Introduction to Modern Economic Growth c(t) c(t)=0 c* k(t)=0 c’(0) c(0) c’’(0) k(0) k* kmgr kgold k k(t) Figure 9.3 Steady state and transitional dynamics in the overlapping generations model in continuous time this unique intersection is at a capital-labor ratio less than that satisfying the modified golden rule, which is marked as kmgr in the figure Naturally, kmgr itself is less than kgold The phase diagram also makes it clear that there exists a unique stable arm that is upward sloping in the k-c space The shape of the stable arm is the same as in the basic neoclassical growth model If the initial level of consumption is above this stable arm, feasibility is violated, while if it is below, the economy tends towards zero consumption and violates the transversality condition Consequently, the steady-state equilibrium is globally saddle-path stable; consumption starts along the stable arm, and consumption and the capital-labor ratio monotonically converge to the steady state Exercise 9.26 asks you to show local saddle-path stability by linearizing (9.43) and (9.49) around the steady state The following proposition summarizes this analysis 451