Micro Econ Problem Set 1

Micro Econ Problem Set 1 - Rice University Professor...

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Rice University Economics 370 Professor Diamond Microeconomic Theory PROBLEM SET 1: INTRODUCTION AND APARTMENT SUPPLY AND DEMAND I. Suppose the production function for the output produced by a firm is f ( L , K ) = 40 L 3 / 4 K 1 / 4 , where L is labor and K is capital. 1. What is the marginal product of labor? What is the marginal product of capital? 2. Suppose the rental rate of capital in the market is r =2, the wage of labor is w =10, the price of output is p =1/3 and the amount of capital is fixed at 16 units (in the short run). Assuming that the firm acts to maximize profit, what is the optimal level of labor? Show that both the first and second order conditions for a maximum are satisfied. What is the associated optimal output level? II. Suppose now that the capital stock is variable, but the firm is constrained (by its lenders) to spend no more than a total of C=400. Assume the firm chooses inputs to maximize production and all prices are as indicated above, how much capital and labor will it hire? How much will it produce and what are its profits?
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Micro Econ Problem Set 1 - Rice University Professor...

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