--%>
Assignment Help - homework help

Problem on consumers marginal utility of income

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.

Suppose the consumer cares only about his expected utility of income, which is given by:

Expected Utility = p U (Is) + (1-p) U (Ins)
 
(1) Suppose that the consumer’s marginal utility of income, ∂U/∂I, increases with I. (That is extra income is valued more when this consumer is richer). What does this say about the consumer’s attitude toward risk?
 
Draw the consumer’s utility curve in a plane with utility on the y-axis and income on the x-axis, showing how utility changes with income.
 
On this same graph, show the consumer’s utility when he is sick and when he is well.
 
Show the consumer’s expected utility when p = 1/2.
 
(2) Suppose now that this consumer is considering the purchase of an insurance plan that will charge α1 to the consumer when he is healthy, and provide α2 to the consumer (on net) when he is sick.  Let α = (α1, α2) represent this insurance contract.
 
Provide a definition for actuarially fair insurance in this context.  Provide a definition for full insurance in this context. [Use algebra to develop these definitions].
 
What will α1 be (in terms of p, Is, and Ins) for an actuarially fair full insurance plan? 
What will α2 be (in terms of p, Is, and Ins) for an actuarially fair full insurance plan? 
 
(3) On a fresh copy of your graph from question B(1), show the consumer’s utility level after the purchase of an actuarially fair, full insurance plan.  Also show the consumer’s expected utility level before the purchase of any insurance plan.  How does the purchase of an actuarially fair, full insurance plan affect the consumer’s welfare?
 
What happens to the change in utility from the purchase of actuarially fair, full insurance as the probability of illness approaches zero (the consumer is certainly well)?
 
What happens to the change in utility from the purchase of actuarially fair full insurance as the probability of illness approaches one (the consumer is certainly sick)?

   Related Questions in Advanced Statistics

  • Q : Null hypothesis In testing the null

    In testing the null hypothesis H0: P=0.6 vs the alternative H1 : P < 0.6 for a binomial model b(n,p), the rejection region of a test has the structure X ≤ c, where X is the number of successes in n trials. For each of the following tests, d

    		•
  • 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 : 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 : Describe how random sampling serves

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

    		•
  • 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

    		•
  • Q : Pearsons correlation coefficient The

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

    		•
  • Q : Probability problem A) What is the

    A) What is the probability of getting the following sequence with a fair die (as in dice):B) What is the probability of getting the same sequence with a die that is biased in the following way: p(1)=p(2)=p(3)=p(4)=15%;

    		•
  • Q : Use the law of iterated expectation to

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

    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

    		•