Transitional dynamics in a growth model with government spending, technological progress and population change

This paper extends public spending-based growth theory along three directions: we assume that exogenous and constant technological progress does exist and that both population change and the ratio of government expenditure to income follow a logistic trajectory. By focusing on the choices of a benevolent social planner we find that, if the inverse of the intertemporal elasticity of substitution in consumption is sufficiently high, the ratio of consumption to private physical capital converges towards zero when time goes to infinity. Through two examples we see that, depending on the form of the underlying aggregate production function and on whether, for given production function, technological progress equals zero or a positive constant, our model may or may not yield an asymptotic balanced growth path (ABGP) equilibrium. When there is no exogenous technological progress, an equilibrium where population size, the ratio of government spending to total income and the ratio of consumption to private physical capital are all constant does exist and the equilibrium is a saddle point. In case of positive technological progress numerical simulations show that the model still exhibits an ABGP equilibrium.