Teaser Rates on Credit Cards and Mortgages: Credit card companies often offer “teaser rates” to new customers— i.e. interest rates that are initially very low but then increase dramatically after a year. Mortgage companies did the same during the sub-prime mortgage period prior to the financial crisis of 2007.
A: Consider present-bias as modeled by the beta-delta framework and the explanation it might offer for how students and homeowners end up taking on “too much debt”.
(a) Consider first a college student who receives credit card offers with teaser rates that charge low interest until the student graduates. As a high school senior, our student decides on how much consumption he will undertake once he gets to college (knowing that he will have access to such credit cards. Assuming that δ is the same for present-biased students as it is for students who do not have present-bias, will the plans such students make for consumption while in college differ?
(b) Next, consider the student in his freshman year. How will students deviate in their actual consumption from their previous plans if they are present-biased?
(c) As our student consumes in his freshman year, he plans for consumption in his remaining three years in college. Will the present-biased student’s plans for consuming over the coming years now differ from the non-present biased student (given how each may have deviated from their initial plans during the freshman year)?
(d) Now consider our student in his sophomore year. Will the present-biased student now take on more debt than he planned as he was contemplating his sophomore year during his time as a freshman?
(e) Explain how students might end up with considerably more debt than they had planned to —and how limits on credit card borrowing might improve the welfare of some students.
(f) Prior to 2007, mortgage companies offered low teaser interest rates to new home buyers. Home values increased dramatically from2001 through 2005—allowing homeowners to re-finance at new teaser rates throughout. How might behavioral economists explain the explosion of home foreclosures beginning in 2006 and 2007 when home prices began to level off and then fall?
B: Consider a three period model of a college student in his junior year. Suppose this student has no income in periods 0 and 1 while he is in school but then expects an income I in period 2 after he graduates. Suppose that utility of consumption in period i is given by u (ci) = lnci, where ci is consumption in period i . Suppose further that the student discounts in accordance with the beta delta model — with his utility of a consumption stream (c0,c1,c2) given by U = u(c0)+βδ u(c1)+ βδ2u(c2).
(a) The student is unable to consume in periods 0 and 1 unless he borrows on his income from period 2. A credit card company offers him a credit card that charges no interest while he is in school and an interest rate r thereafter. Thus, he pays no interest for consumption he undertakes in periods 0 and 1 until period 2 when he has to pay interest (1+r) (c1 +c2). Set up this student’s optimization problem subject to a 3-period budget constraint.
(b) Derive his optimal consumption plan c0, c1 and c2 as a function of I, r, β and δ.
(c) Suppose I = $100,000, r = 0.2 and δ = 0.95. If the student does not have present-bias, what consumption levels will the student plan to have in each period—and how much credit card debt does the student plan to have when he graduates?
(d) Suppose that β = 0.5. How much credit card debt does the student plan to have when he graduates?
(e) Calculate the ratio of his period 1 to period 2 consumption plans in the two scenarios. Why are they the same?
(f) How much credit card debt will the student from part (c) actually have when he graduates? What about the student from part (d)?
(g) Now consider the student with β = 0.5 as a sophomore looking ahead to being a junior. He is fully supported by his parents in his sophomore year, but he knows they will no longer support him in his junior year when he is able to get credit. (Assume that credit card companies do not offer cards to sophomores but only to juniors). As he thinks about how much he will end up borrowing, will his plan differ from the student who is not present-biased? How much more credit card debt will he end up with than he planned to as a sophomore?
(h) True or False: Regulations that limit the amount of credit card debt that students can take on can improve the welfare of present-biased sophomores.