Question

In: Economics

1. Ichiro has a utility of U = 0.1M0.5 and is considering the purchase of insurance...

1. Ichiro has a utility of U = 0.1M0.5 and is considering the purchase of insurance against accident damage to his $100,000 Range Rover, which is his only asset. There is a 5% probability of an accident that would cause $40,000 in damage. Insurance that would completely compensate him for that damage is available.

a.What is the certainty equivalent value to him of the gamble of not buying insurance?

b.What is the most Ichiro would be willing to pay for the insurance?

Solutions

Expert Solution

Expected Value =0.95(100000)+0.05(60000)=95000+3000=98000

Expected Utility=0.95(0.1*100000^0.5)+0.05(0.1*60000^0.5)=31.26

Certainety equivalent an be found as

u(CE(x))=EU(x)=31.26

0.1*CE(x)^0.5=31.26

CE(x)=312.6^2=$97718.6

Answer for b)

As CE(x)<E(x)

Ichiro's WTP for insurance is =Acturially fair premium=E(x)-CE(x)=98000-97718.6=$281.4

Rahul Sunny answered 2 years ago
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