Question

Do the following production functions exhibit increasing, decreasing, or constant returns to scale? Explain your answer

a. Q=16L^0.4K^0.6+K+2

B. Q=L^0.4+K^0.6

Answer 1

(a) Q= 16L^0.4 K^0.6 + K +2

Double the inputs K and L ,we get :

= 16(2L)^0.4 (2K)^0.6 + (2K) +2

= 2 ( 16 L^0.4 K^0.6 ) + 2K +2

= 2 [ 16L^0.4 K^0.6 + K +1] < 2Q

Doubling the inputs K and L , increases the output by less than that amount. This implies that production function exhibits decreasing returns to scale.

(b) Q = L^0.4 + K^0.6

Double the inputs K and L ,we get

= (2L)^0.4 +(2K)^0.6

= 2^0.4 L^0.4 + 2^0.6 K^0.6 < 2Q

Doubling the inputs K and L , increases the output by less than that amount . This implies that production function exhibits decreasing returns to scale.