Question

Given the following production function: f(L,K)=KθLα

α,β→ Constant ​
If α+θ<1 What kind of return to scale this production function experiences?

Answer 1

The production function f(L, K) = KθLα exhibits decreasing returns to scale if α + θ < 1, meaning output increases by a smaller percentage than the increase in inputs.

Step-by-step explanation:

If the production function is given by f(L, K) = KθLα with α and θ as constants, and if α + θ < 1, then this production function exhibits decreasing returns to scale. This means that if we were to increase the inputs (labor and capital) by a certain percentage, the output would increase by a smaller percentage. It's a scenario where doubling the inputs will result in less than double the output.

The basis of this conclusion lies in the concept of returns to scale in the long-run when both capital and labor can be varied. In contrast, in the short run, capital is fixed and the production function can be written as Q = f(L), focusing on labor as the variable input. In the long-run context, increasing all inputs by a factor of λ (lambda) would increase output by less than λ if α + θ < 1, confirming decreasing returns to scale.