You are making a movie with a 20% chance of making a ton-load of money, and 80%

Question

You are making a movie with a 20% chance of making a ton-load of money, and 80% chance of earning nothing.

Your utility is the square root of income (Utility = Y1/2); you will have $1,000,0001/2 happiness if your movie succeeds but 01/2 happiness if it fails.

(1 point) What is the expected value of your movie? What is your utility at that income?

Note that in EXCEL, the square root function is “=X^.5” for the number X

(1 point) What is your expected utility from your movie? (Note: this is the weighted average of utility when the app succeeds and when it fails where the weight is the probability of success.)

(1 point) What would be the price, P, of a risk-neutral insurance plan where you have a guaranteed income of a successful movie and the insurance company breaks even without make profit?

(1 point) What is the maximum price you would be willing to pay? (Hint: what is the expected utility with and without insurance? The premium is the maximum amount that you would sacrifice to be guaranteed as much utility as without insurance.)

(1 point) Considering your answer to part A, in general, why do people buy insurance? How can insurance companies profit?   What happens to expected utility when people can buy insurance at a fair market price?

f)      (2 points) How else can insurance companies make profits? What is moral hazard and what is adverse selection. How do these affect insurance markets? Give examples from the marketing of automobile insurance. Would you expect markets with moral hazard and adverse selection to provide the optimal amount of car insurance at an efficient price?

Explanation / Answer

With the given probability, we have the wealth as

W = 1000000 with pr = 0.2 or 0 with pr = 0.8

Expected Wealth: W* = E(W) = 1000000 * 0.2 + 0 * 0.8 = 200000

Expected Utility: E[U(W)] = 0.2 * (1000000)^0.5 + 0.8 * (0)^0.5 = 0.2 * 1000 = 200

Utility of Expected Wealth: U(W*) = 200000^0.5 = 447.214

So, U(W*) > E[U(W)] , thus a producer will buy an insurance

Now expected utility under insurance where insurance premium is denoted as 'P'

E[U(insurance)] = 0.2 * U(1000000 - P) + 0.8 * U(1000000 - P)

[Since producer will get full 1000000 when he purchases insurance]

E[U(insurance)] = (1000000 - P)^0.5

equating the above equation with E[U(W)] , we get

(1000000 - P)^0.5 = 200

P = 1000000 - 40000 = 960000

Expected profit of the insurance company = 960000 - (0.2 * 0) - (0.8 * 1000000) = 960000 - 800000 = 160000

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.