--%>
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 : What is your statistical decision

    Question 1 Do parents with more children travel more than parents of small families? To find out, a survey was done of a large number of adults. Respondents were asked how many children they had and how many times

    		•
  • 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 : Pearsons correlation coefficient The

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

    		•
  • 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 : Find the cumulative distribution

    You must use the pre-formatted cover sheet when you hand in the assignment. Out full detailed solutions. Sloppy work will naturally receive a lower score. 1. Suppose at each step, a particle moving on sites labelled by integer has three choices: move one site to the right with pro

    		•
  • 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 : 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 : Correlation Define the term Correlation

    Define the term Correlation and describe Correlation formula in brief.

    		•
  • Q : Probability and Statistics

    Instructions: Do your work on this question and answer sheet. Please print or write legibly, and, as always, be complete but succinct. Record your answer and your supporting work in the designated space. Explain your method of solution and be sure to label clearly any

    		•
  • Q : Probability Distributions and Data

    1. A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is canceled before 6:00 p.m. deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find the exact value and the normal approxi

    		•