Final answer:
In a Cobb-Douglas function, to achieve constant returns to scale, the sum of the exponents α (alpha) and β (beta) must equal one, indicating that output scales proportionally with inputs.
Step-by-step explanation:
To make a Cobb-Douglas function exhibit constant returns to scale, the exponents α (alpha) and β (beta) must sum to one. This mathematical condition implies that if all inputs are scaled by a common factor, then output will also be scaled by the same factor. In more technical terms, if Q is output, K is capital, L is labor, and Q = KαLβ, then for constant returns to scale, α + β = 1. In such a situation, doubling both inputs (capital and labor) would result in doubling the output, indicating that there is no change in productivity or cost per unit as scale changes. This concept is closely related to the middle portion, or the flat portion, of the long-run average cost (LRAC) curve around the quantity Q3, where increasing the scale of production neither decreases nor increases the cost per unit of output. The perfectly elastic supply curve in a constant cost industry is analogous to this condition.