Consider a 2 periods Overlapping generations economy in which /-young individuals are born each period. Individuals are endowed with y = 10 units of the consumption good when young and nothing when old. Agents have only the option to acquire money to consume in the second period. The utility function of one typical agent is a typical time-separable CRRA: "(CI. (2) = is + 7-#. 0 is the inverse of the elasticity of intertemporal substitution. Population of the future generations are determined by Ne+1 = n.N.for all t 2 1, No = 100. The government has to pay for expenses worth G: = 2N, every period.~ 1. What is the equation for the feasible set of this economy?~ 2. 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 solution, find the optimal allocations as a function of parameters only.~ From now on, assume that the government budget constraint is balanced and G is financed via seignorage G: = M - M-1 where Me = zMIN 3. Let's Find the competitive equilibrium allocation: (i) Write down the future and initial generations problem for this economy (ii) State the definition of a competitive equilibrium. (i) Find the FOCs of the future generations problem (v) Find the rate of return of money (vi) Find the stationary equilibrium allocation (C1,c2) as a function of parameters.~ 4. How does equilibrium consumption of the young change when z changes? [HINT: you should find cases for o]~ From now on, assume o = 1, n = 2.~ 5. Find the money growth rate z that makes the government budget balanced.~ 6. Compare the equilibrium consumption in each period with the planner's solution. Which one provides higher utility for a typical individual?~ 7. Is there a way to have in equilibrium the same allocation as in the Planner's solution while keeping the government budget balanced? How? What is z in that case?~