Knowledge that Transforms

THE MULTI-PRODUCT firm occupies a prominent place among important but neglected topics in economic theory. Barring the programming approaches, a search of the literature reveals no comprehensive theoretical treatment of the subject. Indeed the brief development by Hicks in the mathematical appendix to Value and Capital [6] is probably the most thorough treatment in the sense of considering both the production and sales activities of the firm. Since Hicks allots only four pages to this topic, this is a remarkable state of affairs. While the literature on all phases of the multi-product firm is scanty, a few writers have considered the selling side of such a firm; the works of Bailey [1], Clemens [3], and Weldon [10] may be cited in this connection. On the cost and production side the literature is virtually non-existent. Even the work of Carlson [2], a standard reference for twenty years, deals only with the special case of joint cost but not with any other aspect of the multi-product firm. The purpose of this paper is to present a theory of cost and production for the multi-product firm. In developing this theory, the traditional concept of the firm as a social mechanism that connects the markets for factors of production with the markets for finished products will be retained. This is in contrast to the usual inward looking view of the firm that appears in the programming literature. But once the problem is clearly stated in traditional terms, it becomes apparent that the Kuhn-Tucker theorem, which can be thought of as the logical basis of the optimization techniques of activity analysis, can be used in a straightforward way to solve the problems of cost and production in the multi-product firm. The solution of the problem will show that the optimum conditions for the multi-product firm are different from those of the single-product firm. These differences are discussed briefly in the final section of the paper.

The preference for decentralization in the classic debates about planned production in a economy has appeared more recently in the context of an organization that maximizes, subject to constraints, a scalar-valued function of its decisions. This article seeks a basis for the preference. A class of schemes for organizational decision-making is defined, and decentralized (in the classic sense), centralized, and unrestricted subclasses are considered. Criteria for ranking the schemes are obtained and applied in a simple illustrative organization. It is found that a general preference for one of the subclasses cannot be defended without further restricting the model substantially. THIS PAPER concerns an economic organization which is an abstraction from the profit-maximizing firm. It concerns the problem which confronts the organization when it must choose among alternative schemes, exhibiting varying degrees of centralization, for sharing among its members the task of regularly revising its decisions in the face of a changing environment. 1. BACKGROUND OF THE PROBLEM Some of the major issues involved in this choice appeared originally in the old economic debate about decentralized versus centralized planning in a state. Recently these issues seem to have been revived in the different context of the organizations which concern us here. Several decentralized schemes have recently been shown to approach optimal decisions in such organizations, and it has been regarded as promising that they are in some important respects analogous to the decentralized schemes which were the final fruit of the debates of socialist economics. The outcome of the debate about the centralized control of a economy, which started with Barone [4], gained momentum with Hayek [9] and von Mises [10], and petered out after Lange [13] and Lerner [14],2 was as follows: virtually all participants3 agreed that there exists only one feasible mechanism for solving the of equations in millions of unknowns required to find a Pareto Optimum (in which no one's consumption of any commodity can be increased without decreasing someone's 1 This paper is based on [16], a longer study. For guidance in the original study the

The traditional method of estimating Engel curve parameters uses either (recorded) income or total expenditure as an independent variable in least squares analysis. Neither of these is, however, a satisfactory index of the economic position of the family. This results in biased estimates of the income elasticities of the various consumption categories. The bias can, however, be eliminated in large samples by using both income and total expenditures in the estimation procedure. This can be accomplished by applying the method of variables to Engel curve analysis, with recorded income serving as the instrumental variable. Having formulated consistent estimation procedures, we use empirical data to investigate and analyze the direction and size of the biases in the traditional estimates of income elasticities of various commodity groups. IT IS COMMON practice to use current Y, or perhaps more often, total expenditures, C, as independent in least squares analysis of Engel curves. Strong objections, however, have recently been raised against the applications of the least squares procedures to family budget studies. Friedman [3] argued that spending decisions are based on permanent income, a concept which is generally inadequately represented by Y as obtained from household records. The divergence between the empirical measure of income and its theoretical counterpart leads in Friedman's model to biased estimates of the true parameters. The objection to the use of C as regressor has been raised and analysed by Summers [9]. The main point of Summers' contribution is that C and its components (the dependent variables) are endogenous to the consumer and are determined simultaneously. As is well known, the classical method of least squares leads in the above circumstances to biased estimates of the true parameters, i.e., the parameters of the relation between the systematic parts of C and its components. In this paper we shall present a method of obtaining consistent estimates of the true parameters of Engel curves when C is used as an explanatory variable. Our method consists of using Y (as recorded in budget studies) as an instrumental variable which eliminates the simultaneous equations bias from the relation between C and its components. Some empirical estimates