I study an economy based on Lagos and Wright (2005) where agents can modulate the probability with which they are successfully matched to a trade. A market traded search good is specified which is the input for the matching function and increases the probability of a successful match. By studying a version where search goods are exogenously endowed to agents, the model shows that the Friedman rule is optimal and search goods and money are complimentary. When the production of search goods is endogenized and when bargaining power is split among buyers and sellers there are certain values of inflation for which aggregate production is increasing in inflation. This is due not to a money-search tradeoff, as the demand for search goods and money always move together, but to the search externality which implies that inflation has different impacts on buyers and sellers. In some cases, the benefit of selling outweighs the cost of holding money and thus causes the demand for both money and search goods to rise. The welfare curve is thus non-monotonic.
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