Time-inconsistent discounting and the Friedman rule: roles of non-unitary discounting

We examine the optimality of the Friedman rule by considering recent development of behavioral economics. We construct a simple macroeconomic model where agents discount consumption and leisure at different rates. We also consider a standard exponential discounting model and a hyperbolic discounting model, by assuming that the same discounting applies to both consumption and leisure. Money is introduced via a cash-in-advance constraint. Although the three models are observationally equivalent, they provide different policy implications. The Friedman rule is optimal in the latter two models, while it is not optimal in the first model if agents discount consumption is at a higher rate than leisure.