Exercise 1: Consider the perfectly competitive market for gasoline. The aggregate demand for gasoline is Q = 100 – p, while the aggregate supply is Q = 3p 1. Calculate the equilibrium price and quantity. At this equilibrium, compute the consumer surplus, producer surplus and total surplus.
2. Suppose now that the government is concerned because many gas stations are going out of business, so it decides to set a minimum price of p = 30 to help them. What will be the new equilibrium price and quantity with this intervention? Compute the consumer surplus and producer surplus; who gains and loses from this regulation? How is the total surplus affected? Briefly explain the intuition.
3. Suppose now that instead of regulating prices, the government decides it is better to help gas stations by setting quantity regulations. In particular, the government sets a quota of q = 70 (this means that aggregate quantity supplied can’t exceed 70 units). What will be the new equilibrium price and quantity with this regulation? How does it compare to the results obtained with the minimum price?
4. Suppose now that because of a conflict in the Middle East prices of oil increase, increasing the cost of supplying each unit of gas by $x. Find the minimum value of x such that the regulations discussed above become irrelevant to determine the market equilibrium.
5. From this question onward assume that instead of perfect competition, there is a monopolist in this market. Its cost curve is C = Q2/6. Assume it sets a uniform price. What price and quantity does the monopolist set? Compute the consumer surplus, producer surplus, total surplus and the deadweight loss in this case. Compare your results to the perfectly competitive case and explain.
6. Suppose that the government would like to help the monopolist by setting a minimum price. What price should it be?
7. Now suppose that the government wants to set a price ceiling in order to maximize welfare (total surplus). What price should it set and what would be the resulting total surplus?
8. If the monopolist were able to practice perfect price discrimination, what quantity would it produce? Compute the consumer surplus, producer surplus, total surplus and the deadweight loss in this case.