Study Guide for Microeconomics
9th Edition
ISBN: 9780134741123
Author: Robert Pindyck, Daniel Rubinfeld
Publisher: PEARSON
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Question
Chapter 5, Problem 9E
To determine
The utility curve.
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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?
Can you explain how Constant Relative Risk Aversion utility function should be understood and how it works mathematically
In the field of financial management, it has been observed that there is a trade-off between the rate of return that one earns on investments and the amount of risk that one must bear to earn that return.
a) Draw a set of indifference curves between risk and return for a person that is risk-averse (a person that does not like risk).
Chapter 5 Solutions
Study Guide for Microeconomics
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- . 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.arrow_forward. 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.arrow_forwardAn agent makes decisions using U(ct) = (ct−χct−1)1−γ 1−γ . Answer the following: (a) Suppose χ = 0. Derive an expression for the coefficient of relative risk aversion RR(ct)? (b) Suppose 0 < χ ≤ 1. Derive an expression for the coefficient of relative risk aversion RR(ct)?arrow_forward
- Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I (U’ > 0) and convex (U’’ > 0). a) Draw a utility function in U - I space that fits this description. b) Explain the connection between U’’ and risk aversion.arrow_forwardPlease draw a utility function that exhibits risk-loving behavior for small gambles (low values)and risk-averse behavior for larger gambles (high value).arrow_forwardPriyanka 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? Explainarrow_forward
- Risk aversion is best explained by a. Timidity b. Increasing marginal utility of income c. Constant marginal utility of income Decreasing marginal utility of income A Risk Lover prefers the expected utility of wealth to the utility of the expected value of wealth. a. TRUE. It is because a risk lover has a convex utility function b. FALSE. It is because a risk lover has a concave utility functionarrow_forwardIf a risk-averse individual owns a home worth $100,000, and that individual is willing to pay $1,000 for an annual fire insurance policy that covers the entire loss in the event of a fire, then we know that?arrow_forward. 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?arrow_forward
- Consider the following utility functions for wealth w: (i) u(w) = 3w, (ii) u(w) = w^1/3, (iii) u(w) = w + sqrt(w), (iv) u(w) = w*sqrt(w). Which of these is most risk-averse (has the highest Arrow-Pratt coefficient of absolute risk aversion) at w = 1?A. (i)B. (ii)C. (iii)D. (iv)arrow_forwardPlease answer true or false for each of the following statements. A risk-averse consumer has increasing marginal utility. A risk-neutral consumer is willing to pay a positive risk-premium to avoid risk. A risk-neutral consumer has a linear utility function. A risk-loving consumer has a convex utility function. A risk-averse consumer can increase her expected utility by buying multiple stocks whose outcomes are not closely related, instead of buying only one stock.arrow_forwardShow that an agent with utility function u(x) = log x is more risk aversethan an agent with utility function ˜u(x) = √x.arrow_forward
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