Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 7

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 = C 1 /3C 0
MRS for Glitter = 3C 1 /C 0
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 C 0 and C 1 so as to satisfy the condition for utility maximization subject to her two-period budget constraint? How much will Prudence borrow or save in period 0?
d. Answer part c for Glitter and discuss whether these two consumers' names are justified.