Problem 1 Suppose Madison Gas and Electric (MGE) is a natural monopoly in Madison for electricity. This rm faces a demand function P = 20 -2Q and has a total cost function TC = 12+SQ. a. What is this rm's marginal cost function? On a graph illustrate the Demand curve, Average Total Cost curve, Marginal Cost Curve, and Marginal Revenue Curve for this rm. b. The government decides to regulate this market using marginal cost pricing. That is, the rm is told to produce that level of output where MC is equal to P for the last unit produced. Calculate the minimum amount of subsidy that will be necessary in order to keep this monopolist in business. c. Suppose the government decides to use average cost pricing regulation. That is, the government tells the monopoly to produce that level of output where the rm earns zero economic prot. Identify in your graph the equilibrium price and quantity that corresponds to this type of regulation (don't compute the values,just mark what the Pm. and QM are in your graph). ls this price and output combination allocatively efcient? Problem 2 There are 10 households in Lake Wobegon, Minnesota, each with a demand for electricity of Q = 50 P. Lake Wobegon Electric's (L WE) cost of producing electricity is TC: 500 + Q. a. If the regulators of L WE want to make sure that there is no deadweight loss in this market, what price will they force 1. WE to charge? What will output be in that case? Calculate consumer surplus and L WE's prot 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, consumer surplus, and prot. Is there any deadweight loss? c. Kristina knows that deadweight loss is something that this small town can do without. She suggests that each household be required to pay a xed amountjust 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 xed 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 3 A monopolist faces the following demand curve: Q : [44/132, where Q is the quantity demanded and P 1/2 is price. lts average variable cost is A VC : Q , and itsjixed cost is 5. a. What are its prot-maximizing price and quantity? What is the resulting prot? b. Suppose the government regulates the price to be no greater than $4 per unit. How much will the monopolist produce? What will its prot be? c. Suppose the government wants to set a ceiling price that induces the monopolist to produce the largest possible output. What price will accomplish this goal? Problem 4 A rm has two factories for which costs are given by: Factory #1: C(91) = IOQf Factory #2: C3(Q_=) = 20Qg'7 The rm faces the following demand curve: P z 700 SQ where Q is total outputi iie.. Q: Q] + Q2. a. On a diagram, draw the marginal cost curves for the two factories. the average and marginal revenue curves. and the total marginal cost curve tie, the marginal cost of producing Q = Q 1 + Q2). Indicate the prot-maximizing output for each factory. total output, and price, b. Calculate the values of Qt Q3. Q. and P that maximize prot. c. Suppose that labor costs increase in Factory 1 but not in Factory 2. How should the rm adjust (i.e., raise, lower. or leave unchanged) the following: Output in Factory 1? Output in Factory 2? Total output? Price
