Modeling monetary economies: an equivalence result

This paper offers a methodological contribution to monetary theory. First, it presents a model economy with cash-in-advance constraints, following the work of Lucas in the early 80’s; then, it specializes the model to preferences and shocks assumed in the Lagos and Wright (2005) framework. Second, it derives the main equations describing allocations under competitive pricing and demonstrates that the two models—which on the surface appear different—are mathematically equivalent. Such equivalence result is extended to stationary equilibrium under non-competitive pricing; in both models, allocations depend on a free parameter controlling price markups.