Question

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2. (21 points. Suppose a firm's production function is given by Q = L 1/2*K12. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL = 72 L 1/2K1/2and MPK = 12L12K-1/2 a) Suppose the price of labor is w=18, and the price of capital is r=2. Derive the firm's total cost function. b) What is the firm's marginal cost?

Answer 1

2 ay objective is to minimize C = 18L + 2K subject to 5 = LY2kl2 7 At equilibrium, MRTS = x a MPL w TA on Y2 L-/kY2 - 18 /₂ L 2k-Y2 = 2 on k = 9 kaaL put this in Q = 2%2442 funchan [/2 (94) %2 = 0 A and k = ax 95 = 3 ē so, cost fundron, @= 18x + 2x 35 = 6 + 6 = 120 by Marginal cost delay = (129) = 12 - 12

at a 212 C = 12x12 = 144 SO Tuu=182+2 ok on K = 72-9L when, kao L20 K272 at Q = 12 KV212 TO carlo HL 4 8 9 16 36 72 2

At min. paint k=9L happens so, o 144 =182+2K an luu = 18L + 162 an L = 4 and ka 9XL = 989 = 36 and L=9, then, 9/K 122 12 I nkaro 2 4 2 = 16 and K =9, then, 1/ 2 9 /2 2 12. La 4²216 Lau, then, 4½ kV2 = 12 when, ir k= 6² = 36 then, K2 = 12 = 2 k24