Consider a simple example of moral hazard. Suppose that Lucas goes into a casino to make one bet a day. The casino is very basic; it has two bets: a safe bet and a risky bet. In the safe bet, a nickel is flipped. If the nickel lands on heads, Lucas wins $100 If it lands on tails, Lucas loses $100 The risky bet is similar: a silver dollar is flipped. If the silver dollar lands on heads, Lucas wins $5,000 If it lands on tails, Lucas loses $10,000. Each coin has a 50% chance of landing on each side.What is the expected value of the safe bet?safe bet: $What is the expected value of the risky bet?risky bet: $Now suppose that an insurance company opens outside of the casino. They notice that Lucas, like everyone else, always leaves the casino having played the safe bet, so they offer to sell Lucas insurance for $50 that, if he loses, covers his losses. If Lucas wins, he does not have to pay anything extra, having already paid the $50. Note that as long as Lucas does not change his behavior, the insurance company makes $0 in expectation.Once Lucas buys the insurance, what are his expected winnings from the safe bet? Ignore the cost of the insurance.safe bet: $Once Lucas buys the insurance, what are his expected winnings from the risky bet? Ignore the cost of insurance.risky bet: $If the insurance company sells insurance to Lucas, should you expect to find that it loses money? Why?-Yes; since Lucas 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 Lucas still chooses that one.-Maybe; the bets now have an equal expected value, so Lucas might pick either one.

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