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A note on concavity, homogeneity and non-increasing returns to scale

Prada-Sarmiento, Juan David (2010): A note on concavity, homogeneity and non-increasing returns to scale.

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Abstract

This paper provides a simple proof of the result that if a production function is homogeneous, displays non-increasing returns to scale, is increasing and quasiconcave, then it is concave. If the function is strictly quasiconcave or one-to-one, homogeneous, displays decreasing returns to scale and if either it is increasing or if \mathbf{0} is in its domain, then it is strictly concave. Finally it is shown that we cannot dispense with these assumptions.

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