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Quiz _3 - Production Function - Solutions

Quiz _3 - Production Function - Solutions - MP L = dQ/dL =...

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Quiz #3 – Production Functions 1) Currently the wage rate is \$6/hr and capital is rented at \$12/hr. Assume the marginal product of labor is 50 units of output per hour and the marginal product of capital is 75 units of output per hour. a) Is the firm using the cost-minimizing combination of labor and capital? How do you know? Since r w MP MP K L , we know that the firm is not using the cost-minimizing combination. b) If not, should the firm increase or decrease the amount of capital used in its production process? Since 6 50 = w MP L > 12 75 = r MP K the firm is getting more “bang for its buck” from labor. It should therefore decrease the amount of capital used and instead use more labor. 2) A firm’s production function is given by 2 1 2 1 L K Q = and its capital is fixed at 1 unit. a) Calculate the marginal product of labor (MP L ) when 4 units of labor are utilized. i. ( Hint : remember that MP L is dQ/dL, or the derivative of the prod function with respect to L.)

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Unformatted text preview: MP L = dQ/dL = L K 1 * * 2 1 remember that we’ve fixed K=1, and substituting in L=4 leaves us with: MP L = ½ * 1 * ½ = ¼ //home/vdimitrov/16843/625943b21c521351703364700710e2e7932bd68c.doc 1 b) Suppose the firm can hire labor at a wage of \$5 per hour and output can be sold at a price of \$25 per unit. Determine the profit-maximizing levels of labor and output. i. ( Hint : Remember that the firm maximizes its profit when VMP = P * MP L = w ) Part 1: From the hint, \$25 * MP L = \$5 Hence, the firm profit-maximizes when MP L = \$5 / \$25 = 1/5 Part 2: At what point does MP L = 1/5? (Remember, capital is still fixed at K=1) In other words, at what level of labor L does the marginal product of labor = 1/5? MP L = L K 1 * * 2 1 = 5 1 ; since K=1, this simplifies to: 5 2 1 = L so 2 5 = L or L = 25/4 //home/vdimitrov/16843/625943b21c521351703364700710e2e7932bd68c.doc 2...
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Quiz _3 - Production Function - Solutions - MP L = dQ/dL =...

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