5. [20 points] Consider a consumer who is looking to buy a house. The consumer's utility of obtaining a house is u (h, c) = h - vc, where h > 0 is the housing premium and will be obtained immediately after the consumer successfully purchases a house. Also, c is the amount of money spent on the house. There are two houses available for sale. House A is listed at $490,000 and currently has one other offer on it. The consumer is willing to pay the listed price and her offer will be accepted with probability 1/2. House B currently has two other offers on it and is listed at $360,000. [Continue...] Page 4 of 4 pages With probability 1/2, the owner will simply accept one of the three offers, in which case the consumer's will be accepted with 1/3. With probability 1/2, the owner will "send back" all three offers and ask for revised offers. In this case, the consumer must offer $640,000 in order to obtain this house. The consumer is only allowed to make an offer on one of the two houses. Assume that the consumer will choose A if she is indifferent between trying to obtain either house. (a) What is the maximum value of h such that the consumer will make an offer on house A? (b) Assume h = 1200. The offer situation on both houses remain the same. Suppose one of the two other individuals interested in house B tries to buy the consumer out from making an offer on B. The individual offers to pay her a dollars conditional on that she makes an offer on A and that her offer is accepted. In this case, the associated utility for the consumer to obtain house A is h - v490000 - x. What is the lowest a such that the consumer will accept the proposal