AbstractThis paper analyzes the long‐run dynamics with which decreasing marginal impatience (DMI) is consistent with a saddle‐path equilibrium in a Sidrauskian economy. With exogenous growth, this occurs with a strong substitutability between capital and money. Otherwise, diminishing returns to capital have to be stronger than in a nonmonetary setting if capital and money are complements. With endogenous growth, saddle‐path stability ensues when the rate of time preference—the rate at which “impatience” is increasing—exceeds the rate at which the real economy is growing along a balanced growth path. Two monetary implications also emerge. One, DMI can be consistent with both a negative and positive long‐run inflation‐growth nexus. Two, under capital‐money substitutability, the Friedman optimal rule might even fail to hold.