Naïve agents with non-unitary discounting rate in a monetary economy

Abstract

We incorporate naïve agents with a non-unitary discounting rate into a cash-in-advance (CIA) model. Through this extension, we obtain the following results. First, we show that there exists an equilibrium in which the CIA constraint does not bind when individuals discount their utilities from future consumption lower than their utilities from future leisure time. Notably, this non-binding equilibrium exists even if the nominal interest rate takes a positive value. Second, we demonstrate that increases in the money supply growth rate decrease individuals’ saving rates in equilibrium, where the CIA constraint does not bind. Third, we exhibit that when the equilibrium where the CIA constraint does not bind exists, the welfare level of this equilibrium can be higher than that of the equilibrium in which the CIA constraint binds. Moreover, we deduce that the Friedman rule cannot be optimal in the equilibrium in which the CIA constraint binds and present the result that the optimal level of the optimal nominal interest rate is affected by the difference in the discount rates.