Homework #1 (due September 14th, 2012) EconS 330

Homework #1 (due September 14th, 2012) EconS 330
Instructor: Ana Espinola, Hulbert 111C, anaespinola@wsu.edu
Office hours: Tuesdays 9.00 – 10.00am, or by appointment.
Question #1 (15 Points)
A coral reef area will either be protected or mined. A set of costs and benefits is given for
a 10-year period. Find the Net Present Value for an interest rate of 5% and 10%.
Problem Set 1. Discount rates
Project 1. Pullman Marine Park
Years
0 1 2 3 4 5
Costs (thousands of $)
Construction 1250
Recurring costs 150 200 150 100 100
Foregone recreation 50 50 50 50 50 50
Benefits
Increased tourist revenue 500 700 800 900 900 900
Net -800 500 550 700 750 750
NPV @ 5% [1984.41] -800 476.19 498.87 604.69 617.03 587.64
NPV @ 10% [1612.96] -800 454.55 454.55 525.92 512.26 465.69
Question #2 (15 Points)
Let’s assume that we are interested in the preservation of a river. Therefore, static efficiency requires us
to ask: What is the efficient number of miles preserved Use the graph to answer this question
Price
Net Benefit when q=27.5
700
Marginal
Cost
600
Marginal Cost = Demand
550
500
Demand
0
20.6 27.5 31.55
55
Quantity
1

Find the net benefit when (Please show your calculations: if you do the problems by hand or calculator,
show your intermediate formulas):
a. Quantity is 27.5
b. Quantity is 31.55
c. Quantity is 20.6
Question #3 (15 Points)
Are the following statements true or false Explain why
a. If your consumption of cigarettes produces negative externalities for your partner (which you
ignore), then you are consuming more cigarettes than is Pareto efficient.
TRUE. With negative externalities the market equilibrium quantity in general exceeds the Paretoefficient
level.
b. It is generally efficient to set an emission standard allowing zero pollution
FALSE. If some production process generates a nonzero level of pollution, but the benefits exceed
the cost. Then this production is socially optimal and should be allowed. Hence the emission
standards should allow for a certain nonzero pollution level.
c. A tax on cigarettes induces the market for cigarettes to perform more efficiently
TRUE. Smoking generates negative externalities, and the market outcome is efficient.
d. A ban on smoking is necessarily efficient.
FALSE. A ban on smoking reduces the utility of the smokers and the profits of the cigarette
makers. The utility of nonsmokers and the profits of the producers of substitute goods (chewing
tobacco) will increase. The effect on aggregate welfare function is the sum of these offsetting
effects and may be positive or negative.
2

Question #4 (20 Points)
One convenient way to express the TWP relationship between price and quantity is to use the inverse
demand function. In an inverse demand function, the price consumers are willing to pay is expressed as
a function of the quantity available for sale.
Suppose the inverse demand function of a product is P= 100 - .5q, and the marginal cost of producing it
is MC = q+10, where P is the price of the good and q is the quantity demanded and/or supplied.
a. Draw a graph showing the demand curve and the marginal cost curve.
b. How much would be supplied in a static efficient allocation (Illustrate the quantity on your
graph)
c. What would be the magnitude of the net benefits (Illustrate the net benefits on your graph)
a. Graph
Price
100
Marginal
Cost
Marginal Cost = Demand
70
10
Demand
60
200
Quantity
b. The static efficient allocation is when MC=D
P=MC
100 – .5q = q + 10
-1.5q = -90
q = 60
c. The magnitude of the benefit is:
3

Question #5 (35 Points)
Consider a variation of the chemical manufacturing example. Suppose the inverse demand curve for the
chemical (which is also a marginal benefit curve) is Pd = 24 – Q, where Q is the quantity consumed (in
millions of tons per year) when the price consumer pay is Pd (in dollars per ton).
The inverse supply curve (also the marginal private cost curve) is MPC = 2 + Q, where MPC is the
marginal private cost when the industry produces Q.
The industry emits one unit of pollutant for each ton of chemical it produces. As long as there are fewer
than 2 million units of pollutant emitted each year, the external cost is zero. But when the pollutant
exceeds 2 million units, the marginal cost is positive. The marginal external cost is:
MEC =
where MEC is marginal external cost in dollars per unit of pollutant when Q units of pollutant are
released.
Also supposed the government wants to use an emissions fee of $6 per unit of emissions to induce the
market to produce the economically efficient amount of chemical.
a. Draw a graph showing the demand curve, the MPC and the MEC.
b. Construct a table comparing the equilibria with and without the emission fee.
c. Explain why the following sum is the same with and without the fee: consumers surplus +private
producer surplus-external cost + government receipts from the fee + deadweight loss
Price
MSC
24
22
=(9x3)/2
MPC
MEC
16
TAX
13
10
9
6
4
2
Demand
2
8
11
24
Quantity
-2
4

) Without Tax Tax
CS (24-13)X11/2=60.5 (24-16)X8/2=32
PS (13-2)X11/2=60.5 (10-2)X8/2=32
CE (11-2)X9/2=40.5 (8-2)X6/2=18
GTR - (16-10)X8=48
DWL 13.5 0
P = MPC
24 – Q = 2 +Q
-2Q = -22
Q = 11
If Q = 11 then the price (using demand curve) is: P= 24 – 11 = 13
The social Optimal quantity is : P = MSC. Therefore we need to identify the MSC curve:
MSC = MEC + MPC
= [2 + Q] + [-2+Q]
MSC = 2Q
24 – Q = 2Q
-3Q = -24
Q = 8
Substituting Q=8 into the demand function we have that P=16 (24-8)
Finally, when the quantity produced is 8 then the MPC is (substituting 8 into MPC equation):
MPC = 2 + 8 = 10
Notice that DWL (without taxes): (9X3)/2=13.5
c) consumers surplus +private producer surplus-external cost + government receipts from the fee + deadweight
loss.
Case without Tax: 60.5 + 60.5 -40.50 +0 +13.5=94
Case with Tax: 32 + 32 - 18 + 48 =94
These results can be explained by the DWL and the fact that the government internalizes the negative externalities
through the emission fee. The emission fee eliminates the DWL, reduces the cost of externalities and increases the
government revenues.
Notation:
CS = Consumer Surplus, PS = Producer surplus, MPC= Marginal Private Cost, MSC= Marginal Social Cost, CE= Cost of Externality, GTR =
Government Revenue from Taxes, NSB= Net Social Benefit, DWL= Deadweight lost, MEC= Marginal External Cost
5