Question

2 Two Period Model of Consumption/Saving Decisions with Taxes (8 points) Assume a consumer who has current period income y200, future period income y-150, current taxes t = 40, and future taxes t' 50, and faces a market interest rate of r-5 percent or .05. The consumer would like to consume such that e'=e*(1+r) if possible. However, this consumer is faced with a credit market imperfection, in that no borrowing is allowed. That is s must be greater or equal to zero. 1. Show the consumer's lifetime budget constraint and indifference curves in a diagram. (2 points) 2. Calculate the optimale and c' for this consumer and show this in your diagram. (2 points) 3. Suppose that everything stays the same except that t - 20 and t' 71. Calculate the effects on c, c', and s. Show this in your diagram. (2 points) 1. Now, suppose that y - 100. Repeat the previous 3 parts and explain any differences. (2 points)

Answer 1

Graph- DF

Consumer lifetime budget constraint- C'=C*(1+r), So that the lifetime budget constraint is C+CP/1+r Then C+C'/1.05=200-40+ 150-50/1.058 C +0.95 C = 255.2 E1=(160,100) initail endowment point and BEID=Initial budget constraint. Thus a kink at El because the consumer cannot borrower and canot consume more than 160 (which is y-t) in the first period Now we calculate optimal C and C' for the consumer C=C.C+0.95 C = 255.2 C=C'=130.7 and S=y-t-c S=160-130.7=29.3 In this situation, the fact that the consumer cannot borrow does not matter for the consumer's choice, as the consumer decides to be a lender. Suppose that everything unchanged, except the nowt=20andt=72 then we calculate the effect of C+C'/1.05= 200-20 + 150-72/1.05 Therefore, the lifetime consumer's wealth remains constant at 255.2 and budget constraint shift to BE2F. The new endowment point is E2 = 80, 79). This change does not matter for the consumer again because he chooses to at lender. C=Cº=130.7 and saving(s) = 49.3