Vhat is the behavior of a person with the following utility function? 1 0.8 0.6 5 0.4 0.2 $0 $50 $100 $150 $200 Wealth a) Risk-averse. b) Risk-seeking. c) Risk-seeking up to $100 wealth, then risk-averse after $100. d) Risk-averse up to $100 wealth, then risk-seeking after $100. e) Risk-neutral. Utility

Vhat is the behavior of a person with the following utility function? 1 0.8 0.6 5 0.4 0.2 $0 $50 $100 $150 $200 Wealth a) Risk-averse. b) Risk-seeking. c) Risk-seeking up to $100 wealth, then risk-averse after $100. d) Risk-averse up to $100 wealth, then risk-seeking after $100. e) Risk-neutral. Utility

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.12P

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Draw a utility function (with income on the horizontal axis) for an individual who is risk-loving at low levels of income, risk-neutral at moderate levels of income, and risk-averse at high levels of income (with each of these three regions clearly labeled). How would someone who looked at this graph (and had no other information about the individual) be able to figure out the individual’s attitude toward risk (averse/loving/neutral) in each region?
. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain.
Draw a utility function over income u( I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. Can you explain why such a utility function might reasonably describe a person’s preferences?
. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) √x . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain.
. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) = square root x. There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. b) What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?
Scenario 2 Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function ( sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. Refer to Scenario 2 Calculate Lex’s and Tess' expected utilities without insurance. (each one separated) Round to two decimal places for both
Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) = square root x . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain
Using a basic illustration, explain your understanding of utility theory given uncertainty
Consider the following prospects – A: (0.5, 0, 0.5: $100, $60, $10) B: (0, 0.9, 0.1: $100, $60, $10) C: (0.2, 0.5, 0.3: $100, $60, $10) D: (0.4, 0.2, 0.4: $100, $60, $10) Show that D>A>B>C is consistent with expected utility theory and that this preference ordering implies “risk-loving” preferences. Show that C>B>D>A is consistent with the expected utility theory.
Consider two individuals whose utility function over wealth I is ?(?) = √?. Both people face a 10 percent chance of getting sick, and foreach the total cost of illness equals $50,000. Suppose person A has a total net worth of $100,000, and person B has a total net worth of $1,000,000. Both people have the option to buy an actuarially fair insurance contract that would fully insure them against the cost of the illness. a. Using expected utility calculations, show that person A would certainly buy full, actuarially fair insurance. b. Suppose an insurance company wants to maximize profits and wants to charge each customer the maximum price they are willing to pay. How much should the insurance company charge each client so that both buy the contract? c. What is surprising about your result in part b? What does this tell you about how insurance companies may be pricing health insurance contracts in the real world?
Can you explain how Constant Relative Risk Aversion utility function should be understood and how it works mathematically
Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.