SweptArea = pi.*(Rotor./2).^2; %meters squared 

EnergyProduced = zeros(65,51); 

for i = 1:51 

for j = 1:65 

EnergyProduced(j,i) = int((Shape/Scale(i))*(V/Scale(i))*(exp(- 

V/Scale(i))^Shape)*8760*0.5*rho*SweptArea(j)*Cp*V^3*Ng*Nb/1000,cutin,cutout 

); 

end 

end 

%This matrix is used to match state's electricity need to appropriate size 

%wind turbine for that state (based on wind speeds) 

EnergyProduced 

%Ratings of Wind Turbines Required to Meet Elec Demand for Avg Home in 

%State. The rated wind speed generally corresponds to the point at which 

%the conversion efficiency is near its maximum. 

ratedspeed = 10; %units m/s - speed at which turbines are rated by 

manufacturers 

127

A-5. MATLAB code for calculating solar cost variability in New Mexico: 

%%NewMexico.m 

Appendix 

dbarNM = 21; %average daily electricity consumption (kWh) 

sbarNM = 6.77; %average peak sun hours per day in New Mexico (hours/day) 

cbarNM = 8950; %average cost of solar electric installation in NM ($/kW) 

mbarNM = 11514; %present value of future maintenance costs in NM ($) 

lbarNM = 20; %expected lifetime of installation in NM (years) 

dsdvNM = 3.00; %stdev of daily electricity consumption 

ssdvNM = 0.50; %stdev of peak sun hours per day 

csdvNM = 1500; %stdev of cost of solar electric installation per kW 

msdvNM = 1500; %stdev of present value of future maintenance costs 

lsdvNM = 5; %stdev of lifetime of PV panel 

betaNM = 0.30; %investment tax credit for solar installation (assume 30%) 

dhatNM = normrnd(dbarNM,dsdvNM,[1 1000]); 

shatNM = normrnd(sbarNM,ssdvNM,[1 1000]); 

chatNM = normrnd(cbarNM,csdvNM,[1 1000]); 

mhatNM = normrnd(mbarNM,msdvNM,[1 1000]); 

lhatNM = normrnd(lbarNM,lsdvNM,[1 1000]); 

CsolarNM = zeros(1,1000); 

CsolarNM = ((dhatNM./shatNM).*chatNM.*(1betaNM)*(1.15)+mhatNM)./((365)*(0.9)*(1.15)*(dhatNM).*(lhatNM)); 

muNM = mean(CsolarNM) 

sigmaNM = std(CsolarNM) 

pdfNM = normpdf(-0.2:0.01:0.70,muNM,sigmaNM); 

plot(-0.2:0.01:0.70,pdfNM); 

axis([0 0.60 0 5.5]); 

%figure1 

xlabel('Cost per kWh ($)'); 

ylabel('Density'); 

title('PDF of Solar PV Cost per kWh in New Mexico (30% tax credit)') 

p = 100*(0:0.25:1); 

y = prctile(CsolarNM,p); 

zNM = [p;y]; 

zNM 

NMwindc = 0.11; 

z = ((NMwindc-muNM)/sigmaNM) 

prob = normcdf([-1000,z]); 

prob(2)-prob(1) 

128

A-6. MATLAB code for calculating solar cost variability in all states 

%%SolarCostAllocation.m 

Appendix 

windcosts0 = [2.594723938 0.176704752 2.599649102 0.222667636 0.177191647 

0.132437511 0.226777615 0.223207007 0.223602611 2.595417434 2.596107115 

0.15241116 0.13077839 0.222771653 0.22484129 0.173225314 0.17484687 

2.594688469 2.601675583 0.174133292 0.225803518 0.174768048 0.226539946 

0.172377988 2.603822722 0.223265134 0.131779291 0.175086733 0.152536013 

0.152766422 0.222414576 0.176144175 0.17200815 0.222883262 0.152377618 

0.225548631 0.173213186 0.151401751 0.17586933 0.173147277 2.596384978 

0.153309522 0.222947191 0.226252625 0.176389147 0.154777828 0.22575902 

0.151670857 0.17469029 0.226823923 0.134277327]; 

dhat = zeros(1000,51); %initialize dhat matrix 

shat = zeros(1000,51); %initialize shat matrix 

chat = zeros(1000,51); %initialize chat matrix 

mhat = zeros(1000,51); %initialize mhat matrix 

lhat = zeros(1000,51); %initialize lhat matrix 

dhat = dmatrix; %calls dmatrix in Dmatrix.m file 

shat = smatrix; %calls smatrix in Smatrix.m file 

chat(1:1000,1:51) = 8950; %assume all states have uniform install./kW cost 

mhat = mmatrix; %calls mmatrix in Mmatrix.m file 

lhat(1:1000,1:51) = 20; %assume solar PVs have uniform expected 

lifetimes across US 

dsdv = 3.00; %stdev of daily electricity consumption 

ssdv = 0.50; %stdev of peak sun hours per day 

csdv = 1500; %stdev of cost of solar electric installation per kW 

msdv = 1500; %stdev of present value of future maintenance costs 

lsdv = 5; %stdev of lifetime of PV panel 

beta = 0.00; %investment tax credit for solar installation 

%generate noise 

dnoise = dsdv*randn(1000,51); 

snoise = ssdv*randn(1000,51); 

cnoise = csdv*randn(1000,51); 

mnoise = msdv*randn(1000,51); 

lnoise = lsdv*randn(1000,51); 

%generate n=1000 sample for variables 

d = dhat + dnoise; 

s = shat + snoise; 

c = chat + cnoise; 

m = mhat + mnoise; 

l = lhat + lnoise; 

%generate sample costs for solar PVs by state 

Csolar = zeros(1000,51); 

Csolar = ((d./s).*c.*(1-beta)*(1.15)+m)./((365)*(0.9)*(1.15)*(d).*(l)); 

%initialize vectors 

mu = [1:51]; 

sigma = [1:51]; 

zscores = [1:51]; 

zscores2 = [1:51]; 

%loop to find mu and sigma of *solar costs* and z scores of *wind costs* 

(in the solar cost distribution) for each state 

129

for i=1:51, 

mu(i) = mean(Csolar(1:1000,i)); 

sigma(i) = std(Csolar(1:1000,i)); 

zscores(i) = ((windcosts(i)-mu(i))/sigma(i)); 

zscores2(i) = ((retailcosts0(i)-mu(i))/sigma(i)); 

end 

mu; 

sigma; 

zscores; 

zscores2; 

%initialize vector 

prob = zeros(51,2); 

%loop to return appropriate allocation of solar PVs for each state's 

%electricity portfolio 

for j=1:51, 

prob(j,1:2) = normcdf([-1000,zscores(j)]); 

prob2(j,1:2) = normcdf([-1000,zscores2(j)]); 

end 

prob 

prob2 

SolarAllocationByState = prob(1:51,2) - prob(1:51,1) 

SolarTransferFromRetail = prob2(1:51,2) - prob2(1:51,1) 

State 

Wind 

Percentile 

Retail 

Percentile 

State 

Wind 

Percentile 

Appendix 

Retail 

Percentile 

.Alabama 100.00 2.19 .Missouri 11.22 1.68 

.Alaska 7.51 4.59 .Montana 2.90 8.71 

.Arizona 100.00 45.85 .Nebraska 6.02 4.50 

.Arkansas 22.03 2.99 .Nevada 7.00 7.94 

.California 7.23 13.75 .New Hampshire 12.61 5.59 

.Colorado 5.11 2.79 .New Jersey 7.93 10.23 

.Connecticut 8.26 10.90 .New Mexico 23.79 6.13 

.Delaware 45.49 6.55 .New York 11.75 27.01 

.DC 13.26 6.39 .North Carolina 17.11 28.18 

.Florida 100.00 8.45 .North Dakota 5.32 2.76 

.Georgia 100.00 2.14 .Ohio 13.03 2.96 

.Hawaii 100.00 42.01 .Oklahoma 9.69 2.13 

.Idaho 7.47 2.49 .Oregon 24.56 2.33 

.Illinois 10.90 2.00 .Pennsylvania 29.95 3.39 

.Indiana 12.16 2.82 .Rhode Island 5.49 3.55 

.Iowa 5.09 2.93 .South Carolina 100.00 5.33 

.Kansas 8.42 1.72 .South Dakota 4.11 2.62 

.Kentucky 100.00 1.40 .Tennessee 10.08 21.50 

.Louisiana 100.00 30.51 .Texas 22.29 5.19 

.Maine 10.55 6.41 .Utah 7.27 3.03 

.Maryland 12.93 3.07 .Vermont 9.80 5.12 

.Massachusetts 6.64 6.46 .Virginia 9.16 2.51 

.Michigan 10.01 2.00 .Washington 24.82 4.84 

.Minnesota 34.04 2.54 .West Virginia 2.64 1.62 

.Mississippi 100.00 9.95 .Wisconsin 9.66 2.90 

.Wyoming 10.37 2.15 

130

Appendix 

A-7. Data from the Environmental Protection Agency used in Chapter 4 [86] 

GENERATION RESOURCE MIX (%) 

Other BioGeo- 

State Coal Oil Gas fossil mass Hydro Nuclear Wind Solar thermal Other 

AK 9.5 11.6 56.6 0.0 0.1 22.3 0.0 0.0 0.0 0.0 0.0 

AL 56.9 0.1 10.1 0.1 2.3 7.4 23.1 0.0 0.0 0.0 0.0 

AR 48.2 0.4 12.6 0.0 3.6 6.5 28.6 0.0 0.0 0.0 0.0 

AZ 39.6 0.0 28.5 0.0 0.1 6.4 25.4 0.0 0.0 0.0 0.0 

CA 1.0 1.3 46.7 1.1 2.9 19.9 18.1 2.1 0.3 6.5 0.1 

CO 71.7 0.0 24.1 0.0 0.1 2.6 0.0 1.6 0.0 0.0 0.0 

CT 11.9 9.4 26.4 2.3 2.1 1.4 46.4 0.0 0.0 0.0 0.0 

DC 0.0 100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 

DE 59.4 15.0 19.6 6.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 

FL 28.4 16.9 38.1 0.6 2.0 0.1 13.1 0.0 0.0 0.0 0.8 

GA 63.9 0.7 7.2 0.0 2.3 2.8 23.1 0.0 0.0 0.0 0.0 

HI 14.2 78.8 0.0 1.6 2.6 0.8 0.0 0.1 0.0 1.9 0.0 

IA 77.5 0.3 5.6 0.0 0.3 2.2 10.3 3.7 0.0 0.0 0.0 

ID 0.9 0.0 14.3 0.0 5.3 78.9 0.0 0.0 0.0 0.0 0.6 

IL 47.5 0.2 3.7 0.1 0.4 0.1 48.0 0.1 0.0 0.0 0.0 

IN 94.2 0.2 2.8 2.1 0.1 0.3 0.0 0.0 0.0 0.0 0.3 

KS 75.2 2.2 2.5 0.0 0.0 0.0 19.2 0.9 0.0 0.0 0.0 

KY 91.1 3.8 1.7 0.0 0.4 3.0 0.0 0.0 0.0 0.0 0.0 

LA 24.9 3.8 47.3 3.0 2.9 0.9 16.9 0.0 0.0 0.0 0.3 

MA 25.3 15.0 42.7 1.7 2.5 1.2 11.5 0.0 0.0 0.0 0.0 

MD 55.7 7.3 3.6 1.3 1.0 3.2 27.9 0.0 0.0 0.0 0.0 

ME 1.8 8.6 42.6 1.7 21.9 23.3 0.0 0.0 0.0 0.0 0.0 

MI 57.8 0.7 11.2 0.8 2.1 0.3 27.0 0.0 0.0 0.0 0.0 

MN 62.1 1.5 5.1 0.6 1.9 1.5 24.3 3.0 0.0 0.0 0.1 

MO 85.2 0.2 4.3 0.1 0.0 1.4 8.8 0.0 0.0 0.0 0.0 

MS 36.9 3.2 34.0 0.0 3.5 0.0 22.4 0.0 0.0 0.0 0.0 

MT 63.8 1.5 0.1 0.0 0.2 34.3 0.0 0.0 0.0 0.0 0.0 

NC 60.5 0.4 2.4 0.1 1.4 4.3 30.8 0.0 0.0 0.0 0.2 

ND 94.8 0.1 0.0 0.2 0.0 4.2 0.0 0.7 0.0 0.0 0.0 

NE 66.2 0.1 2.6 0.0 0.1 2.8 28.0 0.3 0.0 0.0 0.0 

NH 16.7 5.6 27.8 0.3 3.8 7.1 38.7 0.0 0.0 0.0 0.0 

NJ 19.1 1.8 25.1 1.0 1.4 0.0 51.6 0.0 0.0 0.0 0.1 

NM 85.2 0.1 11.9 0.0 0.0 0.5 0.0 2.3 0.0 0.0 0.0 

NV 44.9 0.1 47.4 0.3 0.0 4.2 0.0 0.0 0.0 3.1 0.0 

NY 13.8 16.2 22.5 0.7 1.2 16.9 28.7 0.1 0.0 0.0 0.0 

OH 87.2 0.9 1.7 0.2 0.2 0.3 9.4 0.0 0.0 0.0 0.0 

OK 51.7 0.1 43.0 0.0 0.4 3.5 0.0 1.2 0.0 0.0 0.0 

OR 7.0 0.1 27.0 0.1 1.8 62.5 0.0 1.5 0.0 0.0 0.0 

PA 55.4 2.3 5.0 0.6 0.9 0.7 35.0 0.1 0.0 0.0 0.0 

RI 0.0 0.9 99.0 0.0 0.0 0.1 0.0 0.0 0.0 0.0 0.0 

SC 38.7 0.7 5.3 0.1 1.7 1.7 51.8 0.0 0.0 0.0 0.0 

SD 46.0 0.3 4.2 0.0 0.0 47.2 0.0 2.4 0.0 0.0 0.0 

TN 61.0 0.2 0.5 0.0 0.6 9.0 28.7 0.0 0.0 0.0 0.0 

TX 37.3 0.6 49.3 1.3 0.3 0.3 9.6 1.1 0.0 0.0 0.2 

UT 94.3 0.1 3.1 0.0 0.0 2.1 0.0 0.0 0.0 0.5 0.0 

VA 44.9 5.4 10.4 0.7 3.1 0.1 35.4 0.0 0.0 0.0 0.0 

VT 0.0 0.2 0.0 0.0 7.2 21.2 71.2 0.2 0.0 0.0 0.0 

WA 10.3 0.1 8.4 0.4 1.6 70.7 8.1 0.5 0.0 0.0 0.0 

WI 67.3 1.1 10.5 0.1 1.9 2.8 16.0 0.1 0.0 0.0 0.1 

WV 97.7 0.2 0.3 0.1 0.0 1.5 0.0 0.2 0.0 0.0 0.0 

WY 95.1 0.1 0.7 0.6 0.0 1.8 0.0 1.6 0.0 0.0 0.1 

US 49.6 3.0 18.8 0.6 1.3 6.5 19.3 0.4 0.0 0.4 0.1 

131

Appendix 

A-8. Sample MATLAB code for graphing carbon tax, tax credit, and net 

savings to taxpayers in three dimensions (Chapter 5, single-period): 

CarbonTax = [0; 10; 20; 30; 40; 50; 60; 70; 80; 90; 100]; 

GovtITC = [0 10 20 30 40 50 60 70 80 90 100]; 

figure(1) 

surf(GovtITC,CarbonTax,CosttoTP10); 

xlabel('Federal Tax Credit (%)','fontsize',11,'fontweight','b'); 

ylabel('Carbon Tax ($/ton CO2)','fontsize',11,'fontweight','b'); 

zlabel('Savings (Cost) to Society ($)','fontsize',10,'fontweight','b'); 

title({'Net Savings (Cost) to Society with varying Carbon Tax and ITC';'10% 

Decline in Cost of Renewable Technology'},'fontsize',11,'fontweight','b'); 

This code was adapted for all six graphs. Matrices CosttoTP10, CosttoTP30, 

et cetera were produced by a macro in Excel. 

A-9. Sample MATLAB code for graphing solar price decline, wind price 

decline, and net savings to taxpayers in three dimensions (Chapter 5): 

SolarDecline = [0; 10; 20; 30; 40; 50; 60; 70; 80; 90; 100]; 

WindDecline = [0 10 20 30 40 50 60 70 80 90 100]; 

figure(1) 

surf(WindDecline,SolarDecline,Subsidy10); 

xlabel('Wind Tech Cost Decline (%)','fontsize',11,'fontweight','b'); 

ylabel('Solar Tech Cost Decline (%)','fontsize',11,'fontweight','b'); 

zlabel('Savings (Cost) to Society ($)','fontsize',10,'fontweight','b'); 

title({'Net Savings (Cost) to Society with varying Technological 

Improvements';'10% Investment Tax Credit, $0 Carbon 

Tax'},'fontsize',11,'fontweight','b'); 

This code was adapted for all six graphs. Matrices Subsidy10, Subsidy30, 

et cetera were produced by a macro in Excel. 

A-10. Sample MATLAB code for graphing carbon tax, tax credit, and net 

savings to taxpayers in three dimensions (Chapter 5, multi-period): 

CarbonTax = [0; 10; 20; 30; 40; 50; 60; 70; 80; 90; 100]; 

GovtITC = [0 10 20 30 40 50 60 70 80 90]; 

figure(1) 

surf(GovtITC,CarbonTax,PVsocietycost); 

xlabel('Federal Tax Credit (%)','fontsize',11,'fontweight','b'); 

ylabel('Carbon Tax ($/ton CO2)','fontsize',11,'fontweight','b'); 

zlabel('Present Value of Cost to Society 

($)','fontsize',10,'fontweight','b'); 

title({'Present Value of Cost to Society';'Gradual Decline in Tech 

Costs'},'fontsize',11,'fontweight','b'); 

Matrix PVsocietycost was produced by a macro in Excel. 

132

A-11. Renewable Portfolio Standards, by state – April 2010 [88] 

Renewable Portfolio Standards 

State RPS Year Note 

Arizona 15% 2025 

California 20% 2010 

California 33% 2020 

Colorado 30% 2020 IOUs 

Colorado 10% 2020 Electric co-ops, Municipal utilities 

Connecticut 27% 2020 

Delaware 20% 2020 

DC 20% 2020 

Florida 7.5% 2015 

Hawaii 40% 2030 

Illinois 25% 2025 

Iowa 105 MW 2010 Renewable generating capacity minimum 

Kansas 20% 2020 

Maine 40% 2017 

Maryland 20% 2022 

Massachusetts 15% 2020 

Michigan 10% 2015 

Minnesota 25% 2025 

Missouri 15% 2021 

Montana 15% 2015 

Nevada 25% 2025 

New Hampshire 23.8% 2025 

New Jersey 22.5% 2020 

New Mexico 20% 2020 IOUs 

New Mexico 10% 2020 Electric co-ops 

New York 29% 2015 

North Carolina 12.5% 2021 IOUs 

North Carolina 10% 2018 Electric co-ops, Municipal utilities 

North Dakota 10% 2015 

Ohio 25% 2025 

Oregon 25% 2025 

Pennsylvania 18% 2020 

Rhode Island 16% 2019 

South Dakota 10% 2015 

Texas 5,880 MW 2015 Renewable generating capacity minimum 

Texas 10,000 MW 2025 Renewable generating capacity minimum 

Utah 20% 2025 

Vermont 20% 2017 

Virginia 15% 2025 

Washington 15% 2020 

West Virginia 25% 2025 

Wisconsin 10% 2015 

Note: IOUs are Investor-Owned Utilities 

Appendix 

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List of Chapter Images: 

1. http://www.electriccarsite.co.uk/ 

2. http://www.sbc-‐technologies.com/sbc-‐technologies-‐renewableEnergy.php 

3. http://www.homeenergyadvisory.com/ 

4. http://peopleandearth.com/faq.html 

5. http://green.venturebeat.com/2009/10/26/a-‐movement-‐toward-‐locally-‐grown-‐ 

electricity/ 

6. http://www.aabenergy.co.uk/renewable-‐energy-‐studies.php 

142

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