We study competitive search in goods markets in a heterogeneous-agent monetary model. The model accounts for three stylized facts connecting inflation to consumption inequality, to price dispersion, and to the speed of monetary payments. With competitive search, individuals’ endogenous probabilities on trading events give rise to a trading-opportunity (extensive-margin) force that works in opposite direction to well-known redistributive (intensive-margin) effect of inflation. This implies a new trade-off in response to long run inflation targets. Welfare falls but liquid-wealth inequality falls and then rises with inflation as an extensive margin of trade dominates the redistributive intensive margin, when inflation is sufficiently high.