A globally and universally stable quantity adjustment process for an exchange economy with price rigidities

An exchange economy with fixed prices is considered. In this setting a Walrasian equilibrium generically does not exist. In a so-called Dreze equilibrium rationing on excess demand and on excess supply of the non-numeraire commodities is present. In this paper a new type of adjustment process is introduced, namely an adjustment process in quantities or, equivalently, rationing schemes. The total excess demand as a function of the rationing schemes does not satisfy the assumptions under which any of the existing price adjustment processes converges to aWalrasian equilibrium. From the main theorem it follows that the quantity adjustment process converges generically to a Dreze equilibrium. The assumptions made with respect to consumptions sets, preferences and initial endowments are standard. No restrictions are made with respect to the initial state of the economy, which determines the starting point of the adjustment process. Moreover, it follows from the main theorem that the number of Dreze equilibria is generically odd.