ProblemSet6-2009

ProblemSet6-2009 - y = q x 2 1 + x 2 2 . The demand...

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Econ 6202, Fall 2009 Dmitry Shapiro Problem Set 6 Due Tuesday October 27 1. Suppose that the technology for producing q is identical for all firms. The cost function for a representative firm is given by c ( q ) = a + bq + cq 2 , where a > 0 ,b > 0, and c > 0. Find the long-run equilibrium price, and the quantity of output produced by each firm. 2. Consider an industry with 7 identical competitive firms. The production function of a representative firm is q = min { x 1 , x 2 } , where x 1 and x 2 are the inputs that the firm uses to produce output q . Suppose that the input prices are w 1 = 4 and w 2 = 3. The demand function is q D ( p ) = 48 - p . Assume that firms cannot enter or exit the market. Find the equilibrium price and quantity. Compute the profit of each firm. 3. Consider an industry with identical firms and production function
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Unformatted text preview: y = q x 2 1 + x 2 2 . The demand function is q D ( p ) = a-bp , where a > ,b > 0. Compute the long run equilibrium number of rms in the market, and the quantity of output that each rm produces. 4. The demand curve for a good is q D ( p ) = 100-p , and the supply is q S ( p ) = 20 + 3 p . Compute the equilibrium price and quantity. Suppose that the government need to collect 308 in revenues. The gov-ernment can choose between a per unit tax on t on production and a per unit tax t on consumption. Find the values of t and t . If the government wants to minimize the dead weight loss, which tax should it choose? 1...
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