5. [20 points] Cameron is looking to buy a house. He considers making an offer on one of the two houses that he likes equally. Cameron's utility is u (h, c) = h - vc, where h > 0 is the utility benefit of living in a house. The benefit h will be obtained immediately after he successfully purchases a house. Also, c is the amount of money spent on the house. Cameron obtains zero utility if the house purchase is not successful. House A is listed at $400,000 and currently has one other offer on it. Cameron is willing to pay the listed price and his offer will be accepted with probability 1/2. House B currently has two other offers on it and is listed at $360,000. Again Cameron is willing to offer just the listed price. With probability 3/4, the owner will simply accept one of the three offers, in which case Cameron's will be accepted with 1/3. With probability 1/4, the owner will "send back" all three offers and ask these offers to be revised. In this case, Cameron will have to re-offer $60,000 above the listed price in order to successfully purchase this house. Cameron must make an immediate decision on which house to make an offer on (making offers on both houses simultaneously is not a feasible option). (a) Which house should Cameron make an offer on? (b) Suppose right before Cameron makes a decision, he receives a proposal from one of the two other individuals interested in house B. The individual offers to give Cameron r dollars just so that Cameron will give up making an offer on house B. What is the lowest value of a so that Cameron will accept the proposal