Q:

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 ?, ? and n only.

4. How does consumption when young respond to changes in ?? What about ?? And n?

Consider an Overlapping generations economy in which Nt young individuals are born each period. Individuals are endowed with y : 15 units of the consumption good when young and nothing when old. The utility function of one typical agent is a typical time-separable la lcr CRRA: u(cl,c2) = 6110 +561: inverse of the elasticity of interternporal substitution. Population of the future generations are determined by Nt+1 = n.Nt for all t 2 1, N0 = 100. . 5' E (0,1] is the time discount factor and a > 0 is the 0