A recent politician in Peru, Keiko Fujimori, has proposed a policy intended to provide social insurance to a large number of Peruvians that, because they do not pay income taxes, do not have acess to social security. She proposes that the government should provide consumption rebate (S) financed with lump sum taxes T. The motivation of the politician is that because peruvians pay a sales tax, they can keep track of peoples savings. The idea of this question is to show that the logic of this policy has pervasive effects. We start with the standard Ricardian equivalence learned in class. The government budget constraint is The time 1 budget contraint is The time 2 budget contraint is S = (1 r)T a = y1 T c1 c2 =y2 S (1 r)a 1. Derive the intertemporal budget constraint. The replace consumption rebate (S) with the expression given in the government budget constraint. Does consumption tax affect household intertemporal budget constraint? 2. Solve for (1) consumption in the first period (c1), (2) consumption in the second period (c2) and (3) saving (a) with lumpsum tax. Suppose income in the first period is $200, income in the second period is $105