Government Spending in a Simple Model of Endogenous Growth

Abstract

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.The distortion from the income tax implies that the decentralized equilibrium is not Pareto optimal; in particular, the growth and saving rates are too low from a social perspective.In a command optimum, growth and saving rates are higher, but g/y = a turns out still to be the best choice for the size of government.The command optimum can be sustained by picking the expenditure ratio, g/y = a, and then financing this spending by lump-sum taxes.If the share of productive spending, g/y, were chosen randomly, then the model would predict a non-monotonic relation between g/y and the economy's long-term growth and saving rates.However, for optimizing governments, the model predicts an inverse association between g/y and the rates of growth and saving.