On a Monetary Equilibrium in a Generation Overlapping Economy

Abstract

In 1958 Samuelson considered an economy with overlapping generations and argued that some financial intermediary (or introduction of money) is essential to achieve an efficient allocation. The results in his paper have been extended and criticized by various authors (e.g., Cass-Yaari [1966, 1967], Diamond [1965], Gale [1973]). Recently, the same idea was brought into slightly different framework: a general equilibrium approach to an economy with fiat money. Hayashi, in his recent paper [1976], argues that in some special class of economies there exists a monetary equilibrium (an equilibrium with positive price of money) if we consider an infinite horizon economy. This result is remarkable, although intuitively straightforward, since it is impossible to obtain this equilibrium result in a finite horizon economy without some artificial money absorbing scheme (e. g., Starr [1974], Kurz [1974], Heller [1974], Okuno [1976]). In an infinite horizon economy, any consumer can pass money to another consumer, while there must be some consumer who must end with money holding in a finite economy. Yet, the existence of a monetary equilibrium is not as simple as the previous sentence may suggest, for all other consumers may refuse to accept money if they do not wish to hold it. Hayashi's contribution is important in that he characterizes an economy where such incentives for trades of money exist. However, his model is restricted in two ways. First, he considers an economy where the timing of sales and purchases is exogenously determined for all individuals. This enables him to consider a group of buyers and a group of sellers at each moment. A seller at some instant would become a buyer in the next moment and then leave the market. A consumer's preference is defined over consumption for these two periods (when he is a seller and when he is a buyer). As Hayashi himself observed, one of the most important problems in monetary theory is the existence of idle balances. It would certainly be more interesting to consider an economy where the decision to enter the market and therefore the decision of idle balances are also endogenous. Secondly, all of the previous works on consumption loan models (including Hayashi's) deal essentially with a stationary or balanced growth economy. One