Dave and Christy 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:
Period 1: Dave 100,000, Christy 40,000
Period 2: Dave 100,000, Christy 100,000
Period 3: Dave 100,000, Christy 160,000
Period 4: Dave 0, Christy 0
Period 5: Dave 0, Christy 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 (that is, their accumulated saving) at the beginning of each period, including period six.
c. Graph consumption, income, and wealth for each of them, with the period on the horizontal axis.
d. Suppose now that consumers cannot borrow, so wealth cannot be negative. How does that change your answers above? Draw a new graph for part (c) if necessary.