Using US cross-sectional data, this paper calculates the welfare cost of a 10 percent inflation for different individuals and finds that the difference in cost between the poorest 20 percent, measured by their net worth, and the richest 20 percent is in the order of 102 percent. That is, a poor person is on average willing to forgive 102 percent more of their total consumption in order to have inflation reduced from 10 percent to 0. In absolute terms this represents a cost of 0.461 percent of consumption for the poorest and 0.228 percent for the richest. I accomplish this by introducing preference heterogeneity in a monetary search model first developed by Lagos and Wright, and calibrate the model to match each agent's type of cash holdings, approximated by their holdings in transactional accounts that bear almost no interest, as a fraction of their net worth using data from the Survey of Consumer Finances. I also show that this welfare difference increases to 130 percent (2.28 percent for the poorest 20 percent and 0.992 percent for the richest 20 percent) whenever frictions in the use of money are imposed (holdup problem). This distributional effect is further augmented if more frictions in the terms of trade are present. The ability to explicitly model these frictions is the advantage of using this model. Hence, inflation in this framework, as other studies have shown, acts as a regressive consumption tax; and this regressiveness is augmented with the holdup problem.