Optimal monetary policy and economic growth

A question at the center of many analyses of optimal monetary policy is, why do central banks never implement the Friedman rule? To the list of answers to this question, we add neoclassical production (specifically, the Tobin effect) as one possible explanation. To that end, we study an overlapping generations economy with capital where limited communication and stochastic relocation create an endogenous transactions role for fiat money. We assume a production function with a knowledge externality (Romer style) that nests economies with endogenous growth (AK form) and those with no long-run growth (the Diamond model). The Tobin effect is shown to be always operative. Under CRRA preferences, a mild degree of social increasing returns is sufficient (but not necessary) for some positive inflation to dominate zero inflation and for the Friedman rule to be sub-optimal, irrespective of the degree of risk aversion.