Olowolayemo and Mrs$.$ Ade both follow the life$-$cycle hypothesis: they smooth consumption as much as possible. They each live for five periods, the last two of which are retirement. Here are their incomes earned during each period:

Mr$.$ Olowo, period one$=50,000$; period two$=150,000$; period three$=120,000$; period four $=0$; period five $=0$; and Mrs$.$ Ade $,$ period one$=40,000$; period two$=120,000$; period three $=160,000$; period four $=0$ period five $=0$

They both die at the beginning of period six. To keep things simple, assume that the interest rate is zero for both saving and borrowing and that the life span is perfectly predictable.

$($a$)$ For each individual, compute consumption and saving in each period of life.

$($b$)$ Compute their wealth $($their accumulated saving$)$ at the beginning of each period, including period six.

$($c$)$ Describe the evidence that was consistent with Keynes$’$s conjectures and the inconsistent evidence