Two Monetary Models with Alternating Markets

We examine two monetary models with periodic interactions in centralized and decentralized markets: the cash-in-advance model and the model in Lagos and Wright (2005). Given conformity of preferences, technologies and shocks, both models reduce to a single di?erence equation. In stationary equilibrium, such equations coincide when the price distortion present in one model, due to Nash bargaining, is replicated in the other using a tax on cash revenues. In that case, the quantitative implications for the welfare cost of in?ation in each model are also comparable. Di?erences in the model’s performance reduce to di?erences in the pricing mechanism assumed to govern those transactions that must be settled with the exchange of cash.