This study analyzes the effects of inflation on the long-run nexus between unemployment and economic growth. We introduce money demand via a cash-in-advance (CIA) constraint on R&D investment into a scale-invariant Schumpeterian growth model with matching frictions in the labor market. Given the CIA constraint on R&D, a higher inflation that raises the opportunity cost of cash holdings leads to a decrease in innovation and economic growth, which in turn decreases labor-market tightness and increases unemployment. In summary, the model predicts a positive relationship between inflation and unemployment, a negative relationship between inflation and R&D, and a negative relationship between inflation and economic growth. These theoretical predictions are consistent with recent empirical evidence. Therefore, when inflation is a fundamental variable that affects the economy, unemployment and economic growth exhibit a negative relationship.