Problem 1- Consider an industry with demand q = 120 - 3p and supply q = 2p - 10. Suppose that production is polluting the environment and that the marginal social cost of production is given by MSC(q) = ½q2.
(a) What is the level of production in the market equilibrium?
(b) What is the socially optimal level of production?
(c) Determine the Pigou tax that achieves the social optimum.
Problem 2 - Different divisions within a firm frequently compete for a common resource. Suppose that divisions 1 and 2 of a given firm share a common facility F. Let yi be the service level used by division i = 1; 2). Division i's gross benefit in terms of improved divisional earnings is given by yi = 0.25yi2 - 0.1(y1 + y2).
(a) What are the equilibrium levels of yi if the various divisions act separately?
(b) What are the optimal levels of yi from an overall firm point of view?
(c) Explain the difference between the results in (a) and (b).
(d) How can equilibrium and optimality be reconciled?
Problem 3 - Consider a monopolist with demand D = 120 - 2p and marginal cost MC = 40. Determine profit, consumer surplus, and social welfare in the following two cases:
(a) single-price monopolist;
(b) perfect price discrimination.
Problem 4 - Sal's satellite company broadcasts TV to subscribers in LA and NY. The demand functions are given by
QNY = 50 - 1/3PNY
QLA = 80 - 2/3PLA
where Q is in thousands of subscriptions per year and P is the subscription price per year. The cost of providing Q units of service is given by TC =1,000 + 30Q where Q = QNY + QLA.
(a) What are the profit-maximizing prices and quantities for the NY and LA markets?
(b) As a consequence of a new satellite that the Pentagon developed, subscribers in LA are now able to get the NY broadcast and vice versa, so Sal can charge only a single price. What price should he charge?
(c) In which situation is Sal better off? In terms of consumers' surplus, which situation do people in LA prefer? What about people in NY? Why?
Problem 5 - A market consists of two population segments, A and B. An individual in segment A has demand for your product q = 50 - p. An individual in segment B has demand for your product q = 120 - 2p. Segment A has 1000 people in it. Segment B has 1200 people in it. Total cost of producing q units is C = 5000 + 20q.
(a) What is total market demand for your product?
(b) Assume that you must charge the same price to both markets. What is the profit-maximizing price? What are your profits?
(c) Imagine noe that members of segment A all wear a scarlet "A" on their shirts or blouses and that you cna legally charge different prices to these people. What price would you charge to the scarlet "A" people? What price would you charge to those without the scarlet "A"? What are your profits now?