Ruhr Economic Papers

Ruhr Economic Papers #82

Is there a Walrasian Equilibrium in Exchange Markets with Endowment Effect

by Christian Schwarz and Uwe Stroinski

Universit├Ąt Duisburg-Essen, 01/2009, 19 S./p., 8 Euro, ISBN 978-3-86788-091-6

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Abstract

We provide an axiomatic framework for exchange markets with a willingness- to-pay/willingness-to-accept discrepancy. First, we obtain a two parameter family of market invariants under price-scaling representing the excess demand. One of the parameters can be identified as endowment. The other is a new feature, called demand-supply gap, that leads to classical general equilibrium if zero. Second, we provide representations of price and demand as unbounded operators on an infinite dimensional Hilbert space. We prove that neither can this space be finite dimensional nor can these operators be bounded. Third, if the demand-supply gap is not zero we obtain that price and demand are not simultaneously sharply measurable and consequently a Walrasian equilibrium does not exist.

JEL-Classification: D50, D51, D01, D03

Keywords: General equilibrium theory; endowment effect; non-existence of equilibrium

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