The East Chester Tribune must decide whether to publish an online Sunday edition. The publisher thinks...

The East Chester Tribune must decide whether to publish an online Sunday edition. The publisher thinks that the probability that this Sunday edition would be a success is equal to 60%, and it will be failure 40% of the time. If it is a success the profit will be $100. If it is a failure, it will be only $64.

a. If the manager is risk-averse (consider ?(?)=√?) what will be the premium for an insurance that will assure the manager that it will get a profit of $100 no matter what?

b. If the insurance company is risk-neutral, will the company offer such insurance (do not assume or talk about moral hazard). Why?

Solutions

Expert Solution

There is a 60% chance of profit = 100 and 40% chance of profit =64

so the expected utility can be written as

and we also know that so the equivalent wealth will equal

so w = 9.2^2 = 84.64

which means that this bet is equivalent to utility of a guaranteed wealth of 84.64$ so the manager is willing to pay 100-84.64$

that is 15.36$. so the premium will be 15.36$.

if the company is risk neutral its expected utility will be the same as expected wealth which will be

so the premium required 14.4$

so the company will offer the insurance as it is getting more than this required premium as the manager will be willing to pay 15.36

Rahul Sunny answered 1 year ago

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