Do question B

2. [21] points] The taxes paid by consumers in chapter 9 [denoted t and t'} are what we call lumpsum taxes. In reality many taxes are proportional. In this question1 consumers pay lump sum taxes and consumption taxes. Let's denote the mnsurnption tax rate in the current period by :1: and the consumption tax rate in the future period by 1:". As usual, :1; and 3? denote the mnsurner's income in the cln'rent and future periods, respectively. The total amount of taxes paid by the conslnner in the current period is t + :1:c. The total amount of taxes paid by the couslnner in the future period is tJr + m'c". {a} [3 pts] You can take as given that the mnsurner's lifetime budget constraint is y't' 1+5" [1+r}[1+r} = t .. 4 1+.r"+1+:1:'{y } 1+3:Ir P fl) Write the expression corresponding to the slope of the consumer's lifetime budget mnstraint. Imagine that you want to draw the lifetime budget (nostraint on a graph with c" on the verticai axis and c on the horizontal axis. 11' From now on, assume that y = Z. 31": 151], t' = 25, 1" = [1.1 and of = [1.25. {b} [4 pts] Suppose that initially1 we have t1 = 51] and 3:1 = [1.5 and that the optimal bundle selected by the couslnner is (:1 = l and c"l = l. 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 = l, c"; = l} satises lifetime budget constraint [4]