Only ANSWER Part D

2. [20 points] The taxes paid by oonsumers in chapter '5} (denoted t and t'] are what we call lumpsum taxes. In reality nmnyr taxes are proportional. In this question, consumers pay lump sum taxes and mnsurnption taxes. Let's denote the consumption tax rate in the current period by :1: and the consumption tax rate in the future period by 9:". its usualj y and 1:)" denote the consumer's income in the current and future periodsj respectively. The total amount of taxes paid by the consumer in the current period is t + Ic. The total amount of taxes paid by the consumer in the future period is t' + I'c\". {a} [3 pts] You can take as given that the consumer's lifetime budget txinstraint is yr-t' 1+1" {l+r}[l+:r} -3 _\" l+m'+l+1"(y ) 1+.r' r {4) 1Write the expression ourresponding to the slope of the consumer's lifetime budget constraint. Imagine that you want to draw the lifetime budget mnstraint on a graph with r." on the vertical axis and c on the horizontal axis. From now on, assume that y = , if = 150? t' = 25, 1' = [ll and a," = {125. {h} [4 pts] Suppose that initially, we have t1 = 5n and .121 = {15 and that the optimal bundle selected by the consumer is c1 = 1m and r'i = 100. I am using the subscript \"1\" here to refer to the initial situation [that is, before the taxation policy changes}. Prove that the bundle {c1 = 1|)!le c"1 = lfl] satises lifetime budget constraint (4} {c} [3 pts] Draw the txinsurner's budget constraint on a graph [c' on the vertical axis and c on the horizontal axis] and represent the oonsumer's optimal consumption bundle. Note that your answer must also include an indifference curve. 2 {d} [2 pts] The total amount paid in taxes; in the current period is l' when r: = me Now suppose that the government reduces the consumption tax rate I from 9:1 = [Hi to 3:2 = [125. Calculate the new value of 1: {denote it t2] that would make total tax payments in the current period equal to me {still using c = 1m}. Show your work