Showing papers in "Econometrica in 1959"

The simplex method for quadratic programming

Abstract: : A computational procedure is given for finding the minimum of a quadratic function of variables subject to linear inequality constraints. The procedure is analogous to the Simplex Method for linear programming, being based on the Barankin-Dorfman procedure for this problem.

Substitution versus fixed production coefficients in the theory of economic growth: a synthesis

Abstract: Mosti growth models are based either on the assumption of fixed production coefficients for labour and capital or on the assumption of substitutability between factors. The present paper proposes a hypothesis which is a compromise between these extremes, viz., that any increment in production can be obtained by different combinations of increments in labour and capital inputs, whereas any piece of capital which is already installed will continue to be operated by a constant amount of labour throughout its life span. First, a "general model" is presented. Next, the model is solved in different special cases. In conclusion it is suggested that the proposed hypothesis would be particularly appropriate in studying the introduction of new techniques and therelationship between population growth, the rate of saving and "structural" unemployment.

Centralization and decentralization in economic organizations

Abstract: The preference for decentralization in the classic debates about planned production in a socialist 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 socialist 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 socialist 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 "millions 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

Prices of the factors of production in international trade

Abstract: The problem of international factor-price equalization is studied by using a technique which combines the Walrasian theory of general equilibrium with the theory of welfare economics. The principle of the complete or partial equalization was first enunciated by Eli Heckscher in his 1919 paper and was later elaborated by Bertil Ohlin, Paul A. Samuelson, and others. The present study shows in particular that the complete factor-price equalization occurs only in the cases in which the factor endowments in the countries are precisely the ones that arise in an equilibrium position of world trade where the factors of production as well as the commodities can move internationally.