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Inventories and Money Holdings in a Search Economy

Peter Diamond
Joel Yellin

Abstract

We analyze steady state equilibrium of the circular flow of money and goods in a continuous time model with infinitely lived agents. Workers sell their endowments of labor on a Walrasian labor market. Labor is used in production, the output of which flows into inventories. Capitalists consume directly out of their own inventories and use remaining inventories in a retail market. The retail market is characterized by random sequential search with prices set by capitalists on a take-it or leave-it basis. Workers thus receive a continuous flow of wages and spend money in discrete jumps at times set by a Poisson process. The equilibrium distribution of money holdings is the asymptotic steady state of this stochastic process. The economy has a unique uniform price steady state equilibrium. The more rapid the search process in the retail market the higher the absolute retail price and wage, and the higher the real wage. The instantaneous effect of an equal per capita infusion of money is to raise the price, wage, real wage, and transactions rate. The immediate post-infusion price and wage can overshoot their new asymptotic values.