Q1. Suppose a firm has the Cobb-Douglas production function Q = f(K, L) = AK LB,...

 

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Q1. Suppose a firm has the Cobb-Douglas production function Q = f(K, L) = AK "LB, where a, ß > 0, a + B = 1; A is a positive parameter that represents technology, K is capital, and L is labor. Using this function, show the following. (1) Does this production function exhibit increasing, constant, or decreasing returns to scale? Why? (2) Please draw the set of three isoquants that support your answer in part (1). What are the characteristics of these isoquants? (3) Please find MP, and MPK. (4) Please show diminishing marginal productivities for both K and L. (5) Given the total cost outlay such as C = wL + rK where w is the wage of labor and r is the rental price of capital. Please determine the amount of labor (L*) and capital (K*) that the firm should use in order to maximize output. (6) Suppose that Q = 5√KL,w = 5, r = 20, C = 1000. Please find the optimal quantities of labor and capital that this firm should hire. How much output can the firm produce? Q1. Suppose a firm has the Cobb-Douglas production function Q = f(K, L) = AK "LB, where a, ß > 0, a + B = 1; A is a positive parameter that represents technology, K is capital, and L is labor. Using this function, show the following. (1) Does this production function exhibit increasing, constant, or decreasing returns to scale? Why? (2) Please draw the set of three isoquants that support your answer in part (1). What are the characteristics of these isoquants? (3) Please find MP, and MPK. (4) Please show diminishing marginal productivities for both K and L. (5) Given the total cost outlay such as C = wL + rK where w is the wage of labor and r is the rental price of capital. Please determine the amount of labor (L*) and capital (K*) that the firm should use in order to maximize output. (6) Suppose that Q = 5√KL,w = 5, r = 20, C = 1000. Please find the optimal quantities of labor and capital that this firm should hire. How much output can the firm produce?

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Answer 1 This function exhibits constant return to scale because ... View the full answer