Knowledge that Transforms

Abstract : This paper shows that control through decentralization can be affected in general if additional information in the form of preemptive goals is delegated to individual units as well as prices. It is shown that the procedure is a robust one and results in small errors in profit. The technique of preemptive goals providing further control advantages in an economy where structural change is taking place over time as reflected by changing technological coefficient matrices of individual units is indicated.

Given a set of economic agents and a set of coalitions, a non-empty family of subsets of the first set closed under the formation of countable unions and complements, an allocation is a countably additive function from the set of coalitions to the closed positive orthant of the commodity space. To describe preferences in this context, one can either introduce a positive, finite real measure defined on the set of coalitions and specify, for each agent, a relation of preference or difference on the closed positive orthant of the commodity space, or specify, for each coalition, a relation of preference or indifference on the set of allocations. This article studies the extent to which these two approaches are equivalent.

Pontryagin's Principle can be and has been used in inventory theory, production theory, capital theory and growth theory. The idea presented in this paper shows how the principle can be used also when a firm operates in a market economy or a country in a world market. The resulting jumps in the state variables-amount of capital, amount sold of a commodity, etc.-will disappear through a reinterpretation of the system. The idea is that time is one of the variables and the speed of time can be controlled. By stopping time and letting the other variables change, one can get jumps with respect to time.