Consider the production function $q = \left( k ^ { \alpha } + l ^ { \alpha} \right) ^ { \beta }$ . For this function to have diminishing marginal productivities and increasing returns to scale,it must be the case that A)α 1 αβ 1 αβ 1. C)α

Question

Consider the production function $q = \left( k ^ { \alpha } + l ^ { \alpha} \right) ^ { \beta }$ . For this function to have diminishing marginal productivities and increasing returns to scale,it must be the case that A)α > 1 αβ < 1. B)α > 1 αβ > 1. C)α < 1 αβ < 1. D)α < 1 αβ > 1.

Quizplus · Accepted Answer

For a production function to have diminishing marginal productivities and increasing returns to scale, it must be the case that the sum of the exponents of input factors is greater than 1, but the exponent of any individual input factor is less than 1. That is, α + β > 1 and α < 1, β < 1. In this case, we have α = 0.5 and β = 0.5, which satisfies the condition of α < 1 and α + β > 1. Therefore, the correct choice is D, which satisfies both conditions.

Consider the Production Function q=(kα+lα)βq = \left( k ^ { \alpha } + l ^ { \alpha} \right) ^ { \beta }q=(kα+lα)β

Consider the Production Function $q = \left( k ^ { \alpha } + l ^ { \alpha} \right) ^ { \beta }$