Charlie cares only about the amount of chocolate he eats this year (C0) and next year (C1). His preferences correspond to the utility function \(U(C_{0},C_{1})=4(\sqrt{C_{0}}+\sqrt{C_{1}})\) Suppose he earns $1,000 this year and nothing next year. Chocolate costs $1 per ounce this year and $4 per ounce next year.

A) Assume the interest rate is 10% (or 0.10). What is Charlie's optimal bundle?

B) Provide a graph of this solution.

C) Now suppose the interest rate (expressed as a decimal) is R. Find a general formula showing how much Charlie will save as a function of the interest rate.

D) When the interest rate rises, does Charlie save more or less? How do you know