Productive government expenditure in a stochastically growing economy

This paper analyzes productive government expenditure in a stochastic AK gr owth model. First, a centrally planned economy is characterized, emphasizin g the trade-off-between the effects of both deterministic and stochastic go vernment expenditures on the equilibrium growth rate and its variance. Both the growth-maximizing and the welfare-maximizing shares of government expe nditure are derived and shown to depend (differentially) upon the degree of risk in the economy. Whereas production risk reduces the welfare-maximizin g share of government expenditure, it may either increase or decrease the g rowth-maximizing share, depending upon the degree of risk aversion. Next, t he stochastic equilibrium in a decentralized economy is derived. The first- best optimal tax structure is characterized and its dependence on risk is d etermined. The formal analysis is supplemented by some numerical simulation s to assess the quantitative significance of risk and the divergence that t his generates between the welfare-maximizing and growth-maximizing size of government.