Traditionally, the Las Vegas Home Bank made only prime loans providing mortgages just to people who were likely to repay the loans. However, Jack, a senior executive at the bank, is considering offering subprime loans mortgages to speculators and other less creditworthy borrowers. If he makes only prime loans, the bank will earn $160 million. If he also makes subprime loans, the bank will make a very high profit, $800 million, if the economy is good (few defaults), while a loss of $320 million if the economy is bad. The probability that the economy is bad is 0.75. Jack will receive 1% of the bank's profit if positive. He believes that if the bank loses money, he can walk away with no compensation but no other repercussions. Jack is risk neutral. a. Does Jack provide subprime loans? What would the bank's stakeholders prefer that Jack do (if they knew the risk ex ante)? [8%] b. Consider the contract which includes a fix salary to Jack of $1.15 million and a 0.25% of the bank's profit as bonus. Does this contract prevent him from undertaking irresponsible damaging actions? [12%] C. Suppose the reservation wage of Jack is $1 million. What is the most profitable contract (fixed salary + bonus) for the bank which solves the moral hazard problem? [30%] Traditionally, the Las Vegas Home Bank made only prime loans providing mortgages just to people who were likely to repay the loans. However, Jack, a senior executive at the bank, is considering offering subprime loans mortgages to speculators and other less creditworthy borrowers. If he makes only prime loans, the bank will earn $160 million. If he also makes subprime loans, the bank will make a very high profit, $800 million, if the economy is good (few defaults), while a loss of $320 million if the economy is bad. The probability that the economy is bad is 0.75. Jack will receive 1% of the bank's profit if positive. He believes that if the bank loses money, he can walk away with no compensation but no other repercussions. Jack is risk neutral. a. Does Jack provide subprime loans? What would the bank's stakeholders prefer that Jack do (if they knew the risk ex ante)? [8%] b. Consider the contract which includes a fix salary to Jack of $1.15 million and a 0.25% of the bank's profit as bonus. Does this contract prevent him from undertaking irresponsible damaging actions? [12%] C. Suppose the reservation wage of Jack is $1 million. What is the most profitable contract (fixed salary + bonus) for the bank which solves the moral hazard problem? [30%]
