In the Republic of Pecunia. 1100 individuals are bem in period t. The population grows according to N; = 1.1N3_1. Each citizen in Pecunia is endowed with y] = 15 units of the consnmption good when yolmg, and y; = 5.5 units when old. Preferences are such that individuals will always want to consume more than their endowment when old. The at money stock in period t amounts to 2500. The Peeunian government is increasing the stock of at money in circulation by 5 percent each period (2 = 1.05}. The additional units of money printed every period are noted to purchase Gt units of the consumption good for government consumption which is wasteful from the perspective of the Pecunian citizens. Assume stationarity throughout the exercise. {a} (5 points] Dene total uses and total sources of goods in this economy in period f. and derive the (percapita) feasible set. Use g; = N'ELI. (b) [5 points] New look at the monetary equilibrium. Combine the constraints on rst and secondperiod consumption for a typical person into a lifetime budget constraint. Hint: Melee sure to consider eff available endowments. (c) [5 points] Derive the real rate of return of at money. Plug into the lifetime budget constraint. (d) [5 points] New amume that the government raises lumpsum taxes T from young indi viduals to nance its government consumption G; and does not print new at money [:5 = 1). Show how this policy affects the life-time budget constraint of an individual born in it both directly and indirectly through changes in the rate of return to at money. {e} [5 points] Express the feasible set in terms of 1". (f) [5 points] Considering the welfare of all future generations, explain in your own words why the second policy option [lump51ml taxes 9 = in? and z = 1) is preferable to the expansionary monetary policy in the rst scenario [1' = [l and s 3: 1}