I would like you to solve and show the answer for

1. (b) Explain how these decisions relate to the marginal rate of substitution you found above

2. (b) How does this relate to the convexity of indifference curves for this consumer? and

(c) Why do you think this is the case (Hint: what happens if you take a log of the original utility function?)

1. A consumer has utility function over two goods, apples (A) and bananas (B) given by U(A, B) = 3A + 5B (a) What is the marginal utility of apples? What is the marginal utility of bananas? What is the marginal rate of substitution of apples for bananas? (b) A consumer currently has 10 apples and 10 bananas. If their goal is to get the most possible utility, would they be willing to trade 5 apples for 4 bananas? 5 apples for 2 bananas? What is the minimum number of bananas the consumer would need to receive in exchange for 5 apples? Explain how these decisions relate to the marginal rate of substitution you found above. 2. A consumer has a utility function over two goods :1: and 3; given by U($, y) = $1/3y2/3 (a) Find the MRS of a: for y given this utility function (b) As the ratio of :1: to y increases, what happens to the MRS? How does this relate to the convexity of indifference curves for this consumer? (c) Consider a different utility function U (at, y) = 111(37) + 2 1n(y) Show that this utility function has the same MRS as the original. Why do you think this is the case? (Hint: what happens if you take a log of the original utility function?)