Question

A consumer's income in the current period is y=100, and income in the future period is y' =120. He or she pays lump-sum taxes t =20 in the current period and t' =10 in the future period. The real interest rate is 0.1, or 10%, per period. Also assume that this consumer likes to consume the same amount of consumption each period, that is, c = c. Questions: a) [5 points] Calculate the lifetime wealth for this consumer. b) [4 points] Calculate the optimal amount of current consumption, savings and future consumption. Is the consumer a borrower, a lender or neither? Show your calculations to justify your answer. c) [4 points] For this part, suppose that the current period income, y, is equal to 140 instead of 100. Is the consumer now a borrower, a lender or neither? Show your calculations to justify your answer.

Answer 1

Income after tax in current period = 100 - 20 = 80

Income after tax in next period = 120 - 10 = 110

a) Lifetime wealth of this consumer = 80+110 = 190 (without considering any lending and borrowing)

b) If this consumer wants to have equal consumption in both periods, let's assume she borrows x from next period

So, 80 + x = 110 - x*1.1

2.1x = 30

x = 30 / 2.1 = 14.29

She borrows $14.29 from next period

c) If the current income is 140, then post tax it will be 140-20 = 120

Assuming a lending (since next period income is 110, which is lower than current period) of y

120 - y = 110 + 1.1y

2.1y = 10

y = 4.76

She lends $4.76