Question

Hello, I have been struggling with this problem from my Economics homework, and I can't see to find a solution/learn how to do it. Help would be greatly appreciated, thanks in advance!

An industry can be characterized by the following production function:

Q=2.5L^.60C^.40

A) What is the algebraic expression for the marginal productivity of labor?

B) What is the algebraic expression for the average productivity of labor?

C)How would you characterize the returns-to-scale in the industry.

Answer 1

Given

Q=2.5L^0.60C^0.40

a)

Marginal Productivity of labor=dQ/dL=0.60*2.5L^0.60-1C^0.40=1.50L^-0.40C^0.40

b)

Average Productivity of labor=Q/L=2.5L^0.60C^0.40/L=2.50L^-0.40C^0.40

c)

Q=2.5L^0.60C^0.40

Let L and C are increased to xL and xC. New output is given by

Q'=2.5(xL)^0.60(xC)^0.40=2.5*x^0.60+0.40*L^0.60C^0.40=x*2.5*L^0.60C^0.40=xQ

We see that output is also increased to xQ. It means that industry exhibits constant return to scale.