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.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Homogeneity; Concavity; Non-Increasing Returns to Scale; Production Function
• Subjects: D - Microeconomics > D2 - Production and Organizations > D20 - General; D - Microeconomics > D2 - Production and Organizations > D24 - Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General

References

Bone, J. (1989): “A Note on Concavity and Scalar Properties in Production,” Bulletin of Economic Research, 41(3), 213–217.

Dalal, A. (2000): “Strict Concavity with Homogeneity and Decreasing Returns to Scale,” Atlantic Economic Journal, 28(3), 381–382.

Friedman, J. W. (1973): “Concavity of Production Functions and Non-Increasing Returns to Scale,” Econometrica, 41(5), 981–984.