Since   \(L_{r+\pi^e} < 0\)  ; \(L_Y > 0\)  ;   \(0 < \frac{\partial p}{\partial m} < 1\)     and   \(\frac{\partial \pi^e}{\partial m} > 0\), an increase i the money supply will still lower the real interest rate. Compared to question (b),   \(\frac{\partial r}{\partial m}\) is larger because of the effect of inflation expectation on \(\frac{\partial r}{\partial m}\)    is positive. This means that to achieve a given change in r, a smaller change in m is required than in question (b).

Hence an increase in the money supply does not affect the real interest rate in the case of a complete and instantaneous price adjustment.