Problem Set 9 (75 points) 1. A student argues, "If a monopolist finds a way of producing a good at lower cost, he will not lower his price. Because he is a monopolist, he will keep the price and the quantity the same and just increase his profit." Do you agree? Use a graph to illustrate your answer. The argument is incorrect. As the graph shows, a reduction in marginal cost will cause a monopolist to reduce his price. 2. Economist Harvey Leibenstein argued that the loss of economic efficiency in industries that are not perfectly competitive has been understated. He argued that when competition is weak, firms are under less pressure to adopt the best techniques or to hold down their costs. He referred to this effect as "x-inefficiency." If x-inefficiency causes a firm's marginal costs to rise, show that the deadweight loss in Figure 10.10 understates the true deadweight loss caused by a monopoly. If the monopoly were more efficient, its marginal costs would fall from MC 1 to MC 2 in the figure. As the figure shows, if a monopoly has higher costs (MC 1 ) because it does not face competition, then the true deadweight loss is increased. The darker shaded area shows the original deadweight loss as it was in Figure 10.10. The lighter shaded area shows the additional deadweight loss from taking into account x-inefficiency that is, from the firm not producing more efficiently, at quantity Q CX.
3. Use the following graph for a monopoly to answer the questions. a. What quantity will the monopoly produce, and what price will the monopoly charge?
To maximize profits, the monopoly will produce the quantity where marginal revenue equals marginal cost. So, the monopoly will produce 20 units and charge a price of $30. b. Suppose the government decides to regulate this monopoly and imposes a price ceiling of $18 (in other words, the monopoly can charge less than $18 but can't charge more). Now what quantity will the monopoly produce, and what price will the monopoly charge? Its marginal revenue curve is now a flat line at $18, running from the vertical axis to the demand curve, so the monopoly will produce 33 units and charge a price of $18. c. Will every consumer who is willing to pay this price be able to buy the product? Briefly explain. The quantity demanded at a price of $18 is 40, but the quantity supplied is only 33, so there will be a shortage of 7 units, and some consumers will not be able to buy the product. 4. John Gardner is the city planner in a medium-sized southeastern city. The city is considering a proposal to award an exclusive contract to Clear Vision, Inc., a cable television carrier. Mr. Gardner has discovered that an economic planner hired a year before has generated the demand, marginal revenue, total cost and marginal cost functions given below: P = 28-0.0008Q MR = 28-0.0016Q TC = 120,000 + 0.00062 MC = 0.0012Q, where Q = the number of cable subscribers and P = the price of basic monthly cable service. Conditions change very slowly in the community so that Mr. Gardner considers the cost and demand functions to be reasonably valid for present conditions. Mr. Gardner knows relatively little economics and has hired you to answer the questions listed below. a. What price and quantity would be expected if the firm is allowed to operate completely unregulated? Without regulation we would expect the firm to behave as a monopolist, equating MR and MC. 28-0.0016Q = 0.0012Q Q = 10,000 P = 28-0.0008(10,000) P = $20 b. Mr. Gardner has asked you to recommend a price and quantity that would be socially efficient. Recommend a price and quantity to Mr. Gardner using economic theory to justify your answer. Economic theory suggests that price should be equal to MC to achieve allocative efficiency. P = 28-0.0008Q MC = 0.0012Q 28-0.0008Q = 0.0012Q 28 = 0.002Q Q = 14,000 P = 28-0.0008(14,000) P = 28-11.20 P = 16.80 c. Compare the economic efficiency implications of (a) and (b) above. Your answer need not include numerical calculations, but should include relevant diagrams to demonstrate deadweight loss.
In (a), the price is higher ($20 as opposed to $16.80), and quantity lower (10,000 as opposed to 14,000). The monopolistʹs higher price and smaller quantity result in a deadweight loss as shown below. 5. A pure monopsony buyer of a resource has a marginal value curve for the resource expressed as: MV = 100-0.4Q. Its marginal and average expenditure functions are: ME = 20 + 0.023Q AE = S = 20 + 0.011Q. a. What is the price and quantity that would prevail in a competitive market? The Q C is computed as follows: Equate S to MV. 20 + 0.011Q = 100-0.4Q 0.411Q = 80 Q C = 194.65 P C = 20 + 0.011(194.65) = 22.14 b. What quantity is purchased by a monopsonist, and at what price? The Q M is computed as follows: Equate ME to MV. 20 + 0.023Q = 100-0.4Q 0.423Q = 80 Q M = 189.13 P M = 20 + 0.011(189.13) = 22.08 c. Compute the deadweight loss that results when the firm acts to maximize profit (that is, takes advantage of its monopsony power). Compute the height of MV between H M and H C. H M = 100-0.4(189.13) = 24.348 H C = 100-0.4(194.65) H 1 = 24.348-22.140 = 2.208 The area under the MV curve is AM. AM = 0.5*H 1 (Q C Q M ) = 0.5*(23.24)(194.65-189.13) AM = 6.09
Compute height of AA H M = 20 + 0.011(189.13) = 22.08 H C = 20 + 0.011(194.65) = 22.14 H 2 = 22.14 22.08 = 0.06 The area under AE is AA. AA = 0.5*H 2 (Q C Q M ) = 0.5*(0.06)(194.65-189.13) AA = 0.1656 Deadweight loss becomes AM + AA = 6.09 + 0.1656 = 6.25 6. McCullough has a monopoly on rental dwellings in the local community. The demand for rental dwellings is Q D = 70,000-50P P = 1,400-0.02Q D. The resulting marginal revenue function is MR(Q) = 1,400-0.04Q D. McCulloughʹs marginal cost of providing rental dwellings is MC(Q) = 0.01Q + 20. Suppose that to ease the burden on renters, the local community has instituted a price ceiling of $480. a. Graph the Demand, Marginal Revenue, and Marginal Cost curves. Note that the marginal cost curve intersects the y-axis at 20 (not 4 as in the picture below). b. What are the consumer and producer surpluses had the price ceiling not been instituted? Show graphically. CS = A + B PS = C + D + F + G c. Does consumer surplus increase due to this price ceiling? Explain. Consumer Surplus increases with the price ceiling. A competitive market sets price equal to marginal cost. At $480, demand is 46,000. Marginal cost at 46,000 is exactly $480. This means that the profit maximizing solution for McCullough is to provide 46,000 units at the price ceiling of $480 per unit. Therefore, consumers gain from being able to obtain more units at a lower price. d. Does social welfare increase as a result of the price ceiling? Explain. Before the price ceiling is imposed, McCullough was charging a price of $832 per unit. Since McCullough has market power, we know that social welfare is less than it would be in a competitive market. Since the price equals marginal cost, the
market enjoys the competitive market price. In this case, we know that societal welfare exceeds welfare in a monopoly market.