Taxes on Interest Income (23 pts)In this exercise, we want to look at the impact of placing a tax on interest income. We will have a typical two-period consumption savings model. Where an individual wishes to maximize the sum of their lifetime utility. The only difference is that the government has imposed a proportional tax on income from interest payments. This means that the income gained from savings (or income lost from borrowing) in the second p erio d is given by: (1 + (1 T)r)s1, instead of the usual (1 + r)s1. In addition to saving, Agents receive a fixed income in each period, y1 and y2 representing income in period 1 and period 2 respectively. Other than the tax the problem remains identical to before. The agent's total lifetime utility is given by: U(c1,c2) = ln c1 + ln c2 Where c1, c2 are consumption in time 1 and time 2 respectively and 0 < < 1. Agents. You may assume there is a non-Ponzi scheme condition in place and so s2 0. (a) (3pts)What are the per-period budget constraints of the household? (b) (3pts)Rewriting the pre-period budget constraints in part (a) as the lifetime budget constraint? What is different about how present value is being calculated? (c) (2pts)What is the natural b orrowing limit? That is, what is the largest value c1 can get above y1, and what is the largest absolute value s1 can be negatively Most importantly how does the tax impact this? (d) (5pts)Set up the household lagrangian, and take FOC's (You may attempt this with either the per-period budget constraint way, or you can with the lifetime budget constraint whichever you feel most comfortable). Combine your FOC's so that you have the two optimality conditions for the household (The intertemporal Euler Equation and the Budget Constraint) (e) (5pts)Solve for consumption demand in both period 1 and period 2. How does the tax impact consumption demand in period 1? Why? (f ) (5pts)Solve for savings demand s1. (Recall this is just y1 c1), how is it changing with respect to taxes? What are the taxes encouraging?