Albert and Franco both follow the life-cycle hypothesis: they smooth consumption
ID: 1204637 • Letter: A
Question
Albert and Franco 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.
1 A=100,000 F=40,000
2 A=100,000 F=100,000
3 A=100,000 F=160,000
4 and 5 are 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.
Explanation / Answer
The life cycle hypothesis assumes that individuals smoothen out their consumption over their life time such that :
Where W is the wealth accumulated over the years, R is the number of years in his life, Y is his annual income , and T is the number of periods he has to consume.
The consumption function of this person can be written as
They each live for five periods, the last two of which are retirement. Here are their incomes earned during each period.
1 A=100,000 F=40,000
2 A=100,000 F=100,000
3 A=100,000 F=160,000
4 and 5 are 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.
Y W C S
100000 3 300000 60000 40000
100000 2 200000 240000 60000 180000
100000 1 100000 280000 93333.33 186666.7
0 2 0 186666.7 93333.33 93333.33
93333.33 93333.33 0
Y W C S
40000 3 40000 8000 32000
100000 2 100000 132000 33000 99000
160000 1 160000 259000 86333.33 172666.7
0 2 0 172666.7 86333.33 86333.33
86333.33 86333.33 0
The life cycle hypothesis assumes that individuals smoothen out their consumption over their life time such that : Where W is the wealth accumulated over the years, R is the number of years in his life, Y is his annual income , and T is the number of periods he has to consume. The consumption function of this person can be written as They each live for five periods, the last two of which are retirement. Here are their incomes earned during each period. 1 A=100,000 F=40,000 2 A=100,000 F=100,000 3 A=100,000 F=160,000 4 and 5 are 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. Y W C S 100000 3 300000 60000 40000 100000 2 200000 240000 60000 180000 100000 1 100000 280000 93333.33 186666.7 0 2 0 186666.7 93333.33 93333.33 93333.33 93333.33 0 Y W C S 40000 3 40000 8000 32000 100000 2 100000 132000 33000 99000 160000 1 160000 259000 86333.33 172666.7 0 2 0 172666.7 86333.33 86333.33 86333.33 86333.33 0
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