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.
Berentsen, A., Camera, G., & Waller, C. (2004). The distribution of money and prices in an equilibrium with lotteries. Economic Theory, 24(4), 887–906. http://doi.org/10.1007/s00199-004-0485-5