Garfield cares only about the amount of lasagna he eats this year and the amount of lasagna he eats next year. We will use L0 to stand for lasagna this year and L1 to stand for lasagna next year. His preferences correspond to the utility function U(L0, L1) = L0 - Z) L1 - Z), where Z is some fixed number. For that utility function, the marginal utility of lasagna this year is MU0 = L1 - Z, and the marginal utility of lasagna next year is MU1 = L0 - Z. Suppose he earns $500 this year and nothing next year. Lasagna costs $10 per kilogram in both years and the interest rate (expressed as a decimal) is R.
Find a formula showing how much Garfield will save as a function of the interest rate (as well as Z).When the interest rate rises, does Garfield save more or less? How does the answer depend upon Z?