Question

Cobb-Douglas Production Function & Cost of Production

1. A firm’s production function is given as –

q = 2K^0.4N^0.6

1. What kind of returns to scale does this production technology exhibit? Justify your answer.
2. Find out the expression for the marginal product of labor.
3. Find out the expression for the marginal product of capital.
4. Find out the expression for MRTS.

Answer 1

a)

Given production function is Cobb-Douglas. Let us check sum exponents.

Sum of exponents=0.40+0.60=1.0

Since sum is equal to 1, we can say that production function exhibits constant returns to scale (CTS)

b)

Marginal product of labor can be determined by differentiating q with respect to N, we get

MP_N=dq/dN=0.6*2K^0.4N^0.6-1=1.2K^0.4N^-0.4

c)

Marginal product of capital can be determined by differentiating q with respect to K, we get

MP_K=dq/dK=0.4*2K^0.4-1N^0.6=0.8K^-0.6N^0.6

d)