Two roommates, Prudence and Glitter, graduate from college and get identical jobs that pay them $50,000 this year and $55,000 next year. The roommates have different utility functions so that the marginal rates of substitution are given by
MRS for Prudence = C1/3C0
MRS for Glitter = 3C1/C0
Assume that the real interest rate is 10 percent.
a. What is the present value of each student's income?
b. Focusing first on Prudence, what is her condition for utility maximization?
c. How should Prudence choose C0 and C1 so as to satisfy the condition for utility maximization and so that the present value of her consumption equals the present value of her income? How much will Prudence borrow or save in period 0?
d. Answer part c for Glitter.