3. For each of the three utility functions, below, that Jim might have over beer (b, in pints) and coffee ( c, in cups), do the following three problems.

(i) What is Jim's Marginal Rate of Substitution of beer for coffee, as a function of b and c? [Beer is X, Coffee is Y] (ii) Given your answer to (i), if Jim chooses to buy 4 pints of beer and 9 cups of coffee, what must be the ratio of the price of pints of beer to the price of cups of coffee?

(iii) Solve for the formula of Him's indifference curve at utility level U(b, c) = 10. That is, find the function c(b) such that U(b, c(b)) = 10. (If you were to graph the indifference curve for U = 10 in Excel, this is the formula you would want to use.)

(a) U(b,c)=bc (b) U(b, c) = 10b2 c (c) U(b, c) = 2b + 3c