Question

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?

Answer 1

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