Question 1 (20 marks) (a) How do financial intermediaries solve the problem of adverse selection? (4 marks) (b) Sam is in the market for a used motorbike. At a used bike shop, Sam roughly knows that the price of a used motorbike is between $40,000 and $48,000. If Sam believes that the dealer knows as much about the bikes as him, how much do you think that Sam is willing to pay? Explain. Assume that he only cares about the expected value of the bike he buys and that the bike values are symmetrically distributed. (3 marks) (c) Sam now decides to go to a different town to search for a used motorbike and believes that the dealer knows more about the used motorbikes than him. How much do you think that Sam is willing to pay? Explain your answer. How can this be resolved in a competitive market? (3 marks) (d) You wish to hire Melissa to manage your Kansas operations. The profits from the operations depend partially on how hard Melissa works, as follows: Profit = $20,000 Profit = $100,000 Lazy Worker 65% 35% Hard Worker 30% 70% If Melissa is lazy, she will surf the Internet all day, and she views this as a zero cost opportunity. However, Melissa would view working hard as a personal cost" valued at $2,000. What fixed-percentage of the profits should you offer Melissa? Assume Melissa only cares about her expected payment less any personal cost. (Show your steps!) (10 marks)