Mathematical programming in economics by physical analogies

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Abstract
This article is the third of a series of three in which we establish and solve a physical analogy of the economic model underlying mathematical programming. In the third article the concept of equilibrium is de rived from the basic notion of a static mechanical system at rest, and it is shown how, by refining this concept, it can be extended to dynamic physical systems. In this process it is also explained why an extremum value of a state-function determines an equilibrium state of a system. From an economic viewpoint the physical concept of equilibrium is identified with that of a perfectly competi tive market, and it is demonstrated how this concept dif fers from the equilibrium concept of a monopolist. For comparison, industries with one and two outputs are considered. From a mathematical programming viewpoint both linear and quadratic problems are discussed in terms of methods of classical mechanics. In particular it is shown that the simplex method can be derived from Fourier's inequality for equilibrium on a boundary and that the Kuhn-Tucker conditions are statements analogous to Kirchhoff's mesh law for an electrical network.

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