Mr. Raffles has a 40% chance of becoming ill and having to pay $1000 for medical...

Mr. Raffles has a 40% chance of becoming ill and having to pay $1000 for medical care, and a 60% chance of being healthy and not having to pay anything for medical care. He is just indifferent between taking this risk and paying a $500 premium for health insurance that will give him exactly $1000 for health care when he is sick. Is John risk adverse, risk neutral, or risk loving? Explain. Draw a utility function to explain your answer.

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Solution

Mr.Raffles needs has 2 choices -Opt for health insurance and not to opt for Health insurance.He chooses the option which is having the highest utility (in general/ situation).So,calculating the utilities of both the choices:

Cost of Not Opting for Insurance

40% * (1000) + 60%* (0) i.e.,( 0.4 * 1000) + (0.6*0)

= $400

Cost of opting for insurance

$500 (insurance premium)

So,Mr.Raffles will not opt for Insurance as $500 is more than $400

Correction: In the Question,it is addressed as John instead of Raffles.I am assuming it is Raffles.

Raffles is risk neutral (ex:her in this case) if he chooses to opt for no insurance.If he opts for insurance inspite of it's utility/ value being lesser then he is said to be risk averse.

In case if the utility / expected value of opting for insurance is more less than that in case of not opting .Inspite of this condition,if Mr.Raffles is not opting for insurance then he is said to be risk loving.Here,he is taking the risk by not considering / obeying the concept of expected value / utility.

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Rahul Sunny answered 1 year ago

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