5. In this question you should assume that the Marginal Propensity to Consume out of permanent income is one [i.e., no bequest motive + perfect consumption smoothing: c1, = c2 = c3]. Consider the following disposable (i.e., after tax) income stream: yt = 100, yt+1 = 160, yt+2 = 120.
a) What is the wealth of this individual if r = 1.06? Show your work.
b) If r = 1.06 and if permanent income (yp) is the constant income stream with the same present value as the actual income stream, calculate yp. Show your work.
c) Suppose that income rises by 10 in each period. By how much will consumption rise in each period?
d) Suppose that income rises by 10 in the current period only. By how much will consumption rise in each period?
e) Calculate the Marginal Propensity to Consume out of current disposable income for parts c and d. How do you explain the difference?