--%>
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 : Use the law of iterated expectation to

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

    Q : Random variables Random variables with

    Random variables with zero correlation are not necessarily independent. Give a simple example.    

    		•
  • 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 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

    		•
  • 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 : How you would use randomization in

    The design of instrument controls affects how easily people can use them. An investigator used 25 students who were right-handed to determine whether right-handed subjects preferred right-handed threaded knobs. He had two machines that differed only in that one had a

    		•
  • 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 : Statistics Homework with SAS File is

    File is attached, need it by 8:30 AM Pacific (Seattle, WA) time. No delay acceptable. Need it March 25, 2014 on 8:30 AM Pacific time.

    		•
  • Q : Calculate confidence interval A nurse

    A nurse anesthetist was experimenting with the use of nitronox as an anesthetic in the treatment of children's fractures of the arm.  She treated 50 children and found that the mean treatment time (in minutes) was 26.26 minutes with a sample standard deviation of

    		•
  • Q : Pearsons correlation coefficient The

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

    		•