The Transition from a Drèze Equilibrium to a Walrasian Equilibrium

In this paper a continuous time price and quantity adjustment process 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. Next prices are assumed to move upwards in case of demand rationing on a market and downwards when supply rationing occurs. Markets are kept in equilibrium by infinitesimal quantity adjustments such that at every moment in time a fixed price equilibrium results. Using only standard assumptions on the primitive concepts of the economy it is shown that the price and quantity adjustment process indeed converges to a fixed price equilibrium for the initially given prices. Moreover, in the long run, when prices are allowed to change, the process is shown to reach a Walrasian equilibrium. A simplicial algorithm is developed to approximate the price and quantity adjustment process arbitrarily close. It is shown that the path of price systems and rationing schemes generated by the algorithm converges to the path of the adjustment process.