This paper investigates the effects of productive government spending on the relationship between
growth and inequality in an economy subject to idiosyncratic production shocks and heterogeneous
endowments. Assuming lognormal distributions, we derive tractable closed form solutions describing
the equilibrium dynamics. We show how the effect of government investment on the equilibrium
dynamics of both inequality and growth depends crucially upon the elasticity of substitution between
public and private capital in production. This has important consequences for the growth- and welfaremaximizing
rates of government investment. Finally, we supplement our theoretical analysis with
numerical simulations, calibrated to approximate the productive characteristics of a real world economy.
With the empirical evidence strongly supporting the complementarity between public and private capital,
our simulations suggest that conclusions based on the commonly employed Cobb-Douglas production
function may be seriously misleading.