Question

Returns to scale. A production function has constant returns to scale with respect to inputs with inputs K and L if for any z > 0:

 F(z · K, z ·L) = zF(K, L),

 For example, for a production function with constant returns to scale, doubling the amount of each input (i.e., setting z = 2) will lead to a doubling of the output from the production function. A production function has increasing returns to scale if for any z >1:

 F(z · K, z ·L) > zF(K, L)

 and decreasing returns to scale if for any z > 1:

 F(z · K, z ·L) < zF(K, L)

 Answer the following.

 (a) Show that the Cobb-Douglas production function exhibits constant returns to scale.

 (b) For each of the following hypothetical production functions, determine whether the function has constant, increasing, or decreasing returns to scale. Show your work.

 i. F(K, L) = A+ αK + (1 - α)L

 ii. F(K, L) = A·K·L

 iii. F(K, L) = AK^αL^γ where α +γ < 1.

 

Answer 1

Answer 2

Solution: