This paper develops a monetary endogenous growth model with capital and skill heterogeneity to analyze the relationship among inflation, growth, and income inequality. In the model inflation, growth, and inequality are jointly determined. We show that an increase in the long-run money growth rate raises inflation and reduces growth, but its effect on income inequality depends on the relative importance of the two types of heterogeneity. Inequality shrinks with the rise of inflation when capital heterogeneity dominates and enlarges when skill heterogeneity dominates. Therefore, our model supports a negative (positive) inflation–inequality relationship and a positive (negative) growth–inequality relationship when capital (skill) heterogeneity dominates. In any event, inflation and growth are negatively related.
