Macroeconomics
13th Edition
ISBN: 9780134735696
Author: PARKIN, Michael
Publisher: Pearson,
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Chapter 20, Problem 13APA
To determine
Identify the expected wealth and expected utility.
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Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4.
(1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why?
I would like help with the unanswered last parts of the questions.
# 4
Consider an individual with a utility function of the form u(w) = √w. The individual has an initial wealth of $4. He has two investments options available to him. He can eitffer keep his wealth in an interest-free account or he can take part in a particularly generous lottery that provides $12 with probability of 1/2 and $0 with probability 1/2. Assume that this person does not have to incur a cost if he decides to take part in the lottery. (a) Will this individual participate in the lottery? (b) Calculate this individual's certainty equivalent associated with the lottery. What is his risk premium?
Steve has received a stock tip from Monica. Monica has told him that XYZ Corp. will increase in value by 100%. Steve believes that Monica has a 25% chance of being correct. If Monica is incorrect, Steve expects the value of XYZ Corp. will fall by 50%.
a. If Steve's utility of income is U(I)=50I. What is Steve's expected utility from buying $1,000 worth of XYZ Corp. stock?
b. If Steve's utility of income is U(I)=I0.5. What is Steve's expected utility from buying $1,000 worth of XYZ Corp. stock?
Chapter 20 Solutions
Macroeconomics
Ch. 20.1 - Prob. 1RQCh. 20.1 - Prob. 2RQCh. 20.1 - Prob. 3RQCh. 20.1 - Prob. 4RQCh. 20.2 - Prob. 1RQCh. 20.2 - Prob. 2RQCh. 20.2 - Prob. 3RQCh. 20.2 - Prob. 4RQCh. 20.3 - Prob. 1RQCh. 20.3 - Prob. 2RQ
Ch. 20.3 - Prob. 3RQCh. 20.3 - Prob. 4RQCh. 20.4 - Prob. 1RQCh. 20.4 - Prob. 2RQCh. 20.4 - Prob. 3RQCh. 20 - Prob. 1SPACh. 20 - Prob. 2SPACh. 20 - Prob. 3SPACh. 20 - Prob. 4SPACh. 20 - Prob. 5SPACh. 20 - Prob. 6SPACh. 20 - Prob. 7APACh. 20 - Prob. 8APACh. 20 - Prob. 9APACh. 20 - Prob. 10APACh. 20 - Prob. 11APACh. 20 - Prob. 12APACh. 20 - Prob. 13APACh. 20 - Prob. 14APACh. 20 - Prob. 15APACh. 20 - Prob. 16APACh. 20 - Prob. 17APACh. 20 - Prob. 18APACh. 20 - Prob. 19APACh. 20 - Prob. 20APACh. 20 - Prob. 21APACh. 20 - Prob. 22APACh. 20 - Prob. 23APA
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- Paul has a utility function of U =[ i to the power 1/2] with income measured in thousands. He will get a job that either pays 25 thousand a year or 64 thousand a year. What is his expected utility, expected payoff, the utility of his expected payoff, and her risk premium? Additionally, plot Paul's utility and income. Show and label his utility curve, his expected utility, and risk premium. Note: Please solve only the bolded part of the question. The previous part was already answeredarrow_forward‘‘Risk-averse people should only be averse to big gambles with a lot of money at stake. They should jump on any small gamble that is unfair in their favor.’’ Explain why this statement makes sense. Use a utility of income graph like Figure 4.1 to illustrate the statement. For a challenge, demonstrate the statement using a two-state graph like Figure 4.6.arrow_forwardJacob is considering buying hurricane insurance. Currently, without insurance, he has a wealth of $80,000. A hurricane ripping through his home will reduce his wealth by $60,000. The chance of this happening is 1%. An insurance company will offer to compensate Jacob for 80% of the damage that any tornado imposes, provided he pays a premium. Jacob’s utility function for wealth is given by U(w) = In (w). (A) What is the maximum amount Jacob is willing to pay for this insurance? Show work and explain.arrow_forward
- A consumer has utility u(x,y) = x^4 y^2 where x is this year’s consumption, and y is next year’s consumption. She makes 600 dollars income this year and 720 dollars income the next year. There is also a bank where she can borrow money at the interest rate r=%50 and lend money (to the bank) at the interest rate r=%20 (of course, she will decide to borrow or lend this year and pay off her debt or receive her savings the next year). a. Should she borrow money from or lend to the bank this year? How much b. If her utility were u(x,y) = xy2 instead, re-solving (a), would she borrow money or lend? How much? c. If her utility were u(x,y) = x^c y^2, what should “c” be so that she ends up neither borrowing nor lending?arrow_forwardEconomics Consider a potential criminal with a lawful income of $121. Potential loot from robbery is $75. The probability of being caught and imprisoned is 0.50 and a prison term for this type of crime is 0.33 units of time. Round to one decimal place in all calculations. Utility is given by: Utility = (income)1/2 A. Calculate the guaranteed utility from lawful income and the expected utility of committing the crime. What will the potential criminal do? Explain why. Would your answer change if there were an anguish cost of 1 util involved? Explain. B. Suppose all the information given above holds true, except there is no anguish cost. You are a city official who has some extra room in the budget to dedicate towards fighting crime. For the use of these resources, you can choose between either increasing the length of prison term for criminals to 0.595 units of time or investing in GIS technologies and improved policing strategies that will increase the probability of criminals being…arrow_forwardSanjay won a poker game against his friends. Now he has to choose between $600 (the winnings) and the chance to play a new game. In this new game, Sanjay has a 50% chance of winning nothing and a 50% chance of winning $1000. The following graph presents the utility function of Sanjay with respect to money: 1. By how much money would his winnings need to increase or decrease so that Sanjay isindifferent between the $600 and the new game? At a different table, Juan wins $800 in a blackjack game. Similarly, he has to choose between $800 or the chance to win a new game. In this game, Juan has a 45% chance of winning nothing and a 55% chance of winning $1000. The following graph presents the utility function of Juan with respect to money: 2. By how much money would his winnings need to increase or decrease so that Juan is indifferent between the $800 and the new game? Please enter a positive number for an increase or a negative number for a decrease.arrow_forward
- B. Richard's nickname is "No-Risk Rick" because he is an extremely risk-averse individual. His utility function is given by U(W) = √W. where W represents his current wealth in dollars. He currently has $100 worth of property, but there is a 50% chance that all of it will be stolen. What is Richard's expect wealth and expected utility of wealth? An insurance company offers to reimburse Richard for his loss if the money is stolen. What is the most that Richard would pay for such a policy? Explain. Please solve this with in 1 hourarrow_forwardA. From the graph below explain how an insurance plan which provides the buyer a $15,000 wealth level, regardless of any uncertain event, is a good deal for the buyer? In other words, what does the distance between points D’ and C’ represent? Note we are referring to D prime, not D. B. Considering the graph below, can you explain the difference between expected utility and certainty utility?arrow_forwardAdam has just purchased a new car and has to decide whether to buy insurance to cover his new car in the event of a loss. Assume that Adam knows the probability (p) of him having an accident and losing his new car. The car is valued at L and the amount of insurance to purchase for this value is X. Adam’s entire wealth after buying the car is W. Let r be unit price of insurance. Briefly explain the problem of the insurance company and show that for insurance to be actuarially fair, the premium must equal the probability of accident.arrow_forward
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