03 Jun Question Suppose that you are currently a college senior.
Question
Suppose that you are currently a college senior. You are currently working a part-time job that pays
$2,000 per year (call it Y1), but you expect to earn $20,000 next year (call it Y2), after you graduate.
Assume that there is no inflation and that the interest rate is 10% per year.
a) You want to smooth consumption such that consumption this year equals consumption next
year (that is C1=C2.) Solve for consumption this year and next year. What is your saving
(S)? [Hint: in this case S will be negative; you borrow against your future income. You are
dis-saving.]
b) Suppose that your current income (Y1) doubles to $4,000 per year. What happens to your
current consumption? What happens to your saving? [numbers please]
c) Set Y1 back to $2,000. Suppose that expected income (Y2) doubles to $40,000 per year.
What happens to your current consumption? What happens to your saving? [numbers please]
d) Go back to the initial incomes. Suppose that the interest rate suddenly increased to 15%.
Solve for consumption this year and next year.
a. Suppose a person expects to live six periods. This person has no accumulated wealth and receives an
income of $15 in each of the first 4 periods. After period 4 this person retires and receives no wage
income. Assuming this person follows the life cycle consumption function, prepare a table showing
income, consumption and saving in each of the 6 years of the person’s life. Following the presentation in
Mankiw and assume the interest rate is zero for parts a, b and c.
b. Suppose this person wins the lottery in period 1 for $30 (this is equivalent to an increase in wealth).
Prepare a second table showing income, consumption and saving in each of the 6 years of the person’s
life. What is the MPC out of the temporary change in income?
c. Rather than winning the lottery in period 1, suppose this person gets and unexpected salary increase of
$10 per year. Prepare a second table showing income, consumption and saving in each of the 6 years of
the person’s life. What is the MPC out of this permanent change in income?
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