Market equilibria and money

By the first welfare theorem, competitivemarket equilibriabelong to thecoreand hence arePareto optimal. Lettingmoneybe 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 commonfixed pointfor 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 clearandvalue added is nil.