Let the production function be q = AL^aK^b. The function exhibits increasing returns to scale if

Question

Quizplus · Accepted Answer

To determine whether the production function exhibits increasing, decreasing or constant returns to scale, we need to examine the relationship between the output and the factor inputs when all factor inputs are increased in proportion. 
Let's increase all factors by a constant factor k: 
q(kS1, kU1, K) = AL(kS1)U1P1aS1S1P0(K)S1U1P1bS1S1P0 
= k^(a+b)AL(S1)U1P1aS1S1P0(KS1)U1P1bS1S1P0 
= k^(a+b)q(S1, U1, K)

Therefore, the production function exhibits increasing returns to scale if a+b>1, constant returns to scale if a+b=1, and decreasing returns to scale if a+b<1. 
In this case, we have a+b>1, therefore, the function exhibits increasing returns to scale.

Let the Production Function Be Q = ALaKb

Let the Production Function Be Q = AL^aK^b