Let the production function be q = AL^aK^b.The function exhibits increasing returns to scale if A) a + b = 1. B) a + b 1. C) a + b

Question

Let the production function be q = AL^aK^b.The function exhibits increasing returns to scale if A) a + b = 1. B) a + b > 1. C) a + b < 1. D) Cannot be determined with the information given.

Quizplus · Accepted Answer

To test for increasing returns to scale, we need to see how changing all inputs proportionally affects output. Let's multiply all inputs by a constant factor of λ. Then, the new output would be:

q' = ALS1λU1P1aS1S1P0KλS1U1P1bS1S1P0

= λ^(a+b) * q

Since λ^(a+b) > 1 (since a+b > 1), it follows that q' > q. Therefore, the production function exhibits increasing returns to scale if a + b > 1.

Let the Production Function Be Q = ALaKb

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