Answer to Question #152954 in Microeconomics for sara

Question

1. Given the production function:

Q = A L½ K½

What returns to scale, does this function exhibit? Why?

2. Prove that MRTS = MP L / MP K

Answer 1

Solution:

1.). This function exhibits a constant return to scale.

This is because an increase in inputs, which are capital and labor results in the same proportional increase in output. In constant return to scale, increasing the input numbers leads to an equivalent increase in the output numbers.

 

2.). The marginal rate of technical substitution (MRTS) is the rate at which a firm can substitute capital (K) with labor (L). It then equals the change in capital to change in labor which finally equals the ratio of marginal product of labor (MP_L) to the marginal product of capital (MP_K).

MRTS (K, L) = - $(\frac{ΔK}{ΔL} )$ = $\frac{MP_{L} }{MP_{K} }$

Where:

K = Capital

L = Labor

MP = Marginal products of each input

$(\frac{ΔK}{ΔL} )$ = Amount of capital that can be reduced when labor is increased (usually by one unit).