2. Alan lives in a world with two goods (N=2), apples and ban an as. He has a Cobb-Douglas utility function over these goods U(a,b)=a^0.7 b^0.3. Alan has an income I=100, and faces prices pa=2, pb=1. (a) We know that if Alan is optimizing (and consumes a bundle that contains both apples and bananas), that the slope of the budget constraint should be equal to his MRS. Use this and his budget constraint to solve for his optimal bundle. (b) Suppose the price of apples rises to 7 , and the price of bananas rises to 3 . What is his new optimal consumption bun dle? (c) Suppose Alan instead had a utility function given by U(a,b)=a^1.4 b^0.6. Given the same prices and income as in part (b), what is his optimal bundle?