In exercise 29.7, we considered how low “teaser” interest rates impact borrowing when college students are present-biased. We now consider the difference in borrowing responses to such teaser rates by impatient versus present-biased students.
A: Throughout, compare an impatient student without present-bias to a present-biased student assuming both consume (and therefore borrow) the same amount in their junior year. Assume throughout that no credit card offers are made prior to the junior year.
(a) When the two students are sophomores, which of the two plans on accumulating more credit card debt by the time he graduates?
(b) When the two students are juniors, which plan to accumulate more debt by graduation?
(c) In what sense is government regulation to limit student credit card debt more paternalistic when it is motivated by com batting student impatience than it is when it is motivated by com batting present-bias?
B: Consider the same set-up as in part B of exercise 29.7. (You should do exercise 29.7 prior to moving on.)
(a) In B (d) of exercise 29.7, you should have concluded that c0 = $43,262 for the present biased student when I = 100,000, r = 0.2, δ = 0.95 and β = 0.5. What level of δ would be required for the non-present biased student to be sufficiently impatient for him to choose the same c0?
(b) For such an impatient but non-present biased student, what will consumption levels in periods 1 and 2 be? How much credit card debt will he have when he graduates?
(c) Compare your answer to the levels of credit card debt our “patient” present-biased student (with δ = 0.95 and β= 0.5) will have.
(d) Next, compare the impatient student’s level of credit card debt to the level of debt the present biased student plans for when he is a sophomore? Is it greater or less? What about the levels of credit card debt the present-biased student plans for when he is in his junior year?
(e) True or False: Our present-biased student will have greater credit card debt than the impatient student who borrows the same in the junior year—but the impatient student will accurately predict his credit card debt when he graduates while the present-biased student predicts he will end up with much less debt.