Suppose John’s preference between goods A and B is represented by a utility function u(xA, xB) = xAxB, where xA, xB are amounts of A, B consumed.
(a) Suppose John has 40 units of A and 5 units of B. What’s his utility level?
(b) Draw qualitatively the indifference of John that has the same level of utility as 40 units of A and 5 units of B.
(c) Mary offers to give John 15 units of B if he will give her 25 units of A. Would John have a bundle that he likes better than (40, 5) if he makes this trade?
(d) What is the largest number of good A that Mary could demand from John in return for 15 units of B if she expects him to be willing to trade or at least indifferent about trading?
(e) What’s John’s marginal utility of good x and good y respectively when he has consumption bundle (40, 5)?
(f) What’s John’s marginal rate of substitution when he has consumption bundle (40, 5)?
(g) Suppose the market prices for goods A, B are pA = 1, pB = 2. Imagine John can sell the goods he has, namely 40 units of A and 5 units of B, to a trader at the market prices pA, pB and use the money he makes from selling to purchase back any combination of good A and good B affordable at the market prices pA, pB. What would be John’s optimal repurchase choice?