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 = f (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:
q= 8KL + 5L² - (1/3)L³
or, when K = 27,
q= (8x 27xL) + 5L² - (1/3)L³.
Required:
1) The level of output q for 6 units of labor input is ______. (enter your response rounded up to two decimal places).
2) The average productivity of these 6 units of labor is ______.(enter your response rounded up to two decimal places)
3) The marginal productivity of using one more unit of labor input is ______. (enter your response rounded up o two decimal places).
4) Given the relationship between the average productivity and the marginal productivity, the average productivity of labor is ______.