2. Suppose that a farmer usually makes profit of $120,000 per year. Let's say that there is a 2% chance that a tornado will hit the farm. This would strongly hurt farmer's profit, leading to losses of $96,000 with 2% probability. a. What is the actuarially fair insurance?

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Chapter16: Information, Risk, And Insurance
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Problem 10RQ: In an insurance system, would you expect each person to receive in benefits pretty much what they...
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Economics
2. Suppose that a farmer usually makes profit of
$120,000 per year. Let's say that there is a 2%
chance that a tornado will hit the farm. This would
strongly hurt farmer's profit, leading to losses of
$96,000 with 2% probability.
a. What is the actuarially fair insurance?
b. Assume that the farmer utility is given by u = 7
0.5 where 7t represents profit. What is the farmer's
expected utility with no insurance?
c. How much would the farmer be willing to pay to
have insurance?
d. Assume that the farmer expects that the
tornado's effect to your farm is lower, only leading
to losses of $70,000.
i. What is the actuarially fair insurance?
ii. What is the farmer's expected utility with no
insurance?
iii. How much would the farmer be willing to pay
to have insurance?
iv. What is the risk premium?
Transcribed Image Text:Economics 2. Suppose that a farmer usually makes profit of $120,000 per year. Let's say that there is a 2% chance that a tornado will hit the farm. This would strongly hurt farmer's profit, leading to losses of $96,000 with 2% probability. a. What is the actuarially fair insurance? b. Assume that the farmer utility is given by u = 7 0.5 where 7t represents profit. What is the farmer's expected utility with no insurance? c. How much would the farmer be willing to pay to have insurance? d. Assume that the farmer expects that the tornado's effect to your farm is lower, only leading to losses of $70,000. i. What is the actuarially fair insurance? ii. What is the farmer's expected utility with no insurance? iii. How much would the farmer be willing to pay to have insurance? iv. What is the risk premium?
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