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Question: Let's consider a simple of moral hazard. Suppose that Bob goes into a casino to make one bet a da...

Show transcribed image text Let's consider a simple of moral hazard. Suppose that Bob goes into a casino to make one bet a day. The casino very basic – it has two bets: a safe bet and a risky bet. The safe bet is the following: a nickel is flipped. If the nickel lands on "heads, " Bob wins $100. If it lands on "tails, " Bob loses $100. The risky bet is similar: a silver dollar is flipped. If the silver dollar lands on "heads, " Bob wins $5,000. Each coin has a 50% chance of landing on each side. Now suppose that an insurance company opens outside of the casino. They notice that Bob (like everyone else) always leaves the casino having played the safe bet, and so offer to sell Bob insurance (for $50) that, if he loses, covers his loses. If Bob wins, he doesn't have to pay anything extra (having already the $50). Note that as long as Bob doesn't change his behavior, the insurance company makes $0 in expectation. If the insurance company sells insurance to Bob, should you expect to find that it loses money? Why? Yes – since Bob no longer pays for his losses, he gets a higher expected payoff from the risky bet. No – the safe bet has the higher expected value before insurance, so Bob still chooses that one. Maybe – the bets now have an equal expected value, and so Bob might pick either one.

Let's consider a simple of moral hazard. Suppose that Bob goes into a casino to make one bet a day. The casino very basic – it has two bets: a safe bet and a risky bet. The safe bet is the following: a nickel is flipped. If the nickel lands on "heads, " Bob wins $100. If it lands on "tails, " Bob loses $100. The risky bet is similar: a silver dollar is flipped. If the silver dollar lands on "heads, " Bob wins $5,000. Each coin has a 50% chance of landing on each side. Now suppose that an insurance company opens outside of the casino. They notice that Bob (like everyone else) always leaves the casino having played the safe bet, and so offer to sell Bob insurance (for $50) that, if he loses, covers his loses. If Bob wins, he doesn't have to pay anything extra (having already the $50). Note that as long as Bob doesn't change his behavior, the insurance company makes $0 in expectation. If the insurance company sells insurance to Bob, should you expect to find that it loses money? Why? Yes – since Bob no longer pays for his losses, he gets a higher expected payoff from the risky bet. No – the safe bet has the higher expected value before insurance, so Bob still chooses that one. Maybe – the bets now have an equal expected value, and so Bob might pick either one.