Question 2 - Government Debt and Savings (20 points). Imagine an OLG economy where the government has to build roads and bridges totalling an amount of Gt units of the consumption good each period. The government may nance its purchases with lumpsum taxes and Debt. There is no Fiat-money in this economy. Denote governement consumption per capita by 9,3 = Gt/Nt where N: is the number of people in the generation born at time t. Each generation lives for 2 periods. Population grows at N; : nNt_1. Each person receives y1,y2 amounts of the good as labor income when young and old. The agent is taxed lump sum 1'1, 7'2 when young and old. Besides government bonds (8; : Ntbt), the agent may invest in capital k. Each unit invested in capital as young will pay a rate of return a: when old. The government pays the marginal product of capital as interest rate in its debt. A) Find the individual's budget constraints when young and when old. B) State the following: a) Total GDP at time t; b) Feasibility Constraint; 0) Government's budget constraint; d) Government bonds market clearing condition. C) Dene a Competitive Equilibrium. From now on assume that the utility function of a typical agent is given by: MC\