Optimal money supply in models with endogenous discount factor

This paper studies the Friedman rule for the optimal quantity of money in money in the utility (MIU) and cash-credit models while considering two specifications for the endogenous discount factor. In the first specification, the discount factor depends directly on the utility level. In the second, the discount factor depends on every component of the utility function. We show that under the former specification the Friedman rule is the optimal policy. Under the latter, however, while the Friedman rule is optimal for the MIU model, it is not optimal for the cash-credit model.