Charlie cares only about the amount of chocolate he eats this year and the amount of chocolate he eats next year. We will use C0 to stand for chocolate this year and C1 to stand for chocolate next year. His preferences correspond to the utility function U(C0, C1) = 2)√C0 + √C1).
Suppose he earns $1,000 this year and nothing next year. Chocolate costs $2 per ounce this year, but will cost $4 per ounce next year. The interest rate (expressed as a decimal) is R. Find a formula showing how much Charlie will save as a function of the interest rate. When the interest rate rises, does Charlie save more or less?