# ps4 - 2 k 1 2 and the rental price of capital is 16 However...

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Problem Set 3 Due Thursday, Oct. 22nd, by 10pm 1. Consider the production function f ( l, k ) = l α + k α . (a) For what values of α > 0 is the production function quasi-concave? For the rest of this problem, assume α is such that the production function is quasi- concave. (b) Find the conditional input demands for l and k . (c) Find the cost function and show Shephard’s lemma works. (d) Find the supply function. 2. A U.S. textile company named PEW (Pernicious Exploiter of Workers) has a contract to produce 1000 shirts. PEW has two plants, one in the U.S. and one in a developing country. In the U.S., the production function is l 1 / 2 k 1 / 2 , wages are 16, and the rental price of capital is 16. In the developing country, the production function is also
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Unformatted text preview: 2 k 1 / 2 and the rental price of capital is 16. However, wages are 4 and the ﬁrm must pay a ﬁxed cost of 10000 to operate in the developing country if it chooses to produce any shirts there. (a) Explain why it is optimal for the ﬁrm to produce all the shirts at one of the two plants. (b) Given the optimal choices of k and l , what are the costs associated with producing 1000 shirts in the U.S.? In the developing country? Where will the ﬁrm produce? (c) Unions are outraged at the low wages payed by PEW in the developing country and demand that wages in the developing country increase to 9. How does this aﬀect the demand for labor in the developing country? In the U.S.? 1...
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