A price adjustment process in a rationed economy
This paper presents a discrete tatonnement process applied to a pure exchange economy. More generally, the approach is applied to a function of rational excess demand (R.E.D.) which is an extension of the Walrasian excess demand. The author considers the discrete random process of price adjustment. During any period of time only one price can be changed in the process. This price is selected randomly. In the case of shortages of some products the price is increased by a given quantity. In the case of slacks it is decreased by the same quantity if the decrease does not transform the slack of the market into a shortage. The new price is tested and, if shortage appears, the previous price is restored. If all markets are free of slack and the variation of any price by a given quantity results in shortages, then the amount at which the price is varied must be diminished. The paper presents the following steps in proving the main result: Theorem 1 shows the convergence for an algorithm that finds rationing levels that give rise to a fixed price equilibrium for prices in each step of the process. Lemma 1 proofs that the sequence of prices is non- converging to the boundary or to infinity. Lemma 5 shows that for a fixed value of price change, the process reaches a stop point. Theorems 2 and 3 show that the sequence of stop points converges to a competitive equilibrium. An example of an exchange model is presented giving the paper more accuracy. The Appendix contains the proofs of all propositions and theorems. The paper is well-written, with rich bibliographical references and very clear demonstrations.
scientific article; zbMATH DE number 700856
scientific article