Economic growth and economic development 523

Introduction to Modern Economic Growth c˙ (t) = (A − δ − ρ), c (t) θ (11.9) lim k(t) exp (−(A − δ − n)t) = (11.10) t→∞ The important result immediately follows from equation (11.9) Since the righthand side of this equation is constant, there must be a constant rate of consumption growth (as long as A − δ − ρ > 0) The rate of growth of consumption is therefore independent of the level of capital stock per person, k (t) This will also imply that there are no transitional dynamics in this model Starting from any k (0), consumption per capita (and as we will see, the capital-labor ratio) will immediately start growing at a constant rate To develop this point, let us integrate equation (11.9) starting from some initial level of consumption c(0), which as usual is still to be determined later (from the lifetime budget constraint) This gives ả (A δ − ρ)t (11.11) c(t) = c(0) exp θ Since there is growth in this economy, we have to ensure that the transversality condition is satisfied (i.e., that lifetime utility is bounded away from infinity), and also we want to ensure positive growth (the condition A − δ − ρ > mentioned above) We therefore impose: (11.12) A > ρ + δ > (1 − θ) (A − δ) + θn + δ The first part of this condition ensures that there will be positive consumption growth, while the second part is the analogue to the condition that ρ + θg > g + n in the neoclassical growth model with technological progress, which was imposed to ensure bounded utility (and thus was used in proving that the transversality condition was satisfied) 11.1.3 Equilibrium Characterization We first establish that there are no transitional dynamics in this economy In particular, we will show that not only the growth rate of consumption, but the growth rates of capital and output are also constant at all points in time, and equal the growth rate of consumption given in equation (11.9) 509