Economic growth and economic development 443

Introduction to Modern Economic Growth k(t+1) 45° k* k(0) k* k’(0) k(t) Figure 9.2 Equilibrium dynamics in the canonical overlapping generations model the other hand, asks you to analyze the same economy without the Cobb-Douglas technology assumption 9.4 Overaccumulation and Pareto Optimality of Competitive Equilibrium in the Overlapping Generations Model Let us now return to the general problem, and compare the overlapping-generations equilibrium to the choice of a social planner wishing to maximize a weighted average of all generations’ utilities In particular, suppose that the social planner maximizes ∞ X β tS U (t) t=0 where β S is the discount factor of the social planner, which reflects how she values the utilities of different generations Substituting from (9.1), this implies: ∞ X β tS (u (c1 (t)) + βu (c2 (t + 1))) t=0 429