Cash-in-advance constraint, optimal monetary policy, and human capital accumulation

• We investigate optimal monetary policy in an overlapping-generations model of endogenous growth by human capital accumulation with a cash-in-advance constraint.
• Human capital accumulation consists of private education investment, public education and the intergenerational transmission of human capital.
• Public education is assumed to be financed totally by seigniorage.
• We show that there exists an optimal money growth rate that maximizes economic growth rate along the steady growth path.
• We show that when the economic growth rate is maximized, the Laffer curve of seigniorage reaches the maximum point.

This paper investigates optimal monetary policy in an overlapping-generations model with endogenous growth fueled by the accumulation of human capital and under a cash-in-advance constraint. We consider the case where the government finances public education fully by seigniorage. Three main results are obtained. First, there exists an optimal money growth rate that maximizes the economic growth rate along the steady growth path. Second, on this path, the Laffer curve of seigniorage takes the maximum. Finally, the money growth rate for maximizing seigniorage along the steady growth path, which also leads to maximization of the economic growth rate, is lower than that for maximizing seigniorage in the present period.