This study presents a framework to understand the relationship between inflation and income inequality in an open-economy Schumpeterian growth model with heterogeneous households, firm-level innovation, and cash-in-advance constraints on R&D investment. We show that the global real interest rate channel can play a key role in defining this relationship. In smaller economies that have negligible impacts on the global interest rate, income inequality is likely to exacerbate as inflation rates rise. In contrast, for larger economies that can significantly affect the global interest rate, inflation and income inequality may demonstrate a U-shaped relationship. These theoretical predictions are supported by the quantitative analysis in a model calibrated to the economies of the US and the eurozone, as well as empirical estimates using cross-country data.