Abstract
By the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generalizing the second welfare theorem we show that the said solutions may coincide as a common fixed point for one and the same system.Mathematical arguments invoke conjugation, convolution, and generalized gradients. Convexity is merely needed via subdifferentiablity of aggregate “cost”, and at one point only.Economic arguments hinge on idealized market mechanisms. Construed as algorithms, each stops, and a steady state prevails if and only if price-taking markets clear and value added is nil.
Highlights
Consider allocation of perfectly divisible and transferable commodities among diverse parties
Various concepts relate to this question. Most notable are those on competitive equilibrium, core, and Pareto optimum
Neither mentions any mechanism prone to preserve, select, or underpin such states. This silence motivates two questions: First, may the said concepts be brought under one shared umbrella as manifestation of a unifying fixed point?
Summary
Consider allocation of perfectly divisible and transferable commodities among diverse parties. Having preference order , endowment x ∈ dom , and thereby indifference criterion c(· | x), any exogenous price regime x∗ ∈ X∗ offers him value added (2): c∗ x∗ | x := sup x∗x – c(x | x) : x ∈ X .
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