Equilibrium and Linear Complementarity - An Economy with Institutional Constraints on Prices

Hansen, T. & Manne, A.S. (1974). Equilibrium and Linear Complementarity - An Economy with Institutional Constraints on Prices. IIASA Research Memorandum. IIASA, Laxenburg, Austria: RM-74-025

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Abstract

In the theory of perfect competition, it is supposed that there are no institutional restrictions upon prices. Much the same assumption is built into mathematical programming models. The presence of such constraints implies, for example, that the market price and the marginal productivity (shadow price) of the factors of production will not necessarily coincide. Unless such constraints are introduced, models cannot explain the simultaneous existence of excess supply of an item and yet a positive market price.

If there is a gap between market and shadow prices, this raises a question. By what set of prices are the economic agents' actions guided? In this paper, we assume that one sector of the economy, the private sector, is guided by market prices. The other, the public sector, is guided by shadow prices.

With conventional optimization techniques, it is awkward -- and sometimes impossible -- to handle this type of problem. Here we shall show that some of these features can be introduced through linear complementarity. This approach permits us to introduce institutional constraints upon prices -- in addition to the technological constraints that are normally generated through the coefficients of each activity in a linear programming model.

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