Is There a Walrasian Equilibrium in Exchange Markets with Endowment Effect

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 de- mand. One of the parameters can be identified as endowment. The other is a new feature, called demand-supply gap, that leads to classical general equilib- rium if zero. Second, we provide representations of price and demand as un- bounded 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.