Government Spending in a Simple Model of Endogenous Growth

I extend existing models of endogenous economic growth to incorporate a government sector. Production involves private capital (broadly defined) and public services. There is constant returns to scale in the two factors, but diminishing returns to each separately. Public services are financed by a flat-rate income tax. The economy's growth rate and saving rate initially rise with the ratio of productive government expenditures to GNP, g/y, but each rate eventually reaches a peak and subsequently declines. If the production function is Cobb-Douglas with an exponent a for public services, then the value g/y = a maximizes the growth rate, and also maximizes the utility attained by the representative consumer.