Endogenous buyer–seller choice and divisible money in search equilibrium

In the Lagos-Wright model [R. Lagos, R. Wright, A unified framework for monetary theory and policy analysis, J. Polit. Economy 113 (2005) 463–484], the quasi-linear preferences assumption is not necessary to generate simple distributions of money holdings if individuals choose endogenously to go to the search market as buyers or as sellers. The non-convex buyer–seller choice provides an incentive for gambling in lotteries, and, as a result, the value function has a linear interval. As long as this interval is the relevant one for evaluating their future utilities, individuals behave as if their preferences were quasi-linear. In the stationary equilibrium, individuals remain inside this linear interval if the money supply does not decline.