Intermediate Microeconomics: A Modern Approach, Seventh Edition

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Econ 301 – F07 PROBLEM SET 7 – Due Wednesday Dec 5 by noon at Jiyoun's Uris Hall office Wissink 1. You are given the following information about a monopolist who makes gizmos: the monopolist’s production function x=L 1/2 where L is measured in hours; the firm must get a permit to operate and the cost of the permit is $16; the current market wage rate is $1/hour; and market demand is X D = 120 – 2P. a. What are the values for the simple monopoly equilibrium; that is what are x SM , P SM , profit SM , Net Social Surplus SM , Consumers’ Surplus SM , Producer’s Surplus SM and dead-weight-loss SM ? b. Graph this solution. [ANSWER] tc(x) = x 2 +16 atc(x) = x+16/x mc(x) = 2x Demand curve : X D = 120 – 2P P=60-1/2x tr(x) = (60-1/2x)x = 60x-1/2x 2 mr(x) = 60 – x Maximize profit : set mr(x SM )=mc(x SM ) 60-x SM = 2x SM x SM = 20 P SM = 60-1/2x SM = 50 profit SM = 50*20 – (20*20+16) = 584 NSS SM = area OBCD = 60*24*1/2-20=700 CS SM = area P SM BC = (60-50)*20*1/2=100 PS SM = area OP SM CD = 700-100=600
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DWL SM = areaDCA = (50-40)*(24-20)*1/2=20 c. Is the monopolist productively efficient? Defend. [ANSWER] No! x SM is not at the minimum of the lratc curve. However, if you want to argue that the rising part of the lratc makes no sense since the firm would replicate beyond x MES then I would accept “yes” as an answer, provided you provided that proviso! d. Is the monopolist allocatively efficient? Defend. [ANSWER] No! x* = 24 maximizes Net Social Surplus. 2. In a diagram using typical cost curves and a linear market demand curve, show how a PRICE CEILING can be successfully used to get a simple monopolist to put more on the market and sell it at a lower price. [ANSWER] Suppose P C is a price ceiling that the government slaps on the market. A simple monopolist’s new marginal revenue curve is the red line, P C CFD. The monopolist produces q C with the lower price, P C , the price ceiling. Also, consumer surplus increases from P SM AB to P C AC and the dead-weight-loss decreases from GBE to FCE. Note that the efficient price ceiling would be at the price indicated by point E. 3. In a diagram using typical cost curves and a linear market demand curve, show how a PER UNIT TAX ON THE MONOPOLIST’S OUTPUT will alter the profit maximizing quantity and price for simple monopolist. Show how the economic price incidence of the per unit tax is shared (or not) between the buyers and the monopolist. [ANSWER] 2
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After a per unit tax, t, is levied on the monopolist’s output, atc, avc, and mc shift up – and mc shifts up by exactly t(the per unit tax). A per unit tax will cause a monopolist to reduce the profit maximizing quantity from q SM to q t and raise price from P SM to P t for simple monopolist. The profit for the firm decreases since it was maximized before, so by revealed profit analysis, profit must be less at this combination…note the monopolist could have selected this quantity before but did not. The tax is shared since P t -P SM is less than t.
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