Assignment#

You have $20 per week to spend, and two possible uses for this money: telephoning friends back home, and drinking coffee. Each hour of phoning costs $2, and each cup of coffee costs $1. Your utility function is U(X,Y) = XY, where X is the hours of phoning you do, and Y the number of cups of coffee you drink. (X and Y are continuous variables. Interpret fractions as averages over several weeks.) (a) What are your optimal choices? What is the resulting utility level? You can use the standard result on the constrained maximization of such a function, but must state it clearly. (b) Now suppose the price of telephone calls drops to $1 per hour. What are your optimal choices? What is the resulting utility level? (c) How much income per week will enable you to achieve the same quantities at the new prices as the ones you chose before? What income will enable you to attain the same utility as you did before? Which amount is smaller, and why?

In the short run, a price-taking firm has a fixed and sunk cost 5, a fixed but avoidable cost 4, and a variable (therefore also avoidable) cost function Q2 , where Q denotes the quantity of output, and is a continuous variable. In the long run, the fixed and sunk cost will become fixed but avoidable. Find the equations for its supply curves in the short run and in the long run. What will be the long run industry supply curve if all actual and potential firms in the industry have the same cost structure and there is free entry and exit?

In 1975, the demand and supply curves for natural gas in the U.S. were given by the respective equations QD = 30 - 5 P , QS = 16 + 2 P , 5 where the quantity demanded (QD) and the quantity supplied (QS ) were measured in trillions of cubic feet, and the price P in dollars per thousand cubic feet. (a) Draw a rough figure of the demand and supply curves. (b) What is the market equilibrium price and what quantity is supplied and consumed at this price? (c) Suppose the government imposes a price ceiling at $1 per thousand cubic feet. How much gas is produced at this price? Suppose this quantity is allocated in such a way that those consumers with the highest willingness to pay get to buy the gas, but they pay only the ceiling price. What price is the marginal buyer willing to pay? (d) Contrast the price ceiling situation of (c) and the market equilibrium in (b). Because of the price ceiling policy: What is the gain in consumer surplus? What is the loss of producer surplus? What is the deadweight loss? You should mark these surpluses etc. as areas on the supply-demand figure and also calculate the numbers. QUESTION 5: (15 points) B.B. Lean and Rainbow's End are mail-order clothing sellers. The catalogs of both feature very similar sweaters. Consumers look for low prices but have some innate preference for one firm or the other; therefore the sweaters sold by the two firms are close but not perfect substitutes. Specifically, econometricians have estimated that the demand functions for the two firms' sweaters are as follows Q1 = 780 - 18 P1 + 16 P2 , Q2 = 780 + 16 P1 - 18 P2 where the subscript 1 denotes B.B. Lean and subscript 2 denotes Rainbow's End. All prices and quantities are to be regarded as continuous variables. B.B. Lean obtains its sweaters from Thailand at $40 each; Rainbow's End has located a cheaper supplier in Bangladesh, and can obtain its sweaters at $20 each. Each firm sets its price without knowing what price the other is choosing; so they are playing a Bertrand duopoly game. (a) Find expressions for the profits of each firm in terms of the prices of both. (b) Find expressions for their best response (reaction) functions. (c) Calculate the equilibrium prices of the two firms (d) Calculate the resulting quantities sold by the two firms. (e) Calculate the resulting profits of the two firms. QUESTION 6: (15 points) What is meant by moral hazard in insurance? What is the economic efficiency cost of moral hazard? What steps do insurance companies take to mitigate moral hazard? QUESTION 7: (15 points) "If property rights are well specified, and parties can bargain without cost and to their mutual advantage, the resulting outcome will provide an efficient resolution of any externalities, no matter to which party the property rights are initially assigned." Explain this statement using an example.

6. The deadweight loss due to monopoly power is a. equal to the value of monopoly profits. b. equal to the transfer of surplus from consumers to the monopolist when the monopolists raises price above marginal cost. c. created by the monopolist's restriction of output below the competitive level. d. affected in the short run by changes in lump-sum taxes. e. both c. and d. 7. The burden of a tax per unit of output will fall heavily on consumers when demand is relatively ______ and supply is relatively ______. a. elastic; elastic b. inelastic; inelastic c. elastic; inelastic d. inelastic; elastic 8. Read the following game matrix carefully. In each cell, the first number is the Row player's payoff, and the second number is the Column player's payoff. Column Left Right Up 1 , - 1 0 , 0 Row Down 0 , 0 - 2 , 2 In the Nash equilibrium of this game, Row chooses a. Up b. Up with probability 2/3, Down with probability 1/3 c. Up with probability , Down with probability d. Up with probability 1/3, Down with probability 2/3 e. Down 9. Which of the following is TRUE about a college education as a signaling device? a. It is a useful signal only if individuals choose majors related to their ultimate field of employment. b. It is a useful signal only if a college education is open to all individuals, no matter what their previous level of educational accomplishment was. c. It can be a useful signal whether or not people actually learn anything in college. d. It is a useful signal only if the job in question cannot be done without the preparatory coursework the college degree required. e. It is less and less a useful signal in the post-industrial economy, where the skill sets employers need change so rapidly. 4 YOUR NAME: 10. Which of the following is a negative externality connected to attending college? a. The fact that completion of a college degree acts as a signaling mechanism to employers. b. The fact that other costs, such as books and materials, are incurred in addition to tuition and fees. c. The fact that your college has required that all individuals living in student housing either get or show they have already obtained vaccinations against all communicable diseases. d. The fact that the people in the next room play loud music at hours when you want to sleep. e. The fact that you will get benefits from college that you don't currently anticipate.