Download PDF by Trout Rader (Auth.): Theory of General Economic Equilibrium

By Trout Rader (Auth.)

ISBN-10: 0125750404

ISBN-13: 9780125750400

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In particular, if B is positive in every component, then Zj can be set negative for some good j , for which ys is positive, and for all other z, zi can be made positive, zi sufficiently small. Then, over a short time period j will be decreasing in quantity and other commodities will increase in quantity. Therefore, at the end of this short time period in which j is not completely depleted, all commodities will exist in positive quantities. More generally, if B is indecomposable, it can be shown that the system is primitive.

If there is a T such that i t-l ^Σχ^-Σχ* i t-l for all t > T. 36 1. Efficiency In effect, the average consumption of one is better than that of the other. For example, 0t might evaluate only quantities of a utility produced by a consumer good. ), if there is a T such that i t-l T i Σ «* > t-l T Σ * or, what amounts to the same thing, t-i t-i £ ul < Σ \P for all t > T. This is the overtaking criterion presented by von Weizsäcker [1965] and treated by Koopmans [1965], Gale [1967], McFadden [1967], Atsumi [1965], and McKenzie [1968], among others.

This is the general case. For example, consider a reduction of y(t) at time t, say, by free disposal. This normally implies that y(s) is reduced for s > t. We cannot arbitrarily go out in the direction of lesser amounts in a single component, whereupon o^oo(y(0)) cannot have any interior points. Hence, o&oo(y(0)) must be augmented with other points in order to obtain the desired result. We first show that maximality implies a price system. 29 Theorem Suppose 0^oo(y(0)) is convex. Let components of cß/ao{y(Qi)) be bounded by k(t).

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Theory of General Economic Equilibrium by Trout Rader (Auth.)

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