Dave and Christy both follow the life-cycle hypothesis: they smooth consumption
ID: 1211640 • Letter: D
Question
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:
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
Period Dave Christy 1 100,000 40,000 2 100,000 100,000 3 100,000 160,000 4 0 0 5 0 0Explanation / Answer
Consider two consumers, Dave and Christy who expect to live another 5 periods and have no accumulated initial wealth so W equal to zero, and expects to earn income until they retire 3 periods from now. So W = 0, T = 5 and R = 3.
If they wish to maintain a smooth level of consumption over their life, then the consumer’s lifetime resources will be composed of W + RY or simply RY.
Assuming that they wish to achieve the smoothest possible path of consumption over lifetime, they distribute
this total of RY equally among the T years. Annual consumption is C = (RY)/T
For Dave, this C is 3*100,000/5 = $60,000
For Christy, this C is 300,000/5 = $60,000
a) Dave and Christy have the following consumption and savings:
Dave has a continuous stable income so his savings are stable as well. Christy on the other hand, has more fluctutating savings, with some initially borrowing
c) The accumulated wealth at the end of sixth period is zero since lifetime is predicatble so they not leave any savings after their death. This is shown in the table above.
d) Without borrowing, Savings in the first period for Christy will be zero and she will consume only 40,000. But in the subsequent periods she will be saving moer so that she is left with a bequest of $20,000.
Period Dave Consumption Saving Accumulated Savings Christy Consumption Saving Accumulated Savings 1 1,00,000 60,000 40,000 40,000 40,000 60,000 -20,000 -20,000 2 1,00,000 60,000 40,000 80,000 1,00,000 60,000 40,000 20,000 3 1,00,000 60,000 40,000 1,20,000 1,60,000 60,000 1,00,000 1,20,000 4 0 60,000 -60,000 60,000 0 60,000 -60,000 60,000 5 0 60,000 -60,000 0 0 60,000 -60,000 0Related Questions
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