This paper examines a search model of money with divisible commodities of high and low quality, while keeping the assumptions of indivisible money and unit-inventory constraint. With no direct barter and a higher fixed cost of producing high relative to low quality, an increase in the money stock encourages the production of high-quality output by trading off the larger trading opportunities against the significance of higher fixed cost. As long as the fixed-cost differential between high and low quality is sufficiently small relative to the utility gain from high-quality consumption, the quality improvement outweighs the negative effect of higher money stocks on aggregate production, and hence implies higher welfare. The most important function of money is its role as a medium of exchange. Wicksell ([1906] 1967, p. 17) defined a general medium of exchange to be an object 'which is habitually, and without hesitation, taken by anybody in exchange for any commodity.' The main challenge facing monetary theory is to construct a model which permits the object's role in exchange to be endogenous.1 Kiyotaki and Wright (1991, 1993) seems to be the first fully coherent model which specifies the environment and equilibrium concept in a way that does not force at the outset the assumption on which objects will play a special role in trade. The Kiyotaki-Wright model departs from the physical environment of the standard general equilibrium model through the assumption that trading histories are private information. The medium-of-exchange role of money is obtained as an outcome of Nash equilibrium together with some bargaining rule in pairwise random meetings. However, the standard Kiyotaki-Wright model yields an undesirable welfare implication that an increase in the money stock eventually leads to a decrease in welfare because of a decrease in the number of agents who get to consume in a given period. The same welfare property is obtained in the models with divisible commodities, such as Trejos and Wright (1995) and Shi (1995).2 This property has been regarded as the outcome of the original Kiyotaki-Wright assumptions of indivisible money and the inventory constraint - agents can only carry one object, either commodity or money, at a time. Despite simplifying the distribution of money holdings, these assumptions impose the restriction that agents are not allowed to produce while they hold money.
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