Shadow Profit Maximization and a Generalized Measure of Inefficiency

Determining the profit maximizing input-output bundle of a firm requires data on prices. This paper shows how endogenously determined shadow prices can be used in place of actual prices to obtain the optimal input-output bundle where the firm.s shadow profit is maximized. This approach amounts to an application of the Weak Axiom of Profit Maximization (WAPM) formulated by Varian (1984) based on shadow prices rather than actual prices. At these prices the shadow profit of a firm is zero. Thus, the maximum profit that could have been attained at some other input-output bundle is a measure of the inefficiency of the firm. Because the benchmark input-output bundle is always an observed bundle from the data, it can be determined without having to solve any elaborate programming problem. An empirical application to U.S. airlines data illustrates the proposed methodology.

Input Price Variation Across Locations and a Generalized Measure of Cost Efficiency

We propose a nonparametric model for global cost minimization as a framework for optimal allocation of a firm's output target across multiple locations, taking account of differences in input prices and technologies across locations. This should be useful for firms planning production sites within a country and for foreign direct investment decisions by multi-national firms. Two illustrative examples are included. The first example considers the production location decision of a manufacturing firm across a number of adjacent states of the US. In the other example, we consider the optimal allocation of US and Canadian automobile manufacturers across the two countries.