Aa Aa 2. Risk and insurance premiums Maria\'s current wealth is $500, and she is

Question

Aa Aa 2. Risk and insurance premiums Maria's current wealth is $500, and she is debating a trip to Reno. Although she doesn't have a lucky Suppose number, her most recent interest is a new game similar to roulette, in which she places money on black every time. Suppose that there is a 50% chance that the ball will land on black and her wealth will increase to $800, but there is also a 50% chance that the ball will land on red and her wealth will decrease to $200. The following graph shows Maria's utility curve as a function of wealth, U(W). All of the black points (x symbols) on the graph represent various points along this curve. For example, at $500, Maria enjoys utility of 66 utils. That is U(500) = 66 utils. Tool tip: Mouse over the points on the graph to see their coordinates. UTILITY Utils 100 90 80 70 60 50 40 30 20 10 0 100 200 300 400 500 600 700 800 900 1000 WEALTH Dollars

Explanation / Answer

Expected value of her wealth=0.5(800)+0.5(200)=500

Expected utility from the gamble=0.5(U(200))+0.5U(800))=0.5(40)+0.5(76)=20+38=58<U(500)=66

Since current utility is higher than expected utility which makes her Risk averse.

Expected utility from gamble=58=U(around380) thus premium=120

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