Endogenous Search, Inflation, and Welfare

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 matchingunction 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 areomplimentary. 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, theenefit 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.CONTENTS Introduction 5.1 Literature Review................................................................................8 The Basic Model 12.1 The Environment .............................................................................12.2 Individual Maximization ..................................................................15.3 Equilibrium and Steady State ..........................................................22.4 Comparative Statics ..........................................................................24 Endogenous Production of search Goods 26.1 Individual Maximization ..................................................................27.2 Market Clearing.................................................................................29.3 Defining Equilibrium and Welfare..................................................29.4 Inflation and Welfare........................................................................30 Conclusion 35 Appendix 37.1 The slope of z with respect to θ .....................................................37.2 Concavity of the individual’s objective ..........................................38.3 Slope of the welfare function..........................................................39.4 Steady state comparative statics in the second model ..................39.5 Derive inequality (8.12) ...................................................................40.6 Ensuring a slack labor constraint....................................................41eferences 4