Responding to the Inflation Tax

We adopt mechanism design to study the long-run consequences of inflation on aggregate output, trade, and welfare. Our theory captures multiple channels for individuals to respond to the inflation tax: search intensity (the intensive margin), market participation (the extensive margin), and substitution between money and a higher return asset. To determine the terms of trade in pairwise meetings, we consider socially optimal allocations that are individually rational and immune to pairwise defection. We characterize constrained efficient allocations and show that inflation has non-monotonic effects on both the frequency of trades and the total quantity of goods traded. The model reconciles several qualitative patterns emphasized in empirical macro studies and historical anecdotes, including monetary superneutrality for low inflation rates, nonlinearities in trading frequencies, and substitution of money for capital for high inflation rates. While these effects are difficult to capture in previous monetary models, we show how they are intimately related by all being features of an optimal trading mechanism.