Question

Given the short run production function, Q = 3L² – 0.1L³

( a) Write down the equations for,

(i) the marginal product of labor, MPL

(ii) the average product of labor, APL.

(b) Find the value of Q for which the MPL and APL are maximized.

(c) Show that the MPL= APL when the APL is at a maximum

Answer 1

Q = 3L² – 0.1L³

(a)

(i) marginal product of labor, MPL = dQ/ dL

= 6L -0.3L².........................(1)

(ii) average product of labor, APL = Q/L

= 3L - 0.1L²

(b) Maximizing MPL. Taking FOC of (1) wrt L and equating to 0 we get:

6 - 0.6L = 0

=> 0.6L = 6

=> L = 6/0.6 = 10

Maximizing APL. Taking FOC of (2) wrt L and equating to 0 we get:

3 - 0.2L = 0

=> L = 3/0.2 = 15

(c) Maximum APL = 3*15 - 0.1*15²

= 45 22.5 = 22.5

MPL at L = 15 = 6*15  -0.3*15² = 90 - 67.5 = 22.5

Thus, when APL is maximized, MPL = APL