# 5.1 Suppose a person must accept one of three bets:

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5.1 Suppose a person must accept one of three bets:
Bet 1:Win \$100 with probability 1/2; lose \$100 with probability 1/2 Bet 2:Win \$100 with probability 3/4; lose \$300 with probability 1/4 Bet 3:Win \$100 with probability 9/10; lose \$900 with probability 1/10 Show that all of these are fair bets. Graph each bet on a utility of income curve similar to Figure 5.1. Explain carefully which bet will be preferred and why.

Computing Expected Value
Hint Computing Expected Value

Suppose there is a chance that a risk-averse individual with a current wealth of \$20,000 will contract a debilitating disease and suffer a loss of \$10,000. Calculate the cost of actuarially fair insurance in this situation and use a utility-of-income graph (Figure 5-2) to show that the individual will prefer fair insurance against this loss to accepting the gamble uninsured. Suppose two types of insurance policies were available: 1. A fair policy covering the complete loss. 2. A fair policy covering only half of any loss incurred. Calculate the cost of the second type of policy and show that the individual will generally regard it as inferior to the first. c Suppose individuals who purchase cost-sharing policies of the second type take better care of their health, thereby reducing the loss suffered when ill to only \$7,000. In this situation, what will be the cost of a cost-sharing policy? Show that some individuals may now prefer this type of policy. (This is an example of the moral hazard problem in insurance theory)

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