Question 2. An economy exists for only two periods, and the government wishes to maximize the utility function: u(C, C2) = Ei=1ßt-1InC; (2.1) Where C, is consumption in the period t = 1,2 and ß is the...

Please do it ASAP I'll upvote for correct

Extracted text: Question 2. An economy exists for only two periods, and the government wishes to maximize the utility function: u(C, C2) = Ei=1ßt-1InC; (2.1) Where C, is consumption in the period t = 1,2 and ß is the discount factor. There is exogenously given total income Y, in period 1, that must be allocated between consumption (C,), private investment (I,) and a fixed amount of government investment (G). Income in period 2 (Y2) is generated by G and I, according to the following function Y2 = (G + 1,)“, 0 < a="">< 1="" (2.2)="" all="" of="" the="" income="" in="" period="" 2="" (y2)="" is="" consumed="" (i.e.,="" y2="C2)." %3d="" a)="" write="" down="" the="" resource="" (i.e.,="" income="" y,="" )="" allocation="" between="" consumption,="" private="" investment,="" and="" government="" investment="" in="" period="" 1.="" b)="" derive="" the="" optimal="" allocation="" of="" private="" investment="" in="" period="" 1="" (i;)="" in="" the="" economy.="" c)="" draw="" and="" interpret="" the="" diagrams="" of="" the="" total="" and="" marginal="" utility="" of="" investment="" and="" show="" how="" they="" reach="" the="" optimal="" investment.="" page="" 2="" of="" 4="" d)="" how="" does="" a="" change="" in="" the="" initial="" income="" (y1)="" and="" the="" government="" investment="" affect="" the="" optimal="" investment="" (i;)?="" e)="" illustrate="" the="" changes="" in="">