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Unformatted text preview: Econ 121 – Fall 2010 UC Berkeley Professor Cristian Santesteban Problem Set 1 Due: Thursday, September 9th at the beginning of class Problem 1 Is it ever better for a perfectly competitive firm to produce output even though it is losing money? If so, when? Problem 2 If q(P) = 100/P and c(q) = q2 , what is the optimal level of output of the monopolist? Problem 3 Dayna’s Doorstops (DD) is a monopolist in the doorstop industry. Its cost is C = 100 – 5q + q2, and demand is P = 55 – 2q. a. What price should DD set to maximize profits? What output does the firm produce? How much profit and consumer surplus does DD generate? b. What would output be if DD acted like a perfect competitor and set MC=P? What profit and consumer surplus would then be generated? c. What is the deadweight loss from market power in part (a)? d. Suppose the government, concerned about the high price of doorstops, sets a maximum price at $27. How does this affect price, quantity, consumer surplus, and DD’s profits? e. Now suppose the govt. sets the maximum price at $23. How does this decision affect price, quantity, consumer surplus, DD’s profit, and deadweight loss? f. Finally, consider a maximum price of $12. What will this do to quantity, consumer surplus, profit, and deadweight loss? Problem 4 There are 10 households in Lake Wobegon, Minnesota, each with a demand for electricity of Q = 50 – P. Lake Wogegon Electric’s (LWE) cost of producing electricity is TC = 500 + Q. a. If the regulators of LWE want to make sure that there is no deadweight loss (DWL) in this market, what price will they force LWE to charge? What will output be in that case? Calculate consumer surplus (CS) and LWE’s profit with that price. b. If regulators want to ensure that LWE doesn’t lose money, what is the lowest price they can impose? Calculate output, CS, and profit. Is there any DWL? c. Kristina knows that DWL is something this small town can do without. She suggests that each household be required to pay a fixed amount just to receive any electricity at all, and then a per‐unit charge for electricity. Then LWE can break even while charging the price calculated in part (a). What fixed amount would each household have to pay for Kristina’s plan to work? Why can you be sure that no household will choose instead to refuse the payment and go without electricity? Problem 5 A monopolist has a cost function of c(y) = y so that its marginal cost is $1 per unit. It faces the following demand curve: D(p) = 0 if p>20 and if p<=20 =100/p a. What is the profit‐maximizing choice of output? b. If the government could set a price ceiling on this monopolist in order to force it to act as a competitor, what price should it set? c. What output would the monopolist produce if forced to behave as a competitor? Problem 6 A coal mine operates with a production function Q=L/2, where L is the quantity of labor it employs and Q is total output. The firm is a price taker in the output market, where the price is currently 32. The fir mis a monopsonist in the labor market, where the supply curve for labor is w = 4L. a) What is the monopsonist’s marginal expenditure function, ME(L)? b) Calculate the monopsonist’s optimal quantity of labor. What wage rate must the monopsonist pay to attract this quantity of labor? c) What is the deadweight loss due to monopsony in this market? Problem 7 The government imposes a fixed fee per year on each firm that operates in a competitive market. What happens to output, the optimal scale of a firm, and price if there is free entry into the market? Have fun and good luck! ...
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- Fall '07