Microeconomics 2nd Edition by Douglas Bernheim

Exercise 3

Lucy cares only about the amount of lemonade she drinks this year and the amount of lemonade she drinks next year. We will use L 0 to stand for lemonade this year and L 1 to stand for lemonade next year. Her preferences correspond to the utility function
where k is a positive number. Suppose she earns $50 this year and $55 next year. Lemonade costs $1 per gallon in both years and the interest rate is 10 percent. Determine how much Lucy will save or borrow for the following values of k: 0.8, 0.9, 1.0, 1.1. Next, continue to assume that Lucy can save at an interest rate of 10 percent, but that she pays an interest rate of 25 percent when she borrows. Draw her budget line. Determine how much she will save or borrow for the same four values of k.