Shadow profit maximization and a measure of overall 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) The Non-parametric approach to production analysis. Econometrica 52:3 (May) 579-597] based on shadow prices rather than actual prices. At these shadow prices, the shadow profit of a firm is zero. The maximum shadow profit that could have been attained at some other input-output bundle is shown to be 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.