Search and leisure with idiosyncratic endowment shocks in a random-matching model

Agents who realize idiosyncratic endowment shocks (High and Low) choose between leisure and searching for a trading partner. In the non-monetary economy there are two cases: everyone enjoys leisure or everyone enters the market to barter. In the first case, money can generate an equilibrium in which all agents enter the market. In the second, money can generate an outcome impossible without money, in which High agents trade while Low agents rest. Money affects the real side of the economy by driving Low quality goods out of the market, improving the quality of traded goods.