Question

a. Suppose that a firm has the Cobb-Douglas production function = 12K0.75 0.25. Because this function exhibits returns to scale, the long-run average cost curve is , whereas the long-run total cost curve is upward-sloping, with slope. b. Now suppose that the firm's production function is = KL. Because this function exhibits returns to scale, the long-run average cost curve is upward-sloping , whereas the long-run total cost curve is upward-sloping, with slope.

Answer 1

(a) Q= 12K^0.75L^0.25

Double the inputs K and L , we get :

= 12(2K)^0.75(2L)^0.25

= 2^(0.75+0.25)[12K^0.75L^0.25]

= 2(12K^0.75L^0.25) = 2Q

This implies that increasing the inputs K and L increases the output by exactly the same amount. This implies that the production function exhibits constant returns to scale.

When the production function exhibits constant returns to scale, this mean long run average cost is horizontal ,whereas the long run total cost curve is upward sloping with constant slope.

(b)  Q= KL

Double the inputs K and L , we get :

= (2K)(2L)

= 4KL >2Q

This implies that increasing the inputs K and L increases the output by more than that amount. This implies that the production function exhibits increasing returns to scale.

When the production function exhibits constant returns to scale, this mean long run average cost is decreasing,whereas the long run total cost curve is upward sloping with declining slope.