This study investigates the growth and welfare effects of monetary policy in a Schumpeterian economy featuring cash-in-advance (CIA) constraints and two engines of growth: innovation from R&D and human capital accumulation from endogenous fertility. Our theoretical analysis considers the cases of various CIA constraints. When the CIA constraint is only on consumption, higher inflation retards economic growth by weakening human capital accumulation. When the CIA constraint is only on R&D, higher inflation would generate a negative or U-shaped effect on economic growth, depending on the interplay between inflationary effects on innovation and human capital accumulation. When the CIA constraint is only on manufacturing, the growth effect of inflation could be positive (negative) if the positive growth effect from technological progress dominates (is dominated by) the negative effect from human capital accumulation. Our quantitative analysis finds a generally negative inflation-growth relationship in the calibrated economy. Moreover, the welfare effect of inflation is also negative, implying that the Friedman rule is optimal.