Question: 3. Consider the following production function with inputs L and K: Q = (L + K)^2 The input prices of L and K, w and

3. Consider the following production function with inputs L and K: Q = (L + K)^2 The input prices of L and K, w and r respectively, are both 1. (a) Is it constant, increasing or decreasing return to scale? Consider a target production of Q = 64. (b) What are the marginal products of capital and labor respectively at K = 25; L = 9? Should the firm use more labor or capital? (c) What are the marginal products of capital and labor respectively at K = 4; L = 36? Should the firm use more labor or capital? (d) What is the optimal use of capital and labor given the production function and price? What is the cost? ? (e) Now if r = 2 but w = 1 as before, what is the optimal use of labor and capital? How does it different from before? (Leave your answers in decimal places if it is the case.) (f) Now, consider a technological advancement such that Q = 2(L + K)^2 and w = r = 1, then what is the optimal level of K and L? Any change in K/L? What is the new cost? (g) Now, consider a technological advancement that only promotes the productivity of capital Q = (L + 2K)^2 while w = r = 1, then what is the optimal level of K and L? Any change in K/L? What is the new cost?

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