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In the short run, we assume that capital is a fixed input and labor is a variabl

ID: 2441119 • Letter: I

Question

In the short run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q L, K, where q is output,L is workers, and K is the fixed number of units of capital. A specific equation for the production function is given by or, when K 24, The level of output q for 10 units of labor input is enter your response rounded up to two dec mal paces . The average productivity of these 10 units of labor isur response rounded up to to ecimal piaces) The marginal productivity of using one more unit of labor input is (enter your response rounded up to two decimal places). Given the relationship between the average productivity and the marginal productivity, the average productivity of labor is

Explanation / Answer

Production function is given by q = (8 x 24 x L) + 5 x (L^2) - (1/3) x (L^3)

When L = 10, we have

Level of output = q =  (8 x 24 x 10) + 5 x (10^2) - (1/3) x (10^3) = 2086.67

Average productivity = q/10 = 2086.67/10 = 208.67

Marginal product = 8 x 24 + 10 x L - (1/3) x 3 x (L^2) = 8 x 24 + 10 x 10 - (1/3) x 3 x (10^2) = 192

Since AP > MP, it must be true that Average product is falling.