This paper analyzes the redistributional effects of long-run inflation on income, wealth and consumption in the United States in a model economy with heterogeneous agents where money is introduced via a cash-in-advance constraint. A calibrated version of our model is able to generate patterns of income inequality that are very similar to those observed in the United States. On an aggregate level, the cost of 5% inflation is 2.5% consumption. On an disaggregate level, uniform monetary transfers by the central bank result in inflation acting as a progressive tax on consumption.