Answer to Question #135872 in Economics of Enterprise for Hadgu

Question

Consider the following short run production function: Q=8L2-0.3L4
a. Find the value of L that maximizes output
b. Find the value of L that maximizes marginal product
c. Find the value of L that maximizes average product

Answer 1

a.)

First Find the Marginal Product (MP) and then set the MP equal to Zero , then solve for L:

MP = 16L - 1.2L²

16L - 1.2L² = 0

L(16 - 1.2L) = 0

Solving for L = 13.3

b.)

MP = 16L - 1.2L²

Take the derivative and set it equal to zero.

16L - 2.4L = 0

Solving for L = 6.7

c.)

We find where the elasticity of production equals 1 or, where MP = AP [MP / AP = 1]

MP = 16L - 1.2L²

AP = 8L - 0.3L²

16L - 1.2L² / 8L - 0.3L² = 1

16L - 1.2L² = 8L - 0.3L²

8L - 0.9L² = 0

L(8 - 0.9L) = 0

Solving for L = 7.1