1. In a particular competitive market, the sellers have private marginal cost (PMC) equal to 2.5 at every output level. The demand curve has the equation P = 52.5 − (5Q/2), where Q ≤ 21 is the quantity bought at price P ≤ 52.5.
a. Graph the demand curve in this market for prices in the range 0 ≤ P ≤ 15.
b. In the graph of part a, plot the supply curve in this market for prices 0 ≤ P ≤ 15 and quantities of output in the range 0 ≤ Q ≤ 25. Explain why the supply curve looks the way you drew it.
c. Find the competitive equilibrium price Pc and quantity Qc, explaining all your steps. Show Pc and Qc in the graph.
d. Explain how we can tell that the competitive equilibrium quantity maximizes total surplus in this market if marginal damage from trading of the output equals 0 at every output level.
e. The supply and demand curves in your graph of part a seem to match which one of the following markets most closely? (e1) the US market for fresh sweet corn during a harvest month; (e2) the world market for gasoline during a summer month; (e3) the market for gasoline in New York state during a particular summer month; (e4) the market for gasoline sold by a single gas station during a summer month. Justify your answer.
In the remaining parts of this problem, assume that marginal damage from trade of the output in this market is MD(Q) = 0 for 0 ≤ Q ≤ 11 and is MD(Q) = 2Q − 22 for Q > 11.
f. In the market you picked in part e, what might be the source or sources of this marginal damage?
g. Graph the new social marginal cost (SMC) curve in your graph of part a. Find the new efficient output level Qe that maximizes total surplus in this market. Show your work in computing Qe and label it in your graph.
h. Find a unit tax T charged to sellers in this market that makes the competitive equilibrium output quantity with tax Qe. Find the market price when this tax is charged and show it in your graph, labeled PT .
i. Suppose that instead of charging a tax, a gov requires sellers in this market to buy a permit for each unit of output they sell. How many permits should the gov make available for sale in order to have Qe, the efficient number of units, sold? When the gov sells this many permits, what is the new equilibrium price of output that is charged to buyers in this market? What is the price of a permit, assuming the permits are sold in a competitive market? Explain your answers.
j. What is the effect of the permit requirement in part i on the competitive equilibrium total profit of the sellers in this market? Explain.
k. Suppose that the gov has a fairly good estimate of the marginal damage (MD) curve in this market, but cannot tell exactly where the demand curve is, though they do know how many units are sold before they intervene in the market. Which policy (tax or permit requirement) is more likely to make output in the market closer to the efficient level Qe? Explain.