The Production Possibility Frontier as a Maximum Value Function: Concavity and Non-increasing Returns to Scale
This paper makes both a methodological as well as a substantive contribution to the literature on the concavity of the production possibility frontier (PPF). Rather than using the standard, calculus‐based techniques, the method here relies on the fact that the PPF is a maximum value function. The consequent simplification in analysis makes it possible to demonstrate that the conditions which are sufficient to guarantee global concavity of the PPF are considerably less stringent than those stated in the literature. Existing analyses have assumed that production functions are (a) concave and homothetic, or (b) display non‐increasing returns to scale (NIRS) and homogeneity. This paper shows that concavity without homotheticity, or NIRS and quasiconcavity without homogeneity (or even homotheticity) are sufficient, thus greatly increasing the generality of existing results. The analysis can be extended to include situations in which the input set includes industry‐specific factors.
Dalal, Ardeshir J. "The Production Possibility Frontier as a Maximum Value Function: Concavity and Non‐increasing Returns to Scale." Review of International Economics 14, no. 5 (2006): 958-967.