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.