Productive government expenditure in a stochastically growing economy

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