Assume that an individual has the following relationship between income and utility.

Q1) Assume that an individual has the following relationship between income and utility.

Income Utility

30,000 40

40,000 180

50,000 250

60,000 280

70,000 300

The individual has the income 70,000. With probability 0,5 an accident occurs and she has to pay 40,000. With probability 0,5 the accident does not occur and she keeps 70,000. She can also buy a full insurance. Assume that the price of the insurance is fair. Will the individual buy the insurance? Explain. Is it possible that she wants to pay more than the fair premium? If so, how much?

Solutions

Expert Solution

Calculating the fair price for premium probability factored income will be 0.5*(70000-40000)+0.5*70000=50000,

Premium at that value will be 70000-50000=20000

Weighted average utility for the individual would be at 70000 and after accident (70000-40000)=30000 will be 0.5*300+0.5*40=170

At 50000 utility is 250 whereas current utility without insurance comes out to be 170 so individual can pay premium till the levels it's utility remains above 170 hence will be satisfied with fix pay of 40000 with utility of 180 which is above 170.

So she can pay premium up to 70000-40000=30000

Hence Individual will buy insurance and the fair value of insurance is 20000, She can pay upto 30000 as premium which is 10000 more than the fair premium

Rahul Sunny answered 1 year ago

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