# Quiz4 - firm will not produce anything if price is below...

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RUTGERS UNIVERSITY Department of Economics Intermediate Microeconomics Analysis Fall 2009 Instructor: Mriduchhanda Paul Quiz 4 Consider the production function 2 2 5 L K Q = a) Let the wage rate be \$10, and let the rental rate of capital be \$20. Derive the cost- minimizing quantities of labor and capital as a function of Q in the long run. b) Derive the long-run total cost function as a function of Q . The cost minimizing condition for employment of labor and capital is MP L /MP K = w/r Now, MP L = 5K 2 (2)L = 10K 2 L and MP K = 5(2)KL 2 = 10KL 2 Therefore, cost minimizing condition becomes 10K 2 L/10KL 2 = 10/20 That is, K/L = ½ That is, L = 2K Now, Q = 5K 2 L 2 = 5K 2 (2K) 2 = 20K 4 Therefore, K = (Q/20) 1/4 and L = 2K = 2(Q/20) 1/4 Therefore, the long run total cost = wL+rK = 10*2(Q/20) 1/4 + 20*(Q/20) 1/4 = 40(Q/20) 1/4 Suppose a firm’s short-run total cost curve is given by 2 6 5 1 STC Q Q = + + c) What is the equation for the firm’s short-run supply curve? d) How many units will the firm supply if market price is 29 P = ? a) We assume, that non-sunk fixed cost is zero, that is, all the fixed costs are sunk. In that case, the

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Unformatted text preview: firm will not produce anything if price is below the minimum average variable cost and if price more than that, the quantity produce will follow the marginal cost curve. In order to determine the shut down price, that is, the price below which the firm will not produce anything, we need to find out the minimum average cost of the firm. We know, at minimum of average cost, marginal cost and average cost are same. That is, at minimum average cost, 6Q+5 = 12Q+5 , that is 6q=0, that is. Q = 0 when average cost has reached its minimum. Therefore, the minimum AVC = 6*0+5 =5 That is when P<0 Q s =0 (By the way, MC= 12Q+5 and AVC = 6Q+5) When price is more than the shut down price, quantity supplied will follow the MC curve. That is supply function is P = 12Q+5 . That is Q S = (P-5)/12 if P > 5 Q S = 0 if P >=5 b) At P = 29, Q S = (29-5)/12 = 2...
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## This note was uploaded on 02/29/2012 for the course 220 320 taught by Professor Raven during the Summer '10 term at Rutgers.

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Quiz4 - firm will not produce anything if price is below...

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