Problem on utility funtion probability

Suppose that your utility, U, is a function only of wealth, Y, and that U(Y) is as drawn below. In this graph, note that U(Y) increases linearly between points a and b.

Suppose further that you do not know whether or not you will be sick, but you do know that the probability of becoming sick is p (while the probability of staying healthy is 1-p). If you do get sick, your wealth will be Y_s = 0. If you do not get sick, your wealth will be Y_h > 0.

1940_utility function.jpg

(1) Write an expression for expected income, EI, and an expression for expected utility without insurance.

(2) Assume that a < EI < b. Draw, on the graph above, a line showing expected utility without insurance. Also draw a line showing expected utility with actuarially fair full insurance.

(3) Consider an actuarially fair partial insurance contract that offers a if you are sick and b if you are healthy. Would your utility with such a contract be greater or less than your utility with an actuarially fair full insurance contract? Briefly, explain.

View Complete Question

Related Questions in Advanced Statistics

Q : Probability of winning game Monte Carlo

Monte Carlo Simulation for Determining Probabilities 1. Determining the probability of winning at the game of craps is difficult to solve analytically. We will assume you are playing the `Pass Line.' So here is how the game is played: The shooter rolls a pair of

Q : Pearsons correlation coefficient The

The table below illustrates the relationship between two variable X and Y. A

Q : Problem related to playing cards Cards

Cards are randomly drawn one at the time and with replacement from a standard deck of 52 playing cards. (a) Find the probability of getting the fourth spades on the 10th draw. (b) Determine the

Q : Probability on expected number of days

It doesn't rain often in Tucson. Yet, when it does, I want to be prepared. I have 2 umbrellas at home and 1 umbrella in my office. Before I leave my house, I check if it is raining. If it is, I take one of the umbrellas with me to work, where I would leave it. When I

Q : Describe what happens to the confidence

A nurse practitioner working in a dermatology clinic is studying the efficacy of tretinoin in treating women's post partum abdominal stretch marks. From a sample of 15 women, the mean reduction of stretch mark score is -0.33 with a sample standard deviation of 2.46. Describe wha

Q : Correlation Define the term Correlation

Define the term Correlation and describe Correlation formula in brief.

Q : Calculate corresponding t value or s

1) Construct a 99% confidence interval for the population mean µ. 2) At what significance level do the data provide good evidence that the average body temperature is

Q : Statistics A nurse practitioner working

A nurse practitioner working in a dermatology clinic is studying the efficacy of tretinoin in treating women’s post partum abdominal stretch marks. From a sample of 15 women, the mean reduction of stretch mark score is -0.33 with a sample standard deviation of 2.46. Describe what happens to the c

Q : Conclusion using p-value and critical

A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evid

Q : Use the law of iterated expectation to

Suppose we have a stick of length L. We break it once at some point X _

Discover Q & A

Leading Solution Library

Avail More Than 1442398 Solved problems, classrooms assignments, textbook's solutions, for quick Downloads

No hassle, Instant Access

Start Discovering

18,76,764

1936658
Asked

3,689

Active Tutors

1442398

Questions
Answered

Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!

Submit Assignment