The distribution of money and prices in an equilibrium with lotteries

We construct a tractable `fundamental` model of money with equilibrium heterogeneity in money balances and prices. We do so by considering randomized monetary trades in a standard search-theoretic model of money where agents can hold multiple units of indivisible `tokens` and can offer lotteries on monetary transfers. By studying a simple trading pattern, we can analytically characterize the monetary distribution. Interestingly, such distributions match those observed in numerically simulated economies with fully divisible money and price heterogeneity.