The transition from a Drèze equilibrium to a Walrasian equilibrium

Abstract

In this paper a price and quantity adjustment process in continuous time is considered for an economy facing price rigidities. In the short run prices are assumed to be completely fixed and the markets are cleared by quantity adjustments until a fixed price equilibrium is reached where every market is typically characterized by either supply rationing or demand rationing. Using only standard assumptions on the primitive concepts of the economy and a non-degeneracy condition, it is shown that the process indeed converges to a fixed price equilibrium for the initially given prices in the short run. In the long run prices are assumed to move upwards in the case of demand rationing on a market and downwards when supply rationing occurs, while markets are kept in equilibrium by infinitesimal quantity adjustments. Again, under standard assumptions on the primitive concepts of the economy and a non-degeneracy condition, the process is shown to reach a Walrasian equilibrium in the long run. A simplicial algorithm has been developed to make the study of the price and quantity adjustment process possible and the accuracy of this algorithm is discussed.