Question

Woodmaster uses labour (L) and capital (K) to produce furniture (Q). Woodmaster’s production function is given by

=(Kᵃ+ᵃ)¹⁻ᵃ,

where >0,K>0,>0. Suppose =0.73.

(a) The production function exhibits which returns to scale?

a. constant

b. increasing

c. decreasing

Answer 1

Woodmaster's production function, given by Q = (K^aL^(1-a)) with a = 0.73, exhibits constant returns to scale because the sum of the output elasticities with respect to capital and labor equals 1.

Step-by-step explanation:

The production function given by Woodmaster is Q = (KaL1-a), where a stands for the output elasticity with respect to capital. To determine the type of returns to scale that this production function exhibits, we must examine the value of a. In this case, since a = 0.73, it implies that capital contributes 73% and labor contributes 27% to the production process. By analyzing the sum of the exponents of capital and labor (which are a and 1-a, respectively), we can conclude the type of returns to scale.

If the sum of the exponents is equal to 1, the production function exhibits constant returns to scale. If the sum is greater than 1, it exhibits increasing returns to scale. And if the sum is less than 1, it exhibits decreasing returns to scale. Since a + (1-a) = 1, Woodmaster's production function exhibits constant returns to scale.