1 Economics 101 Fall 2011 Homework #6 Due: 12/13/2010 in lecture Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework (legibly). Make sure you write your name as it appears on your ID so that you can receive the correct grade. Please remember the section number for the section you are registered, because you will need that number when you submit exams and homework. Late homework will not be accepted so make plans ahead of time. Please show your work. Good luck! 1. Monopoly Suppose Exxon Mobile purchased every gas company in the world and set their prices. Then, it would have a control of the gas market with no other competition. Thus Exxon Mobile becomes a monopolist in providing gas. The market demand curve faced by Exxon Mobile is P = -Q + 40, and Exxon Mobile’s cost is given by TC=Q2 + 140, and the marginal cost is given by MC=2Q. a) What is the equation for Exxon Mobile’s Marginal Revenue curve? MR = -2Q + 40 b) Draw the Demand Curve, Marginal Revenue Curve, Average Cost Curve and Marginal Cost Curve for this monopolist in a graph. Label your graph carefully and completely. The graph is below c) What is the monopolist’s profit-maximizing production quantity QM? What price will the monopolist charge PM? Use MR=MC, we have -2Q + 40 = 2Q, and we can get QM = 10 Plug QM = 10 into demand equation, we have PM = -10 + 40 = $30 10 20 4020 24 40 Average cost 0 cMarginal revenue bDemand a30 Q P Marginal cost2 d) Compute the consumer surplus, producer surplus and profits for the monopolist. CSM = 10x10/2 = $50 PSM = 10x10 + 20x10/2 = $200 In order to get the profit, First, Profits = TR – TC TR = PMQM = 30x10 = $300 Second, TC = Q2 + 140 = 102 + 140= $240 Then, Profits = TR – TC = $300 - $240 = $60 Now, suppose there is a technological change for the monopolist, and its total cost is now given by TC = 20Q (no fixed cost), and its marginal cost is given by MC = 20. e) What is the monopolist’s profit-maximizing production quantity QM? What price will the monopolist charge PM? Show these values in a graph. Notice that the ATC = MC Use MR = MC, we have -2Q + 40 = 20, and we can get QM = 10 Plug QM = 10 into demand equation, we have PM = -10 + 40 = $30 f) Suppose this market was a perfectly competitive market (i.e., the monopolist’s demand curve is still the market demand curve, but now there are many firms providing gas for the market). Given the market is perfectly competitive, what would be the equilibrium price (Ppc) and quantity (Qpc) in this competitive market? b20 40 Average Total Cost = Marginal Cost 0 Marginal revenue Demand a 1030 Q P 40203 The competitive market equilibrium price should satisfy P = MC, so Ppc = $20 Plug Ppc = 20 into demand, we get 20 = -Q + 40, Qpc = 20. g) Assume the technological change in the market is still true. What is the difference between the consumer surplus in the monopoly case and the consumer surplus in the perfect competition case? CS(monopoly) = (1/2)($40 per unit - $30 per unit)(10 units) = $50 CS(perfect competition) = (1/2)($40 per unit - $20 per unit)(20 units) = $200 So the difference is consumer surplus is $150 greater with perfect competition than with monopoly. h) What is the difference between the producer surplus in the monopoly case and the producer surplus in the perfect competition case? PS(monopoly) = 10x10 = $100 PS(perfect competition) = $0 So the difference is producer surplus is $100 greater with monopoly than with perfect competition. i) What is the dead weight loss caused by the monopolist? TS(perfect comp.) = CS(perfect competition)+PS(perfect competition) = 200+0 = $200 TS monopoly = CS(monopoly)+PS(monopoly) = 50+100 = $150 DWL = [TS(perfect competition)] - [TS (monopoly)] DWL = 200 – 250 = $50 Alternatively, DWL (with monopoly) = (1/2)($30 per unit - $20 per unit)(20 units – 10 units) = $504 2. Natural monopoly a) Suppose Madison Gas and Electric (MGE) is a natural monopoly in Madison for electricity. That is the case where one firm can produce the total quantity in a market more cheaply than multiple firms because there is a large fixed cost or economies of scale in this industry. The Demand curve, Average Total Cost curve, Marginal Cost Curve, and Marginal Revenue Curve for this firm are shown in the picture below. The government decides to regulate this market using marginal cost pricing. That is, the firm is told to produce that level of output where MC is equal to P for the last unit produced. a) Identify in the graph the quantity (QMC) and price (PMC) outcomes under this scheme; label it with the letter “A”. Is this regulatory scheme allocatively efficient? Why or why not? Under this regulatory scheme the equilibrium is when P=MC. QMC = 14 and PMC = $12; The equilibrium is allocatively efficient since it maximizes the total surplus or, alternatively, because P = MC for the last unit produced. Notice also that when P = MC there is no deadweight loss which is another sign that the market is allocatively efficient. b) Compute the profit of the firm. What is the minimum amount of subsidy that will be necessary in order to keep this monopolist in business? TR = PMCx QMC = 12x14 = $168 TC=ATC(atQ=14)x QMC = 18x14 = $252 Profit = TR – TC = -$84 Hence, the minimum amount of subsidy that will be necessary in order to keep this monopolist in business is $84; that is when the monopolist earns zero economic profits. MC4012 20 18 10 14 20MR DATC$Q5 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 firm earns zero economic profit. c) Identify in the graph the equilibrium price and quantity that corresponds to this type of regulation label it with the letter “B”. Under this regulatory scheme the equilibrium is when the monopolist gets zero profits. In the picture, the equilibrium is when Demand=ATC. Hence at this point; QAC = 10 and PAC = $20; d) Is this price and output combination allocatively efficient? Why or why not? The equilibrium is NOT allocatively efficient since it does not maximize the total surplus. Alternatively, the outcome is not allocatively efficient since P is not equal to MC for the last unit produced. In this example P is greater than MC
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