Lucy cares only about the amount of lemonade she drinks this year and the amount of lemonade she drinks next year. We will use L0 to stand for lemonade this year and L1 to stand for lemonade next year. Her preferences correspond to the utility function

where k is a positive number. For that utility function, the marginal utility of lemonade this year is

and the marginal utility of lemonade next year is

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, and 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.

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ULo, L1)= LoL, U(Lo. L1