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Profit-maximizing decision rules, Production-inventory type models, Dynamic optimization


Econometrics | Law and Economics


A large and growing number of studies attempt to determine the important factors affecting firms' decisions with respect to price, output, and inventories. A striking feature of this literature is the embarrassingly large number of alternative models—all allegedly consistent with the principles of profit maximization—which are used to justify various reduced form or behavioral equations to be estimated with the appropriate firm or industry data.

It is rare, however, that the equations to be estimated are derived rigorously from the underlying model. Because of this, the restrictions placed on the equations to be estimated are often limited at worst to nothing more than specifying which variables should be included in the regression, and at best to fixing the algebraic signs of some of the coefficients. As a consequence, it is frequently difficult or impossible to discriminate among different models involving the same list of variables.

The present paper is concerned with these problems. In it, I derive the profit-maximizing decision rules implied by a variety of alternative cost structures. The goal of the study is to demonstrate that different assumptions about the cost structure, perhaps equally plausible on a priori grounds, imply differences in the corresponding optimizing behavior, and to point out specifically what those differences are. In addition, since differences among the decision rules are interesting not only in themselves (for purposes of regression analysis) but also because of the differences they imply in the response of firms to changes in the environment, the decision rules corresponding to the various cost structures are subjected to a dynamic analysis in which various patterns of demand are simulated, and the different behavior patterns compared.

The ultimate goal of the study is to lead to models of the firm that have superior explanatory and predictive power to those encountered to date. Even if that promise is not fulfilled, however, the study should lead to an increased understanding of the way various elements of the objective function interact to generate optimal decisions for the important variables over which the firm has control.

Publication Citation

Published in: American Economic Review, vol. 62, no. 3 (June 1972).