Mathematical programming in economics by physical analogies

REVIEW OF PART I AND PREVIEW OF PART II This article is the second of a series of three in which we establish and solve a physical analogy of the economic model underlying mathematical programming. Basically, the first article (published in SIMULATION last month) was a reexamination of the fundamental assumptions underlying quasi-static models in economics and engineering, with a view to the establishment of a conceptual framework common to both disciplines. At the microscopic level it was demonstrated that the assumptions of perfect competition can be cast in a form analogous to the one used in statistical physics. At the macroscopic level it was shown that measure ments in economics and physics can be classified in iden tical manners with the result that derived relationships, like Ohm's law and demand curves or electric power and total revenue, can be made analogous concepts. On this basis it was then asserted that underlying economics we find two basic laws which, apart from a single change in sign, are completely analogous to the well-known First and Second Laws of thermodynamics. The present article is primarily a reformulation of the Walrasian economic model, which underlies mathemati cal programming, into an analogue electrical network. In accordance with the tradition of physics, the Wal rasian system of equations is derived from the postulates of the First and Second Laws of economics. The advan tage of this approach, which differs from conventional economic expositions, is that it permits a nearly auto matic establishment, term for term, of the corresponding electrical network model. The constraints and state-functions of the electrical analogue are formulated by modern network techniques in order to separate, in the economic formulation of the Walrasian system, the analytical aspects from those more general aspects which are involved in the design of an economic production system.