Imagine an OLG economy where the government has to build roads and bridges totalling an amount of Gr 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 g: = Go/N: where Mis the number of people in the generation born at time t. 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) = ky/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(ccar) = log(Cut) + log(eat) 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 "2.0. (k.CL. "2.)=1 as a function of parameters & )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?~