Homework #3 (due November 4th, 2011) - EconS 330

Homework #3 (due November 4th, 2011) - EconS 330
Instructor: Ana Espinola, Hulbert 111C, anaespinola@wsu.edu
1. During a worldwide recession in 1983, the oil cartel began to lower prices. Why would a
recession make the cartel more vulnerable to price cutting How would the reduced demand be
shared between the competitive fringe and the cartel members in the absence of this price
cutting (8 Points)
2. If the current tension over Iran’s nuclear program leads to war, and this causes higher oil prices,
what would you expect to happen to the demand curve for SUVs For mountain bikes For milk
Illustrate graphically. Explain your reasoning. (10 Points)
3. Regulation of the natural gas industry in the United States has historically been a tumultuous
ride, resulting in dramatic changes in the industry over the past 30 or more years. In November
of 1978, at the peak of the natural gas supply shortages, Congress enacted legislation known as
the Natural Gas Policy Act (NGPA), as part of broader legislation known as the National Energy
Act (NEA). Realizing that those price controls that had been put in place to protect consumers
from potential monopoly pricing had now come full circle to hurt consumers in the form of
natural gas shortages, the federal government sought through the NGPA to revise the federal
regulation of the sale of natural gas. Assume that the demand and supply for natural gas are
P d =50-.85q and P s =2+.15q respectively. Before the NGPA was enacted the government had a
price control policy equal to $3 per barrel. Analyze how this price control affects the consumer
surplus (Use a graph to represent your results). Finally, assume that the firm is able to adjust its
cost structure and the new supply is P * s=0.05426q. Identify the new quantity demanded and
consumer surplus. Discuss the effects of the price control policy on the Consumer Surplus in the
short and long run when the firm is able to adjust its cost structure. (20 Points)
4. Suppose that the long-envisaged “paperless office” finally comes to pass, at least to some extent
that use of information technology means that a large number of businesses and government
agencies can cut down drastically on their paper consumption, and that this happens in fairly
short order.
a) How would this affect the quantity of recycled paper used, and the recycling ratio for paper
You can use the standard assumptions used in the course for modeling the use of recycled vs.
virgin materials. Illustrate your answer graphically. (8 Points)
b) If a sharp reduction in the use of paper leads to a fall in the value of wood, what impact(s)
would this have on the decision about the optimal rotation period for forests Why Illustrate
graphically. Your answer to this question does not need to be linked to your answer in (a). (6
Points)
5. Assume that the U.S. oil demand is represented by the following demand function:
and the Supply curve (which represents the oil producers) is:

where P d and q d are price and quantity demanded respectively. Notice that P s is the price
charged by the suppliers and q s is the quantity supplied.
a) Find the optimal quantity and price in the oil market. (5 Points)
b) Assume that the oil world price is $23. Find the quantity produced by U.S. firms and quantity
demanded by U.S. consumers. (5 Points)
c) How many units U.S. will import (5 Points)
d) Assume that the vulnerability premium is equal to $10. Find the new quantity produced by U.S.
firms and new quantity demanded by U.S. consumers. (5 Points)
e) Identified the new quantity of oil imported from foreign countries. (5 Points)
f) Draw a graph and calculate the size of efficiency loss. (5 Points)
g) Determine the price elasticity of demand when the new price is $23. Is the demand elastic or
inelastic (8Points)
6. Suppose a product can be produced using virgin ore at a marginal cost given by MC 1 =0.7q 1 and
with recycled materials at a marginal cost given by MC 2 = 10 + 0.2q 2 .
a) If the inverse demand curve were given by P = 15 – 0.4(q 1 + q 2 ), how many units of the product
would be produced with virgin ore and how many units with recycled materials (4 Points)
b) If the inverse demand curve were P = 30 – 0.4( q1 + q2 ), what would your answer be (4 Points)
c) Illustrate your answer on a clearly labeled graph (2 Points)
Solutions
Exercise #1
During a recession period people reduce their consumption in fossil fuels. Since the unemployment
rate is high, many people can see their income dramatically reduced and as a consequence it has a
negative impact on fuel demand. Therefore, the cartel has to lower the oil price. In the absence of
this price cutting, it is more likely that the cartel (OPEC) captures a greater percentage of the
demand. Notice that currently the cartel produces more than two-third of the world’s oil.
Exercise #2
The case of SUV’s and oil, we know that this two goods are complements. Therefore, if the price of oil
increases the quantity demanded of SUVs decreases. Graphically:

P SUV
S suv
P 0
P 1
D suv
D* suv
Q
Q Suv
1
Q 0
Therefore, the price of SUVs decreases from P 0 to P 1 and the quantity demanded decreases from Q 0 to
Q 1
In the case of SUVs and mountain bikes they are substitute goods. Therefore, when the price of oil
increases the quantity demanded of mountain bikes increases (people prefer to ride the bicycle- and
consume less fossil fuel- than use the car). Graphically:
P Mountain
S Mountain bike
P 1
P 0
D* Mountain Bike
D Mountain Bike
Q Mountain Bike
Q 0 Q 1
Therefore, the price of Mountain Bikes rise from P 0 to P 1 and the quantity demanded increases from Q 0
to Q 1

Finally, Milk is an inferior good (or a good of first necessity), which means that people will not stop
consuming milk in order to consume more oil. However, an increase in the oil price will increase the
price of milk (for instance, it is more expensive to transport milk from the farm to the supermarket.
Therefore, it increases the production costs)
P Milk
S* Milk
S Milk
P 1
P 0
D milk
Q 0 Q 1
Q Milk
An increase in Milk price will slightly reduce the quantity demanded (since it is an inferior good).
Exercise #3
Assume that the demand and supply for natural gas are P d =50-.85q and P s =2+.15q respectively.
Before the NGPA was enacted the government had a price control policy equal to $3 per barrel.
Analyze how this price control affects the consumer surplus (Use a graph to represent your results).
Equilibrium without Price Control:
Supply=Demand
50-.85q=2+.15q
q=48 and P=50-.85*48=9.2
Equilibrium with Price Control:
2+.15q=3
Quantity supplied is q S =6.67 and the price consumers are willing to pay is P=50-0.85x6.67= 44.33.
Note that the quantity demanded when P=3 is q D =55.29. Therefore there is a shortage of (55.29-
6.67) 48.62 barrels.

Graphically:
P Gas
50
44.33
S
9.2
3
2
D
Price
Control
6.67
48
55.29
Q Gas
CS (without PC): (50-9.2)x48/2=979.2
CS(with PC): (50-44.33)*6.67/2 + (44.33-3)*6.67=18.91+275.67=294.58
Hence a price control reduces the consumer surplus.
Finally, assume that the firm is able to adjust its cost structure and the new supply is P * s=0.0542q.
Identify the new quantity demanded and consumer surplus. Discuss the effects of the price control
policy on the Consumer Surplus in the short and long run when the firm is able to adjust its cost
structure.
New Equilibrium with Price Control:
0.05426q=3
q=55.29
Quantity supplied is q S =55.35 and the price consumers are willing to pay is P=3. Therefore there is
no shortage when the firm adjusts its cost structure.

Graphically:
P Gas
50
44.33
S 0
9.2
S * 0
3
2
D
Price
Control
6.67
48
55.29
Q Gas
CS (without PC): (50-9.2)x48/2=979.2
CS(with PC and S 0 ): (50-43.33)*6.67/2 + (44.33-3)*6.67 =22.24 + 275.67=297.91
CS(with PC and S * 0): (50-3)*55.29/2 =1299.315
Note that consumer surplus is higher when the firm adjust is production process and is able to
produced the entire quantity demanded when the price is $3.
In the short run consumers will be better-off when the firm adjusts its cost structure. However,
natural gas is a Depletable resource and every period will be more expensive to extract this
Depletable resource, hence the supply curve will shift upward, as a consequence the CS decreases
on the long run.
Exercise #4
a)
MC
MC VO
MC RM
Demand 0
VO RM
Q 1 Q 1
RM VO
Q 0 Q 0
Demand 1
Quantity

If the quantity demanded decreases it means that firms will use more virgin materials than
recyclable materials (see graph). Note that Q VO 1 Q 0
b)
The decrease in demand reduces prices and as a consequence the value of wood. We know that the
decision to harvest the forest depends on the maximum net benefit. In this specific case, we assume
that planting and harvesting cost do not change. In addition, the rate of growth of the forest is the
same. Therefore a change in prices increases the optimal rotation period for forests.
Exercise #5
a. In order to find the optimal quantity you have to equalize demand and supply:
and
b. Assume that the world price is $23. The quantity produced by U.S. firms is obtained from the
supply curve:
, we have to analyze what is the quantity that U.S. firms are willing to produce when
price is $15. Therefore:
Solving by q s we have that: =22.86
The quantity demanded by U.S. consumers is obtained from the demand function:
, we have to analyze what is the quantity that U.S. consumers are willing to consume
when price is $15. Therefore:
Solving by q d we have that: =148
c. U.S. will import: q d – q s =148 –22.86 = 125.14 barrels of oil
d. Vulnerability premium is equal to $10. Therefore, the new price will be:

P(new) = World price + Vulnerability premium=23 + 10 = 33
Therefore the new quantity produced by the domestic firms when price is $33 is:
And the quantity demanded by domestic consumers is:
e. U.S. will import (new price $33): 108 – 51.43 =56.57 barrels of oil
f.
P oil
60
S d
S f1
41.25
33
23
S f0
10
D d
22.8
6
51.43
75
108
148
Q oil
The size of efficiency loss is:
g. The price elasticity of demand:
therefore the demand is relatively elastic .

Question6 (10 Points)
Solution
a) 0.7q 1 = 15 – 0.4q 1
1.1 q 1 =15
q 1 =13.63 (2 Points)
10 + 0.2q 2 = 15 – 0.4q 2
0.6q 2 =5
q 2 =8.3 (2 Points)
b) 0.7q 1 = 30 – 0.4q 1
1.1q 1 =15
q 1 =27.27 (2 Points)
10 + 0.2q 2 = 30 – 0.4q 2
0.6q 2 =20
q 2 =33.33 (2 Points)
c) (2 Points)
Price
30
15
MC 1
MC 2
D*
8.33
13.63
27.27
33.33
D
Q Recycled/
Virgin Materials