2. [10 points] Brandon considers putting his house on the market for sale. If he lists the house at $300,000, he will receive 3 potential buyers to come and inspect the house simultaneously. Each potential buyer is willing to pay this list price with probability 1/2. Brandon sells the house at the list price if at least one potential buyer is willing to pay this price. If more than one potential buyers are willing, Brandon will sell the house randomly to one of these willing buyers. If no one is willing, Brandon receives nothing. Brandon's utility is u (c) = ve, where c is the price at which the house is sold. (a) Calculate the expected value, the certainty equivalent and the risk premium of selling the house. (b) Now suppose Brandon can also list the house at $400,000. This list, price will attract 2 potential buyers simultaneously, each of whom is willing to pay this price with probability 1/3. Which list price should Brandon choose, $300,000 or $400,000? Prove your