Question

2. Suppose a firm's short run production function is q = 600L-L. a. At what level of labor does the firm maximize output (total product)? What is the value of total product at this point? b. Does this frim experience increasing marginal product of labor. If so, over what range of output? What happens to total product over this range? c. Over what range of output does this firm experience diminishing marginal product of labor? What is the value of total product when diminishing returns set in? What happens to total product over this range? d. At what level of labor does the marginal product of labor become negative? What happens to total product over this range?

Answer 1

q = 600L² - L³

(a)

Output is maximized when MPL = dq/dL = 0.

MPL = dq/dL = 1200L - 3L² = 0

3L x (400 - L) = 0

Either L = 0 or (400 - L) = 0

L = 0 or L = 400.

When L = 0, q = 0.

When L = 400, q = 600 x (400)² - (400)³ = 600 x 160,000 - 64,000,000 = 96,000,000 - 64,000,000 = 32,000,000

(b)

Increasing MPL occurs when dMPL/dL > 0.

Setting dMPL/dL = 0, we get

1200 - 6L = 0

6L = 1200

L = 200

Therefore, when 0 < L < 200, increasing MPL sets in. In this range, total product increases at an increasing rate, with increase in labor.

(c)

Diminishing MPL sets in when dMPL/dL < 0. Since dMPL/dL = 0 when L = 200, when L > 200, diminishing MPL sets in. In this range, total product increases at a decreasing rate, with increase in labor.

(d)

When MPL = 0, L = 400. Therefore, when L > 400, MPL becomes negative. In this range, total product decreases with increase in labor.