Introduction to Modern Economic Growth per capita is slowed down by the arrival of new individuals at each instance, who have less wealth than the average individual Their lower wealth implies lower consumption and reduces average consumption growth in the economy This intuitively explains why the last term depends on n (the rate of arrival of new individuals) and on k/c (the size of average asset holdings relative to consumption) The equilibrium path of the economy is completely characterized by the two differential equations, (9.43) and (9.49)–together with an initial condition for k (0) > and the transversality condition (9.45) applied to average assets, thus to the capitallabor ratio, k (t) First, a steady-state equilibrium is obtained when both k˙ (t) /k (t) and c˙ (t) /c (t) are equal to zero, and thus satisfies the following two equations: (9.50) (ρ + ν) n c∗ = ∗ ∗ k f (k ) − δ − ρ (9.51) (ρ + ν) n f (k∗ ) − (n − ν + δ) − = k∗ f (k∗ ) − δ − ρ The second equation pins down a unique positive level of steady-state capital-labor ratio, k∗ , ratio (since both f (k) /k and f (k) are decreasing) Given k∗ the first equation pins down a unique level of average consumption per capita, c∗ It can also be verified that at k∗ , f (k ∗ ) > ρ + δ, so that the capital-labor ratio is lower than the level consistent with the modified golden rule kmgr , given by f (kmgr ) = ρ + δ Recall that optimal steady-state capital-labor ratio of the neoclassical growth model satisfied the modified golden rule In comparison, in this economy there is always underaccumulation This contrasts with the baseline overlapping generations model, which potentially led to dynamic inefficiency and overaccumulation We will momentarily return to a further discussion of this issue Before doing this, let us analyze equilibrium dynamics Figure 9.3 plots (9.43) and (9.49), together with the arrows indicating how average consumption per capita and capital-labor ratio change in different regions Both (9.43) and (9.49) are upward sloping and start at the origin It is also straightforward to verify that while (9.43) is concave in the k-c space, (9.49) is convex Thus they have a unique intersection We also know from the preceding discussion that 450