SCHOOL OF ECONOMICS AND FINANCE THE UNIVERSITY OF HONG KONG ECON6021 MICROECONOMICS PROBLEM SET NO.3 COMPETITIVE MARKETS AND MONOPOLY

SCHOOL OF ECONOMICS AND FINANCE THE UNIVERSITY OF HONG KONG ECON60 MICROECONOMICS PROBLEM SET NO.3 COMPETITIVE MARKETS AND MONOPOLY This problem set contains short-answer (true, false, uncertain) problems and longeranswer problems in microeconomics. The short-answer questions should take no more than one page to answer, while the longer-answer questions should generally take no more than two pages to answer. Please write on only one side of the paper. Disclaimer: While this problem set is designed to be reasonably comprehensive, it does not cover every topic that the student should be familiar with for the Economics 60 exams. I do not recommend you prepare for exams by exclusively doing these problems. True,_False, Uncertain (explain your answers):. Marshall Fields, a large department store in Chicago, offers to pay up to $30 for an old piece of luggage as a trade-in on purchase of a new one. The old luggage is worthless to Marshall Fields, which throws it away. Marshall Fields actions contradict the assumption of profit-maximization.. Barbers charge less for children because it is less costly to cut the hair of children. 3. A firm facing a downward-sloping demand curve for the product it produces wil always want to operate on the elastic portion of that demand curve. 4. A competitive firm cannot be maximizing its profit if the last worker hired adds to its output more than the average product of its total labor force. 5. If the demand curve for a monopolist is linear, then the imposition of a specific tax will raise the consumer s price by an amount equal to the tax. 6. If allocation A is efficient, and allocation B is not, then everyone prefers A to B.

Longer-Answer Problems:. Suppose there are a large number of potential firms, all of which can produce widgets with the following long-run total cost function C = + q + q The (inverse) market demand Q for widgets is given by P=5- Q/ What is the long-run competitive equilibrium for this industry in terms of price, market output, and number of firms?. A monopolist s demand curve is Q = 00 - P and the total cost functions of its two plants are: C = 0q C = 0. 5q and Q = q + q Find the best output for each plant and market price for Q. Show the results graphically, including the numerical values for the relevant marginal costs, quantities, and price. 3. A monopolist s demand curve is Q = 360-0P and its long-run total cost function is C = 6Q + 0.05Q Suppose the government wishes to impose a maximum price on Q at the level that will induce the firm to produce the greatest equilibrium output. What price will be set and how much will the firm produce? What is the resulting increase in consumers surplus compared to the unconstrained monopoly? Show the results graphically, including the numerical values for the relevant marginal costs, quantities, and prices. 3

4. A monopolist has two plants with the following total costs: TC = X TC ( + X = 4) + X + ( X ) = 0.5 + X 0. 5 His demand curve is P = 4 ( X + X ) = 4 0.5( X + X ) How much output (if any) will be produced in each plant? What price will be charged? Show your results graphically including the numerical values for P, X, X and X. 5. A monopoly firm produces widgets by using only two factors of production, capital and labor. The firm has a fixed amount of capital and hires all the labor it wants at a wage of w. Initially its profit-maximizing output and price are Q0 and P0 respectively. Suppose the workers organize and form a labor union. They do not attempt to raise wages, but they are successful in obtaining an effective feather-bedding contract, i.e., the firm must employ at least L workers whether it uses them or not, where L is greater than the initial number of employees L 0. Show graphically and explain the effects of the contract on the firm s: (a) Short-run marginal cost function. (b) Short-run average cost function. (c) Optimal price and output levels. (d) What, if anything, can be said about the effects of the contract on the distribution of incomes to the union members and the owners of the firm? 6. A hospital produces services that can be quantified in two dimensions: quantity (Q) and quality (C). It faces infinitely elastic market demands for both of these aspects of service. Prevailing prices are P = $0, P = $4. The hospital s total costs are given by: q c TC = 0.Q + 0.C 5 (a) If the hospital wishes to maximize profits, how much Q and C should be 4

produced? What will profits be? (b) Suppose that the hospital is managed by a nonprofit foundation. The utility of the foundation s president depends upon both hospital outputs according to the following function: U(Q,C) = min(q,c). If the hospital is now constrained to have the same total cost as in the profitmaximizing case, what level of Q and C will be chosen to maximize the foundation president s utility? What will profits be in this case compared to (a)? 7. Suppose that a monopolist can choose both the quantity of output (q) he produces and his level of advertising (A). His inverse market demand function is P = 00 3q + 4A and his total cost function is C = 0q + 4q + A. (a) Find the profit maximizing level of output, advertising, and price. (b) Suppose a law is passed which prevents the monopolist from advertising (constrains A=0). Calculate the profit-maximizing price and quantity. (c) How would you evaluate whether or not the law benefits consumers? 8. Suppose a perfectly competitive industry can produce widgets at a constant marginal cost of $0 per unit. Once the industry is monopolized, marginal costs rise to $ per unit because $ per unit must be paid to lobbyists to retain the widget producers favored position. Suppose the market demand for widgets is given by Q D = 000 50P Calculate the perfectly competitive and monopoly outputs and prices. Calculate the total loss of consumer surplus from monopolization of widget production. Divide the loss of consumer surplus into transfer to profit, cost increase, and deadweight loss. Graph your results and label all relevant points and magnitudes. 9. Some states limit the number of liquor stores that can sell liquor at the retail level in 5

a given area. Assume that the objective of the state is to maximize the revenue from liquor sales, and that the industry has constant marginal costs. (a) Suppose the state gives a monopoly to one seller, and charges a license fee L for the right to the monopoly. Write down the profit function for the monopolist and characterize the profit-maximizing solution. What would be the effect of an increase in the license fee on the price paid by consumers? (b) Instead of a license fee, the state decides to impose a tax on each unit the monopolist sells. What would be the effect of this tax on the price of liquor? Which would be a more effective means of raising revenue, the tax or the license fee? 0. Suppose the market demand for widgets is given by Q D = 00 P and the market supply by Q S = 0 + 6P (a) What will be the equilibrium price and quantity of widgets? (b) Suppose the government levies a tax of $4 per widget. Now what will be the equilibrium quantity? What price will consumers pay and what price will firms receive? (c) How is the burden of the tax shared by buyers and sellers? What is the tax revenue and what is the deadweight loss due to the tax? Show graphically and discuss results.. The demand for bricklayers is given by the function L D = 000 0W and the supply of bricklayers is given by the function L S = 5 W + 90 (a) Determine the equilibrium wage (W), the equilibrium number of bricklayers employed, and the total wage income of the bricklayers. (b) Now suppose that 0 bricklayers immigrate from a foreign country and are willing to work at any wage they can find. What will this influx of workers do to the equilibrium wage rate, the number of employed domestic workers, and the total wage income of domestic workers? 6

(c) Show, graphically and compare the results for (a) and (b).. The bicycle-manufacturing industry is a constant-cost competitive industry. Bicycle brakes may fail due to poor manufacture, incorrect assembly, lack of maintenance, operator misjudgement, etc. Two extreme positions; with regard to product safety are caveat emptor (let the buyer beware) and caveat vendor (let the seller beware). Under the former scheme, producers would have no responsibility for the safety of their products: buyers would absorb all losses. Under the latter scheme, this liability assignment would be reversed: firms would be completely responsible under law for losses incurred from unsafe products. Using supply and demand analysis, discuss how the assignment of such liability might affect the output and price of bicycles to consumers and to manufacturers. State any assumptions made. Would safer products necessarily be produced if firms were strictly liable under the law? Explain. 3. A utility company is a monopolistic supplier of electricity to two types of customers: residential and commercial. Their demands for electricity, Q R and Q C respectively are: Q = 90 0. 5 Q = 00 R P R C P C The marginal cost of supplying electricity is constant and equal to $0. The utility also has fixed costs of $6000. (a) A profit-maximizing and price discriminating utility would produce what output, charge what prices, and make what profit? (b) If the utility is required by law to charge a uniform price, what will it be? Will the social benefits of this action outweigh the social costs? Explain. (c) If the utility is required to set a uniform price equal to marginal cost, what output and price will result? Show graphically and explain. 4. A perfectly competitive constant-cost industry contains a number of firms, each of which has the following long-run total cost function, where q is a typical firm s annual output: 3 LTC = 0.0q.q + q The market demand curve is Q = 6000-0P, where Q is annual industry sales. (a) Calculate the long-run equilibrium price and output of the industry. (b) How many firms are there in the industry in the long-run? 7

(c) Suppose the government decides to reduce the number of firms to 60 and sells licenses annually by competitive bidding. What is the new price of the product? What is the new industry output? What is the equilibrium price of a license? (d) Suppose instead of selling the licenses, the government decides to allocate them without charge to 60 qualified firms. Discuss generally what effect this will have on the nature of equilibrium in the market. 5. The local bus company has 80 buses. The operating cost of a bus is $30 during the day and $60 during the night, when higher wages must be paid to drivers and other workers. The daily capital cost of a bus, whether it is used or not, is $0. The demands for buses aggregated over persons and stops during the hours of day and night, respectively D and N, are Q Q =60 = 80 D P D N P N (a) If additional buses are to be purchased, what is the efficient number of buses? What prices should be charged to induce efficient ridership of them? Will all of the buses be in use at night? (b) If the number of buses is limited to 80, what prices are efficient? (c) Draw a graph which illustrate the outcomes for (a) and (b). 6. An economics professor at Midstate University estimated that student demand for football tickets at the University was significantly different from the demand by the general public. The specific demand functions are P = 800 0 (student demand) s Q s P = 600 0 (general public demand) g Q g for prices measured in cents and quantities in thousands of tickets. The costs of the football program are $50,000 per year for travel expenses and $750,000 per year for scholarships, salaries, etc. (a) Determine a pricing policy that would maximize profits. Show graphically and explain. (b) How would the solution change if stadium capacity were limited to fifty thousand admissions per game? Explain. (c) Is the price structure in (b) sustainable? Explain. 8