A Monetary Theory with Non-degenerate Distributions

We construct and analyze a tractable search model of money with a non-degenerate distribution of money holdings. Analytical tractability comes from modeling decentralized exchange as directed search, which makes the monetary steady state block recursive. By adapting lattice-theoretic techniques, we characterize individuals' policy and value functions, and show that these functions satisfy the standard conditions of optimization. We prove that a unique monetary steady state exists and provide conditions under which the steady-state distribution of buyers over money balances is non-degenerate. Moreover, we analyze the properties of this distribution.