Assignment
1. Price ceilings and monopoly. Suppose the market for hot dogs in Santa Cruz is monopolized by a single firm, Top Dog. Top Dog faces the hot dog inverse demand curve P(q) = 1.00 - 0.01Q, where Q is the number of hot dogs sold. The marginal cost of hot dogs increases with the number of dogs produced, according to MC = 0.10 + 0.01Q.
(a) What is Top Dog's profit maximizing price and quantity sold? Indicate this price and quantity on a graph that includes the demand curve, the marginal revenue curve, and the marginal cost curve. What would the price and quantity be that maximizes the sum of producer and consumer surplus (i.e., the outcome that results from perfect competition)? What is the deadweight loss of monopoly in the Santa Cruz hot dog industry?
(b) Suppose the Santa Cruz city council, appalled at the high hot dog prices in town, sets a price ceiling of $0.60 per dog. Re-draw your graph from part (a), including the price cap and the new marginal revenue curve. Think carefully about how you draw this curve- what is marginal revenue when the price cap is binding? Indicate on the graph the new price and quantity sold of hot dogs in Santa Cruz when the price ceiling is in effect.
(c) Price ceilings often cause producers to produce less than the optimal amount, resulting in a shortage and economic inefficiency. That intuition applies well to settings of perfect competition. Here, however, we have monopoly, and you should have found in part (b) that the price ceiling caused production to increase. Moreover, there is no shortage. Why is this outcome possible in monopoly?
(d) Suppose you run the city council, and want to set the price ceiling so as to maximize the sum of consumer and producer surplus. Where do you set the price ceiling? How does your answer relate to the perfectly competitive price from part (a)?
(e) With monopoly, it is still possible to set a price ceiling that results in a shortage (i.e. the monopolist produces a quantity that is lower than demand at the price ceiling). In our example, what levels of the price ceiling would create a shortage? Show an example using a graph.
2. Cournot equilibrium. Consider the market for snow blowers in Ann Arbor. The inverse demand curve for snow blowers is given by P = 800 - 4Q. There are two firms that make snow blowers, firm 1 and firm 2. Both firms have a marginal cost of 80. The firms compete by simultaneously choosing their production quantities, i.e., Cournot.
(a) Derive the Cournot Nash equilibrium for this game. How many snow blowers will each firm produce, what is the price of a snow blower, and what are the firms' profits?
(b) What is the monopoly output in this market? That is, if only 1 firm were in the market, how many snow blowers would it produce? In the Cournot equilibrium, why isn't the output of each firm just one-half of the monopoly output?
(c) Now suppose that firm 1 has a cost advantage and can produce snow blowers at a marginal cost of 50. Firm 2 still has a marginal cost of 80. What are the quantity produced and profit for each firm now?
3. Cournot merger analysis. Suppose the low-cost firm wants to purchase the high-cost firm to become a monopoly with a marginal cost equal to 50. The Department of Justice (DOJ), however, is skeptical of this merger and fears that the monopoly will harm consumers. The low-cost firm asserts, however, that because it will be operating all production at a low cost, its price will be low and consumers will benefit. The DOJ hires you as a consultant to forecast the effect of the proposed merger. If the merger is approved, what price and quantity will be set by the new monopoly? Will consumers be helped or harmed by the merger? If the DOJ cares only about consumer surplus, should the merger be approved?
4. Homogenous product Bertrand. Suppose that the demand for marbles is given by Q = 80 - 5P, where Q is measured in bags of marbles. There are two firms that supply the market, and the firms produce identical marbles (i.e., they are homogenous products). Firm 1 has a constant marginal cost of $10.00/bag, while firm 2 has a constant marginal cost of $5.00/bag.
The two firms compete in price. In Nash Equilibrium, what prices will the two firms set? How many bags of marbles will each firm sell, and what will be their profits? Assume that prices must be in whole cents.
5. Homogenous product Bertrand with 3 firms. Now suppose that there are three firms in the market, all producing identical marbles. Firms 1 and 2 are as in question 1 above, and firm 3 has a marginal cost of $5.00/bag. Now what prices will the firms set in equilibrium, and how many bags of marbles will each firm sell?
6. Differentiated product Bertrand. Suppose that firm Y produces yellow marbles and that firm W produces white marbles. Further suppose that consumers' tastes are heterogeneous-some prefer yellow marbles while others prefer white ones. Firm-specific demands are given by:
Qy = 90 - 3py + pw
Qw = 90 - 3pw + py
The subscripts y and w refer to yellow and white marbles, respectively.
(a) Suppose both firms have a marginal cost of $15/bag. What are the price and quantity sold by both firms in the differentiated Nash-Bertrand equilibrium?
(b) Now suppose that firm W has a marginal cost of only $10. What are the new prices and quantities sold by both firms?
(c) If you are the owner of a firm that is at a comparative cost disadvantage and compete in a Bertrand game, would you rather be in an industry with differentiated products or an industry with homogenous products? Why?