--%>
Assignment Help - homework help

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 Ys = 0.  If you do not get sick, your wealth will be Yh > 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. 

   Related Questions in Advanced Statistics

  • Q : Problem on Poisson distribution The

    The number of trucks coming to a certain warehouse each day follows the Poisson distribution with λ= 8. The warehouse can handle a maximum of 12 trucks a day. What is the probability that on a given day one or more trucks have to be sent away? Round the answer

    		•
  • Q : Error probability As of last year, only

    As of last year, only 20% of the employees in an organization used public transportation to commute to and from work. To determine if a recent campaign encouraging the use of public transportation has been effective, a random sample of 25 employees is to be interviewe

    		•
  • Q : Problem on income probability Kramer

    Kramer spends all of his income  $270  on two products, soup (S) and on golf balls (G). He always bought 2 golf balls for every 1 cup of soup he consumes. He acquires no additional utility from the other cup of soup unless he as well gets 2 more golf balls a

    		•
  • Q : Problem on layout A manufacturing

    A manufacturing facility consists of five departments, 1, 2, 3, 4, and 5. It produces four components having manufacturing product routings and production volumes indicated below.   1. Generate the from-to matrix and the interaction matrix. Use a

    		•
  • Q : MANOVA and Reflection Activity 10:

    Activity 10: MANOVA and Reflection 4Comparison of Multiple Outcome Variables This activity introduces you to a very common technique - MANOVA. MANOVA is simply an extension of an ANOVA and allows for the comparison of multiple outcome variables (again, a very common situation in research a

    		•
  • Q : Describe how random sampling serves

    Explain sampling bias and describe how random sampling serves to avoid bias in the process of data collection.    

    		•
  • Q : Variation what are the advantages and

    what are the advantages and disadvantages of seasonal variation

    		•
  • Q : Discrete and continuous data

    Distinguish between discrete and continuous data in brief.

    		•
  • Q : Problem on consumers marginal utility

    Consider a consumer with probability p of becoming sick.  Let Is be the consumer’s income if he becomes sick, and let Ins be his income if he does not become sick, with Is < Ins. Suppo

    		•
  • Q : Problem on Chebyshevs theorem 1. Prove

    1. Prove that the law of iterated expectations for continuous random variables.2. Prove that the bounds in Chebyshev's theorem cannot be improved upon. I.e., provide a distribution which satisfies the bounds exactly for k ≥1, show that it satisfies the

    		•