Imagine an OLG economy where the government has to build roads and bridges totalling an amount of G units of the consumption good each period. The government may finance its purchases printing money with a rate of expansion of the fiat money supply of z 2 1. Denote governement consumption per capita by gr = G/Mwhere Mis the number of people in the generation born at time f. Population is constant at N. Each young person receives y amounts of the good as labor income. Besides money, the agent may invest in capital k. Each unit invested in capital as young will become /(k] = kv/2 when old.~ 1. Find the individual's budget constraints when young and when old. [TIP: Government purchases g are not in the agent's BC] 2. State the following: (a) Total GDP at time t; ~ (b) Feasibility Constraint; (c) Government's budget constraint; (d) Money Market Clearing Condition.~ From now on assume that the utility function of a typical agent is given by: u(ciczi) =# log(cir) + log(cat)~ 3. State and find the solution to the Planner's Problem as a function of parameters y.~ 4. Define a Competitive Equilibrium.~ 5. Find the Equilibrium Allocations "20: (. city)i=las a function of parameters zy.A, In which cases the solution to the Planner's Problem and the equilibrium allocation are the same?~ From now on, assume y = 10, n = 1.~ 6. Is GDP higher in the Planner's optimal allocation or in the equilibrium? What about consumption in periods 1 and 2?~ 7. How does consumption in each period change when z changes?~ 8. Find an expression for g in equilibrium as a function of c and parameters.~ 9. What is the maximum amount the government can spend per capita?~