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ps6sol_09

# ps6sol_09 - Cornell University Economics 3130 Problem Set 6...

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Cornell University Economics 3130 Problem Set 6 Solutions 1. True/False/Explain. State whether each of the following is true or false, and explain why. Please limit your answers to no more than two sentences. All credit is based on the explanation. (a) Whenever a firm is maximizing profits, it must also be minimizing costs. True. Suppose that a firm were not minimizing costs. If so, it could change its production to reduce costs, and profits would increase. 2. Suppose your production function is f ( l, k ) = l 1 3 k 1 3 , the price of labor is w and the price of capital is r . (a) Determine the conditional factor demand functions of k and l from the cost min- imization problem. What do these tell you? What is the cost function c ( y, w, r )? The Lagrangian for the cost minimization problem is: L = wl + rk + λ ( y - l 1 3 k 1 3 ) . The FOC’s are as follows l : w - 1 3 λl - 2 3 k 1 3 = 0 k : r - 1 3 λl 1 3 k - 2 3 = 0 λ : y - l 1 3 k 1 3 = 0 Dividing the first by the second gives k = wr - 1 l Substituting into the production function, solving for l , and then using the solu- tion for l to solve for k gives the answer. l ( y, w, r ) = y 3 2 w - 1 2 r 1 2 k ( y, w, r ) = y 3 2 w 1 2 r - 1 2 The cost function is obtained by multiplying the conditional factor demands by the input prices. c ( y, w, r ) = 2 y 3 2 w 1 2 r 1 2 1

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(b) What is the firm’s marginal cost function? What is the firm’s supply function?
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