Given the function u(x) = x0.5 , where x is consumption and represents your preference over...

Given the function u(x) = x^0.5 , where x is consumption and represents your preference over gambles using an expected utility function.

There is a probability of 0.1 in getting consumption xB (bad state) and a probability 0.9 of getting xG (good state).

An insurance company allows people to choose an insurance contract (b, p), where b is the insurance benefit the company pays if the bad state occurs, and p is the insurance premium paid to the company regardless of the state.

Suppose the company's offer is p = 0.2b. People can choose any combination of (b, p) subject to this offer.

(i) Is the insurance contract actuarily fair? How much will people insure (i.e. find the optimal p and b)? (Note that if the insurance contract here is not actuarily fair, you will need to modify the variables accordingly).

(ii) What will the consumption levels be in the two states with the insurance? Are you fully insured?

Expert Solution

Rahul Sunny answered 2 years ago

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