Disequilibrium Trade in a Large Market for an Indivisible Good

Disequilibrium trade can occur in a market lacking both recontracting and a computational system that maps utilities into prices. This paper studies disequilibrium trade in a large market for an indivisible good. We focus on the possible speed of adjustment when arbitrage among periods is feasible and the surplus loss. We find that incentive compatible sequential trade through a disequilibrium path is only compatible with sluggish price adjustments and sufficiently impatient agents. Thus, price adjustment does not depend on excess demand alone but on arbitrage opportunities and the willingness of agents to engage on them. We find that the upper bound on the speed of price adjustment involves a lower bound for the social surplus loss, whatever the kind of rationing. The reason is that even when the market price converges to the surplus maximizing value, as it happens when rationing is efficient, some pieces of surplus are not attainable at the current period due to arbitrage. Moreover, faster price adjustments do not imply less surplus loss, because the effect of price changes on transactions via arbitrage. Finally, under weaker-than-efficient rationing there is a one period incentive compatible trading procedure in which most of the surplus is destroyed. The procedure has the property that almost every agent in the market trades.