hmwk 7 - Q = 4 K 1/2 L 1/2 a) What is the firms short run...

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Economics 100B Jacobsen Homework 7 (11/18/08) 1. Suppose the price of (a pair of) sneakers is $40 and the manufacturer makes them in two factories: Factory (a): Due to excessive crowding an additional worker can only increase output by 1 pair when working for 10 hours. Factory (a) is in a location with low wages, at $3 an hour. Factory (b): Here a worker has enough space and can make a pair of sneakers in 2 hours. The local wages are $20 an hour. What is the marginal revenue product of labor in both factories? Will the firm add more workers to either factory? When will the firm no longer want to hire additional workers? 2. Suppose the market price of output is $2 and Q is given by:
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Unformatted text preview: Q = 4 K 1/2 L 1/2 a) What is the firms short run demand for labor (in terms of w ) when r = 2 and K = 9? Now consider the long run, allowing the level of both r and K to vary in addition to w and L . b) Write down the formal profit maximization problem that will yield factor demands. c) Attempt to solve this problem using the first order conditions, and describe the intuition for the result. (If youd like, you can work out the two-dimensional second order conditions as well, but I wont expect this on an exam.) d) What can we say about the number of firms in long run equilibrium in this industry? Additional practice problems from Perloff Chapter 15: 2, 19, and 21...
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This note was uploaded on 08/09/2009 for the course ECON 100B taught by Professor Rauch during the Winter '07 term at UCSD.

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