Introduction to Modern Economic Growth The only additional condition in this case is that because there is growth, we have to make sure that the transversality condition is in fact satisfied Substituting (8.33) into (8.32), we have ẵ Z t ảắ [ (1 ) g n] ds = 0, lim k (t) exp − t→∞ which can only hold if the integral within the exponent goes to zero, i.e., if ρ − (1 − θ) g − n > 0, or alternatively if the following assumption is satisfied: Assumption ρ − n > (1 − θ) g Note that this assumption strengthens Assumption 4’ when θ < Alternatively, recall that in steady state we have r = ρ + θg and the growth rate of output is g + n Therefore, Assumption is equivalent to requiring that r > g +n We will encounter conditions like this all throughout, and they will also be related to issues of “dynamic efficiency” as we will see below The following is an immediate generalization of Proposition 8.2: Proposition 8.6 Consider the neoclassical growth model with labor augmenting technological progress at the rate g and preferences given by (8.30) Suppose that Assumptions 1, 2, and hold Then there exists a unique balanced growth path equilibrium with a normalized capital to effective labor ratio of k∗ , given by (8.33), and output per capita and consumption per capita grow at the rate g As noted above, the result that the steady-state capital-labor ratio was independent of preferences is no longer the case, since now k∗ given by (8.33) depends on the elasticity of marginal utility (or the inverse of the intertemporal elasticity of substitution), θ The reason for this is that there is now positive growth in output per capita, and thus in consumption per capita Since individuals face an upwardsloping consumption profile, their willingness to substitute consumption today for consumption tomorrow determines how much they will accumulate and thus the equilibrium effective capital-labor ratio 396