We adopt mechanism design to study the effects of inflation on output, trade, and capital accumulation. Our theory captures multiple channels for individuals to respond to inflation: search intensity, market participation, and substitution between money and a higher return asset. We characterize constrained efficient allocations and show inflation has nonmonotonic effects on the frequency of trades (extensive margin) and the total quantity traded (intensive margin). The model features monetary superneutrality for low inflation rates, nonlinearities in trading frequencies, and substitution of money for capital for higher inflation rates. While these effects are difficult to capture in previous models, we show how they are intimately related by all being features of an optimal trading mechanism.