ENERGY ECONOMICS PROBLEM SET
Question 1 - [price ceiling + competitive equilibrium vs. monopoly]:
Consider the global market for crude oil. Suppose there exists a single crude oil producer. This producer has a supply function for crude oil given by: P = 0.25Q.
World demand for crude oil is given by: P = 150 - 0.5Q.
Suppose a global government imposes a price ceiling on the market requiring the price for oil to be less than $70/barrel.
a. If the crude oil producer acts as price-taking firm, what is the firm's change in producer surplus as a result of the price ceiling (relative to no policy)?
b. If the crude oil producer acts as price-taking firm, what is the change in consumer surplus as a result of the price ceiling?
c. If the crude oil producer acts as price-taking firm, what is the change in total welfare as a result of the price ceiling?
d. If the crude oil producer acts as a monopolist, what is the firm's change in producer surplus as a result of the price ceiling?
e. If the crude oil producer acts as a monopolist, what is the change in consumer surplus as a result of the price ceiling?
f. If the crude oil producer acts a monopolist, what is the change in total welfare as a result of the price ceiling?
g. Compare your results from parts c and f. What is the implications for the economy if the government incorrectly assumes a firm is a monopolist when it is actually a price taking firm?
Suppose instead the global government imposes a price ceiling on the market requiring the price for oil to be less than $40/barrel.
h. If the crude oil producer acts as price-taking firm, what is the firm's change in producer surplus as a result of the price ceiling?
i. If the crude oil producer acts as price-taking firm, what is the change in consumer surplus as a result of the price ceiling?
j. If the crude oil producer acts as price-taking firm, what is the change in total welfare as a result of the price ceiling?
k. If the crude oil producer acts as a monopolist, what is the firm's change in producer surplus as a result of the price ceiling?
l. If the crude oil producer acts as a monopolist, what is the change in consumer surplus as a result of the price ceiling?
m. If the crude oil producer acts as a monopolist, what is the change in total welfare as a result of the price ceiling?
n. Compare your results from parts g and m. What is the implications for the economy if the government incorrectly assumes a firm is a monopolist when it is actually a price taking firm?
o. Did your answer to part m differ from your answer to part g? If so, what does this mean for how the government should set a price ceiling if the government does not really know whether a firm is acting as a monopolist?
Question 2 - [subsidy1 + dominant firm]:
Suppose the demand for (blended) fuel F in the U.S. is given by the following demand function: PF = 200 - 4F.
Fuel retailers in the U.S. are indifferent between using corn derived ethanol, E and crude oil derived gasoline from OPEC, G in the fuel they sell to consumers, F. To produce blended fuel, F assume ethanol is splash blended in tanker trucks at no additional cost and there are no limits to how much ethanol can be blended into fuel. Thus fuel retailers in the U.S. are willing to supply fuel according to:
F = E + G.
Assume that fuel retailers are the only demanders for ethanol and gasoline.
Ethanol supply in the U.S. is given by: PE = 3.45 + E.
Gasoline supplied by OPEC is given by: PG = 0.25 + 0.35G.
For simplicity suppose fuel, ethanol, and gasoline are all denominated in the above in energy equivalent gallons of gasoline (hereafter, simply "gallons").
Suppose that demand reflects the behavior of price-taking consumers and that U.S. ethanol producers take prices as given when making production decisions, and thus also act as price-takers. Unlike in problem set 1, now suppose that OPEC acts as a dominant firm supplier of gasoline.
Relative to the competitive market equilibrium:
a. What is the change in producer surplus to U.S. ethanol producers when OPEC acts as a dominant firm?
b. What is the change in U.S. fuel demander's consumer surplus when OPEC acts as a dominant firm?
c. What is the change in total welfare to the U.S. when OPEC acts as a dominant firm?
d. What is the change in producer surplus to OPEC producers when OPEC acts as a dominant firm?
e. What is the change in OPEC plus U.S. welfare when OPEC acts as a dominant firm?
Now suppose that corn growers in Iowa convince the government to subsidize ethanol by $3.00/gallon, claiming it is good for the U.S. Relative to the no subsidy, dominant firm monopoly equilibrium:
f. What is the change in producer surplus to U.S. ethanol producers due to the subsidy?
g. What is the change in U.S. fuel demander's consumer surplus due to the subsidy?
h. What is the final bill to U.S. taxpayers for the subsidy?
i. What is the change in total welfare to the U.S. due to the subsidy?
j. What is the change in producer surplus to OPEC producers due to the subsidy?
k. What is the change in OPEC plus U.S. welfare due to the subsidy?
l. From the perspective of the U.S., is the subsidy good for the U.S.?
Question 3 - [multi-plant monopoly vs. dominant firm]:
Suppose you are running a firm with a marginal cost function given by: P = X + 0.5Q.
Price-taking consumers have a demand function given by: P = 4000 - 2Q.
For each X from 1500 to 3500:
a. Suppose the firm above is a dominant firm, facing a price-taking fringe supply function given by: P = Q + 3000. Compute the implied dominant firm monopoly equilibrium. Using the equilibrium price and quantity calculate point estimates of the elasticity of supply (ηS) and demand (ηD). Graph the Lerner Index under dominant firm (on x-axis) against the ratio of elasticities (times minus one), - ηD/ηS (on y-axis). Explain the curve.
b. Suppose instead the firm above is a multi-plant monopolist, with a supply function for a second plant given by: P = Q + 3000 (the same as in a!). Compute the implied multi-plant monopoly equilibrium. Using the equilibrium price and quantity calculate point estimates of the elasticity of supply (ηS) and demand (ηD). To the graph from a, add a graph of Lerner index under multi-plant monopoly (on x-axis) against the ratio of elasticities (times minus one), - ηD/ηS (on y-axis). Explain the curve.
c. Compare the two curves and explain how they relate to the resulting elasticities.
d. Which model best explains OPEC's behavior in crude oil markets? Given this, for which range of X do you think best explains OPEC's behavior in crude oil markets? Carefully explain your reasoning.