--%>
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 : Analytical Report Hi I WOULD LIKE TO

    Hi I WOULD LIKE TO KNOW IF YOU CAN HELP ME TO DO THE ASSIGNMENT IN HEALTH STATISTICS THANKS

    		•
  • 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 : Binomial distribution 1) A Discrete

    1) A Discrete random variable can be described as Binomial distribution if is satisfies four conditions, Briefly discuss each of these conditions2) A student does not study for a multiple choice examination and decides to guess the correct answers, If the

    		•
  • 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 : 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 : 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 : 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 : 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 : 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

    		•