Question

Suppose that you are given the following production function:

Q = 100K0.6L0.4

For each of the following production functions, determine whether returns to scale are decreasing, constant, or increasing when capital and labor inputs are increased from K = L = 1 to K = L = 2.

a. Q = 25K0.5L0.5

b. Q = 2K + 3L + 4KL

Answer 1

Q = 100K^0.6L^0.4

When K = L = 1, We get Q = 100*1*1 = 100

When K = L = 2, we get Q = 100*2^0.62^0.4 = 200

Since doubling the inputs has led to doubling of output, there are constant returns to scale

(a) Q = 25K^0.5L^0.5

When K = L = 1, We get Q = 25*1*1 = 25

When K = L = 2, we get Q = 25*2^0.52^0.5 = 50

Since doubling the inputs has led to doubling of output, there are constant returns to scale

(b) Q = 2K + 3L + 4KL

When K = L = 1, we have Q = 2 + 3 + 4 = 9

When K = L = 2, we have Q = 4 + 6 + 16 = 26

Since doubling the inputs has led to more than doubling of output, there are increasing returns to scale