EBK INTERMEDIATE MICROECONOMICS AND ITS
12th Edition
ISBN: 9781305176386
Author: Snyder
Publisher: YUZU
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Question
Chapter 4, Problem 10RQ
To determine
Effect of slope on the risk is “priced” in the market is to be ascertained.
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Students have asked these similar questions
Consider the following claim: “If a decision maker prefers one given lottery that yields $x with probability 1 over another given lottery whose expected return is $x, then we can fully characterize the agent's risk attitude. That is, this information comparing two given lotteries is enough to determine if the decision maker is risk averse, risk loving or risk neutral.” If this claim is TRUE, then provide a proof. If it is FALSE, then prove your argument by providing an explanation.
Utility functions incorporate a decision maker’s attitude towards risk. Let’s assume that the following utilities were assessed for Danica Wary.
x
u(x)
-$2,000
0
-$500
62
$0
75
$400
80
$5,000
100
Would a risk neutral decision maker be willing to take the following deal: 30% chance of winning $5,000, 40% chance of winning $400 and a 30% chance of losing $2,000?
Using the utilities given in the table above, determine whether Danica would be willing to take the deal described in part a?
Is Danica risk averse or is she a risk taker? What is her risk premium for this deal?
5.
In economics, an index of risk aversion is defined as:
-U" (m)
U'(m)
I (m)
where m measures how much of a commodity is owned and U(m) is a utility function. Find the index
of aversion, I(m), for both utility functions U₁(m) = √m and U,(m) = m5/8, and determine which
indicates a greater aversion to risk.
Chapter 4 Solutions
EBK INTERMEDIATE MICROECONOMICS AND ITS
Ch. 4.1 - Prob. 1MQCh. 4.1 - Prob. 2MQCh. 4.1 - Prob. 3MQCh. 4.2 - Prob. 1TTACh. 4.2 - Prob. 2TTACh. 4.2 - Prob. 1MQCh. 4.3 - Prob. 1TTACh. 4.3 - Prob. 2TTACh. 4.3 - Prob. 1MQCh. 4.3 - Prob. 2MQ
Ch. 4.3 - Prob. 3MQCh. 4.3 - Prob. 1.1TTACh. 4.3 - Prob. 1.2TTACh. 4.3 - Prob. 2.1TTACh. 4.3 - Prob. 2.2TTACh. 4.3 - Prob. 1.1MQCh. 4.3 - Prob. 2.1MQCh. 4.3 - Prob. 3.1MQCh. 4.4 - Prob. 1TTACh. 4.4 - Prob. 2TTACh. 4 - Prob. 1RQCh. 4 - Prob. 2RQCh. 4 - Prob. 3RQCh. 4 - Prob. 4RQCh. 4 - Prob. 5RQCh. 4 - Prob. 6RQCh. 4 - Prob. 7RQCh. 4 - Prob. 8RQCh. 4 - Prob. 9RQCh. 4 - Prob. 10RQCh. 4 - Prob. 4.1PCh. 4 - Prob. 4.2PCh. 4 - Prob. 4.3PCh. 4 - Prob. 4.4PCh. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Prob. 4.7PCh. 4 - Prob. 4.8PCh. 4 - Prob. 4.9PCh. 4 - Prob. 4.10P
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- Explain intuitively (or give a specific example) and show graphically what a risk premium is.arrow_forward5. You are a risk-averse decision maker with a utility function U(1) = VI, where I denotes your income. Your income is $100,000 (thus, I=100). However, there is a 0.2 chance that you will have an accident that results in a loss of $10,000. Now, suppose you have the opportunity to purchase an insurance policy that fully insures you against this loss (i.e., that pays you $10,000 in the event that you incur the loss). What is the highest premium that you would be willing to pay for this insurance policy?arrow_forwardQuestion 3: Jane has utility function over her net income U(Y)=Y2 a. What are Jane's preferences towards risk? Is she risk averse, risk neutral or risk loving? [Briefly explain your answer] b. Jane drives to work every day and she spends a lot of money on parking meters. She is considering of cheating and not paying for the parking. However, she knows that there is a 1/4 probability of being caught on a given day if she cheats, and that the cost of the ticket is $36. Her daily income is $100. What is the maximum amount of she will be willing to pay for one day parking? c. Paul also faces the same dilemma every single day. However, he has a utility function U(Y)-Y. His daily income is also $100. What is Paul's preference towards risk? Is he risk averse, risk neutral or risk loving? d. If the price of one day parking is $9.25, will Paul cheat or pay the parking meter? Will Jane cheat or pay the parking meter?arrow_forward
- 1. Show if the following utility functions represent risk averse, risk neutral or risk loving preferences. u(c) = 10° + 3 u(c) = C2 + 3C i. ii. ii. u(c) = e4C iv. u(c) = 1 – e-Carrow_forwardQuestion 1 In class we have learned that, given an indirect utility function u(w), there are two relevant measures of risk aversion, namely absolute risk aversion, A(w) = A(w)w. The following questions relate to risk aversion in general, and relationships around these two u" (w) '(w) ' and relative risk aversion, R(w) measures. 1. Utility function u(w) is risk averse if it is concave. Show mathematically that the set of all risk averse functions is a convex set. 2. It is often argued that absolute risk aversion should satisfy DARA (i.e. absolute risk aversion is decreasing in w). Show that, (i) a neccesary but not sufficient condition for DARA is that v(w) = -u'(w) is concave, and (ii) that a necessary and sufficient condition for DARA is that v(w) = -u'(w) is more risk averse than u(w). 3. If u(w) satisfies positive and constant relative risk aversion (CRRA, that is, relative risk aversion is constant in w), show that u(w) also must be DARA. 4. Is the set of all DARA utility functions…arrow_forwardIn 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).arrow_forward
- Consider the lottery that assigns a probability r of obtaining a level of consumption CH and a probability 1-T of obtaining a low level of consumption cL an individual facing such a lottery with utility function u(c) that has the properties that more is better (that is, a strictly positive marginal utility of consumption at all levels of c) and diminishing marginal utility of consumption, u"(c) CL. Consider du(c) for the first derivative of the utility function with respect to dc d²u(c) dc2 du' (c) consumption and u"(c) which is also the derivative of the first derivative of the utility function). to be the second derivative of the utility function dcarrow_forwardIf a risk-neutral individual owns a home worth $200,000 and there is a three percent chance the home will be destroyed by fire in the next year, then we know 15. that: a) He is willing to pay much more than $6,000 for full cover. b) He is willing to pay much less than $6,000 for full cover. c) He is willing to pay at most $6,000 for full cover. d) None of the above are correct. e) All of the above are correct.arrow_forwardSuppose Xavier has tickets to the Super Bowl, but is terribly ill with a noncontagious infection. How would a decision maker perform his economic calculation on whether to attend the game, based on the traditional model of risk behavior?arrow_forward
- Can you explain how Constant Relative Risk Aversion utility function should be understood and how it works mathematicallyarrow_forwardTess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function 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. 1. Suppose the actuarially fair premium charge is 2600, Calculate Tess’ expected utility with full insurance if she is charged the premium. Round to two decimal places. 2. What is the premium that private insurance companies will charge for full insurance? Round to two decimal places. 3.Assume the social welfare function is the sum of the Tess’ and Lex’s utility functions. Select the correct statement regarding the explanation for what has happened in the private market and the role of social insurance. a.Adverse section has lead to market failure. The government could improve social welfare by…arrow_forwardDraw 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?arrow_forward
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