310-1 Winter 2008 PS5

# 310-1 Winter 2008 PS5 - Economics 310-1 Problem Set 5 1...

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Economics 310-1 Problem Set 5 1. Consider the production function Q = 2K 1/3 L 1/3 . What can be said of the returns to scale for this production function? What is the equation of the isoquant when Q = 10? 2. A firm purchases capital and labor at prices of r=8 and w=4, respectively. With the firm’s current input mix, the marginal product of capital is 12 and the marginal product of labor is 20. Is this firm minimizing its costs? If so, explain how you know. If not, explain what the firm ought to do. 3. A firm produces output with the production function Q = K 1/2 L 1/2 . If w = 1 and r = 4, what quantities of capital and labor should the firm employ if its goal is to produce 2 units of output? 4. A firm with the production function Q = 2K 1/2 L 1/2 is currently utilizing 8 units of labor and 2 units of capital. If this is the optimal input mix, and if total cost is 16, what are the prices of labor and capital? 5. Consider a firm faced with the following production technology: Q = F(K,L) = K 1/2 + L 1/2 . Assume that r = 2 and w = 1. a) Suppose first that the firm is operating in the short run so that the level of capital is fixed at K # = 16. Derive the short run demand for labor (i.e., express L as a function of the quantity to be produced, Q). [The answer is L * = 0 for Q no greater than 4 and L * = (Q-4) 2 for Q>4. Show how to derive this result.] b) Derive the SR TVC function. [Answer: TVC(Q) = 0 for Q no greater than 4 and TVC(Q) = (Q-4) 2 for Q>4.] c) Derive the SR TC function. d) What is the SR AVC function for Q > 4? e) What is the SR ATC function for Q > 4? f) What is the SR MC function for Q > 4?

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310-1 Winter 2008 PS5 - Economics 310-1 Problem Set 5 1...

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