Consider an Overlapping generations economy in which Nt young individuals are born cach 15 units of the consumption good when young period. Individuals are endowed with y = and nothing when old. The utility function of one typical agent is a typical time-separable 1-o _1-0 CRRA: u(C₁, C₂) = 1-o 1-o € + ß². ß € (0, 1] is the time discount factor and ♂ > 0 is the inverse of the elasticity of intertemporal substitution. Population of the future generations are determined by Nt+1 = n. Nt for all t≥ 1, No = 100. 1. What is the equation for the feasible set of this economy? 2. Portray the feasible set on a graph. 3. Let's solve the Planner's Problem. (i) State the Planner's problem as a constrained maximization problem. (ii) Write down the Lagrangean for this problem. (iii) What are the FOCs? (iv) Assuming a stationary equilibrium, find the optimal allocations as a function of ß, o and n only. 4. How does consumption when young respond to changes in 3? What about o? And n? 5. Now, B = 0.5 and o = 2 and n = 2. Substitute and find C1 and C2. 6. With arbitrarily drawn indifference curves, illustrate the stationary combination of c₁ and c₂ that maximizes the utility of future generations. 7. Now look at a monetary equilibrium. Write down equations that represent the con- straints on first and second-period consumption for a typical individual. Combine these constraints into a lifetime budget constraint.
