# problemset7 - Middle East Technical University Department...

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Middle East Technical University Spring 2011 Department of Economics ECON 201 Erol Çakmak TA: Osman Değer PROBLEM SET 7 1) A firm has a production function Q(K,L)= 4K 1/3 L 1/3 , where the unit prices of labor and capital are both equal to 1. P is the price of the product in a perfectly competitive market. a. Determine the long run supply function of this firm. b. What is the profit maximizing output level when P=3? c. Derive the short run supply function for K 0 =9. 2) Suppose the inverse demand function for cab rides in Chicago is given by P(Y)= 40000/Y where Y is the total number of cab rides in a given year. Assume that there are 100 identical cabs in this market, and that the cost function for each cab is given by C(y)= 200 + y 2 /2 where y is the number of rides per year produced by a typical cab and 200 represents the annual cost of a taxi license that is issued by the city (for simplicity, we assume away the cost of buying or renting a cab). a. Find the equilibrium price, if all cabs behave as if they operate in a perfectly competitive market. b. Is this equilibrium the industry s long run equilibrium, i.e. will cabs have an incentive to enter or exit at the equilibrium price derived in part (a) ? c. Now assume that, in an effort to raise revenue, the city raises the price of taxi licenses to \$250 per year. i. How many cabs will be buying a license at the new price and offering rides in the

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problemset7 - Middle East Technical University Department...

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