Question 4 (20 points)

A firm has the short-run production function as follows:

Q = L + 15L^2 - 0.5L^3,

where Q = total products per period and L = number of workers employed per period.

4.1) (3 points) Derive the marginal product of labor (MPL).

At what number of workers (L) does the law of diminishing returns begin?

• MPL = f(L) = __________________________________
• Law of diminishing return begins when L = ___________ workers.

4.2) (3 points) Derive the average product of labor (APL). Find the number of workers (L) that maximizes the average product of labor.

• APL = f(L) = __________________________________
• When APL is at maximum point L = ___________ workers.

4.3) (6 points) Determine the boundaries (ranges of number of workers) for the three stages of production process. (Hint: you might use this =242 to solve x in a quadratic equation ax2 + bx + c = 0)

• Stage I: _____ < L _____
• Stage II: _____ < L _____
• Stage III: L > __________

4.4) (8 points) Suppose that the price of a product is $2 per unit. How many workers will the

firm hire to maximize its profit if the wage rate is $100 per period?

The firm should hire ___________ workers to get maximum profit.