A Note on the Relationship among the Shape of the Production Possibility Frontier, ‘Returns to Scale’ and ‘Returns to Factors’ under Cobb–Douglas Production Function

Abstract

The purpose of this study is to examine relationship among returns to scale, returns to factors and the shape of the production possibility frontier under Cobb–Douglas production function. The study asks the following question: How can production possibility frontier be drawn (a) if returns to scale are constant, increasing and decreasing and (b) if returns to factors are constant, increasing and decreasing? The main finding of the study is as follows: When (a) returns to factors are constant or increasing or decreasing and (b) returns to scale (economies of scale internal to the firm) are constant or increasing or decreasing, the production possibility frontier can be bowed in or bowed out or be linear under certain conditions.