Economics 101Fall 2010Homework #5Due: 12/14/2010 in lectureDirections: 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 nameas it appears on your ID so that you can receive the correct grade. Please remember the sectionnumber for the section you are registered, because you will need that number when you submitexams and homework. Late homework will not be accepted so make plans ahead of time. Pleaseshow your work. Good luck!1. Perfect competitionA local microbrewery has total costs of production given by the equation TC=500+10q+5q2. Thisimplies that the firm's marginal cost is given by the equation MC=10+10q (you do not need to be ableto show this). The market demand for beer is given by the equation QD=105 – (1/2)*P.a) Write the equations showing the brewery's average total cost and average variable cost and averagefixed cost, each as a function of q. Show the firm's MC, ATC and AVC on one graph.ATC = TC/q = (500+10q+5q2)/q = 500/q+10+5qAVC = VC/q = (10q+5q2)/q = 10+5qAFC = FC/q = 500/q b) What is the breakeven price and breakeven quantity for this firm in the short run? Note that MC crosses ATC at its minimum. Hence, MC = ATC at that level of output that correspondsto the intersection of the ATC and MC curves.1MC = 10 +10q = 500/q + 10 + 5q = ATC5Q = 500/q5q2 = 500q2 = 100q = 10Then P = MC = ATC = 10 + 10q = 110c) What is the shutdown price and shutdown quantity for this firm in the short run? From the picture above, it is clear that AVC is minimized at q = 0.P = MC = AVC = 10+5(0) = 10Short-run Equilibriumd) If the market price of the output is $50, how many units will this firm produce? The firm will set MC=P=50. Thus, 10 + 10q = 50, hence q* = 4.e) Given a market price of $50, how many firms are in this market?Plug P = 50 in the market demand curve. Thus, we get QD = 105 – (1/2)50 = 80Thus, the number of firms in the short run is equal to: N = 80/4 =20 firms.Long-run Equilibriumf) Assuming the beer industry is perfectly competitive, what output would be produced by the firm inlong-run equilibrium? What would be the long-run equilibrium price?In long run equilibrium, there must be zero profits. Therefore, rewriting the profit function, p = TR – TC = P*q – ATC*q = (P – ATC) *q We can see that zero profit requires that P = ATC. Since in perfect competition it is always the casethat P = MC for a profit maximizing firm, we need to find the price at which MC = ATC. Note that thisis the breakeven price and breakeven quantity for the firm found in part (b).Long run equilibrium quantity for the firm: q = 10 Long run equilibrium price: P = 110g) How many firms will be in the industry in long-run equilibrium?We already know that the long run equilibrium price must be 110. From this information and thedemand curve we can find the quantity demanded in this market in the long run. QD=105-(1/4)*P = 105 – (1/2)*110 = 50In equilibrium, the market demand must equal the market supply. Thus, the number of firms:N = QD/q = 50/10 = 5 firms22. MonopolySuppose Charter Communications is a monopolist in providing cable television services to localconsumers in Madison. The market demand curve faced by Charter Communications is P = -Q + 30,and Charter’s cost is given by TC=Q2/2 + 20, and Charter Communication’s marginal cost is given byMC=Q.a) What is the equation for Marginal Revenue for this monopolist?MR = -2Q + 30 b) Draw the Demand curve, Marginal Revenue curve, and Marginal Cost curve for this monopolist ina graph.c) What is the monopolist’s profit-maximizing production quantity, QM? What price, PM , will themonopolist charge?Use MR=MC, we have -2Q + 30 = Q , and we can get QM = 10 Plug QM = 10 into demand equation, we have PM = -10 + 30 = $20 d) Compute the Consumer surplus, producer surplus and profits for the monopolist CS = 10x10/2 = $50PS = 10x10 + 10x10/2 = $150In order to get the profit, First,30 15 30Q$MRDMC3ATC = Q/2 + 20/Q Second,Profits = TR – TC TR = PMQM = 20x10 = $200 TC = ATC (at QM)xQM = (10/2 + 20/10)x10 = $7x10 = $70 Then,Profits = TR – TC = $200 - $70 = $130Now, suppose there is a technological change for the monopolist and the result of this technologicalchange is that the firm’s cost curves change. Charter Communications total cost is now given by TC =10Q, and its marginal cost is given by MC = 10. e) What is the monopolist’s profit-maximizing production quantity QM? What price, PM, will themonopolist charge?Use MR=MC, we have -2Q + 30 = 10, and we can get QM = 10 Plug QM = 30 into demand equation, we have PM = -10 + 30 = $20 f) Suppose this market was a perfectly competitive market (i.e., the monopolist’s demand curve is stillthe market demand curve, but now there are many firms providing cable television services for themarket). Given the market is perfectly competitive, what would be the equilibrium price (Ppc) andquantity (Qpc) in this competitive market? Assume that each firm’s MC curve is given by MC = 10 forthis question. The competitive market equilibrium price should satisfy P=MC, so Ppc = 10 Plug Ppc = 10 into demand, we get 10 = -Q + 30, Qpc = 20.Now, let us compare the monopoly and perfect competition outcomes. Consider the last technologywhere the firm faces TC = 10Q and MC=10.g) What is the difference between the consumer surplus in the monopoly case and the consumersurplus in the perfect competition case? CS(monopoly) = 10x10/2 = $50 CS(perfect competition) = 20x20/2 = $200So the difference is $50 - $200 = -$150h) What is the difference between the producer surplus in the monopoly case and the producer surplusin the perfect competition case? PS(monopoly) = 10x10 = $100 PS(perfect competition) = $0So the difference is $100 - $0 = $100i) What is the dead weight loss caused by the monopolist? DWL = [CS(perfect comp.)+PS(perfect comp.)] - [CS(monopoly)+PS(monopoly)] DWL = [200+0] - [50+100] = $50 3. Natural monopoly4a) Suppose Madison Gas and Electric (MGE) is a natural monopoly in Madison forelectricity. This firm faces a demand function P =20 −2Q and has a total cost function TC= 12+8Q. We can find this firm’s marginal cost function by taking the first derivative ofthe total cost function with respect to Q. If you do not know how to do this or yourcalculus skills are rusty, then here is the firm’s MC curve: MC = 8. On a graph illustratethe Demand curve, Average
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