Question

The short-run production function in a clothing factory is given by: Q=70L2−1L3 where L denotes the size of the workforce 1. Find expressions for APL​ and MPL​ 2. Use your answers to part 1 to find the value of L which maximizes APL​. Note: round your results to 1 decimal position. The decimal symbol is "." 1. The expressions are: a. APL=70.0L​+−1.0 L2​ b. MPL​=140.0 L+−3.0 L2 2. The average product of labor is a maximum when L=35.0​

Answer 1

the value of L that maximizes APL is 70. 1. Expressions for APL (Average Product of Labor) and MPL (Marginal Product of Labor):

a. APL = Q / L = (70L^2 - L^3) / L = 70 - L

b. MPL = ∆Q / ∆L = (70(L+1)^2 - (L+1)^3) - (70L^2 - L^3) = 140L - 3L^2

2. To find the value of L that maximizes APL, we take the derivative of APL with respect to L and set it equal to zero:

dAPL/dL = -1 = 0

This implies that 70 - L = 0

Solving for L, we find L = 70 Therefore, the value of L that maximizes APL is 70.