Macroeconomics
13th Edition
ISBN: 9780134735696
Author: PARKIN, Michael
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Question
Chapter 20, Problem 7APA
To determine
Identify the expected utilities of J and Z.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Text of the problem from 'An introduction to decision theory' by Martin Peterson:
You prefer a fifty-fifty chance of winning either $100 or $10 to a lottery in which you win $200 with a probability of 1/4, $50 with a probability of 1/4, and $10 with a probability of 1/2. You also prefer a fifty-fifty chance of winning either $200 or $50 to receiving $100 for sure. Are your preferences consistent with von Neumann and Morgenstern’s axioms?
The book proposes as solution 'No. Your preferences violate the independence axiom.' without proposing the steps to reach that solution and I don't know why it is correct.
.What is the probability of getting a king if a card is drawn from a pack of 52 cards?
Jamal has a utility function U= W1/2 where Wis his wealth in millions of 'dollars and Uis 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 $1million with a probability of 0.6 and $9 million with a probability of 0.4.
a. Graph Jamal's utility function. Is he risk-averse? Explain.
b. Does A or B offer, Jamal, a higher expected price? Explain your reasoning with appropriate calculations. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.)
c. Does A or B offer Jamal a higher expected utility? Again, show your calculations.
d. Should Jamal pick A or B? Why?
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
Knowledge Booster
Similar questions
- 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. a. b. c. d. Graph Jamal’s utility function. Is he risk averse? Explain. (2+2) Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why?arrow_forward2. Alex plays football for a local club in Kumasi. If he does not suffer any injury b y the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coa ch worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = √X Assume he could buy insurance at price P that could pay $9,900 in case of inj ury. What is the highest value of P that makes it worthwhile for Alex to purcha se insurance? What is the certainty equivalence for this lottery?arrow_forwardhow do you do you find the expected payback for this problem? Find the expected payback for a game in which you bet $1010 on any number from 00 to 399.399. If your number comes up, you get $400400.arrow_forward
- 6. Jerry plans to buy a new Bluetooth headset. He knows that the same product is offered in different shops with prices of $44, $49, and $60, and with odds of one-third of finding each price. He just stopped at a shop and knows that their price is $49. If the search cost is $1 per additional search, what should Jerry do?arrow_forward10 Use the expected value information to illustrate how having more bidders in an oral auction will likely result in a higher winning bid.arrow_forwardSuppose your wealth is 8 and you are considering a bet of a 50% chance of winning $4 and a 50% chance of losing $4. What is your risk premium given you have In utility ? Draw a diagram and label the relevant values.arrow_forward
- Suppose you have $35,000 in wealth. You have the opportunity to play a game called "Big Bet/Small Bet." In this game, you first choose whether you would like to make a big bet of $15,000 of a small bet of $5,000. You then roll a fair die. If you roll a 4, 5, or 6, you win the game and earn $15,000 for the big bet or $5,000 for the small bet. If you roll a 1, 2, or 3, you lose and lose $15,000 for the big bet and $5,000 for the small bet the game Utility U₂ U₁ BEL 0 11 LATE EE ARTE Are the Small Bet and Big Bet considered fair bets? O Big Bet is fair, but Small Bet is not. No, both are not fair. Yes, both are fair. 20 OSmall Bet is fair, but Big Bet is not. G HA 1 35 D E 1 1 1 1 1 F 1 U 50 Income (thousands of dollars)arrow_forwardThe following table shows the relationship between your wealth (in thousands of dollars) and your utility: Wealth Utility. 15.0 10 23.0 15 30.0 20 36.0 25 41.0 30 46.0 35 50.0 You can invest in asset A, which offers a riskless payoff of $15,000 or in asset B, which pays $5,000 with 40% probability and $25,000 with 60% probaility. Which investment do you choose? A. B, because its expected utility of 31.6 is greater than the utility of A. O B. A, because it is riskless. OC. A, because its utility is greater than the expected utility of B, which is 28.4. O D. B, because its expected utility of 30.6 is greater than the utility of A.arrow_forward1: A risk-averse individual is offered a choice between a gamble that pays £2000 with a probability of 25% and £200 with a probability of 75%, or a payment of £650. Using a diagram explain which he would choose? What if the payment was £640?arrow_forward
- 3. Han Solo is delivering illicit cargo to the rebel forces on Alderaan, a planet blockaded by the galactic empire. In order to deliver his cargo successfully, Han Solo must pass 2 checkpoints, each of which will not detect his cargo with probability q. If Han Solos cargo is detected at one or more checkpoints, then his final wealth is 0. If Han Solo passes both checkpoints undetected, then his final wealth is 100. Han Solo's risk- preference is described by Bernoulli utility function Vw. Thus Han Solo's wealth is described by a lottery: 100 with probability q?, 0 with probability 1- q. (a) What is Han Solo's expected utility? Suppose an Imperial officer makes an offer to Han Solo. The officer will reduce number of checkpoints from 2 to 1, but if Han Solo gets through, he has to pay k to the officer. If Han Solo gets caught, his payoff is 0. If he agrees to this arrangement, then his final wealth is described by a lottery: 100 – k with probability q, 0 with probability 1- q. (b) What…arrow_forward2. Kier, in The scenario, wants to determine how each of the 3 companies will decide on possible new investments. He was able to determine the new investment pay off for each of the three choices as well as the probability of the two types of market. If a company will launch product 1, it will gain 50,000 if the market is successful and lose 50,000 if the market is a failure. If a company will launch product 2, it will gain 25,000 if the market is successful and lose 25,000 if the market will fail. If a company decides not to launch any of the product, it will not be affected whether the market will succeed or fail. There is a 56% probability that the market will succeed and 44% probability that the market will fail. What will be the companies decision based on EMV? What is the decision of each company based on expected utility value?arrow_forwardYou are a hotel manager and you are considering four projects that yield different payoffs, depending upon whether there is an economic boom or a recession. The potential payoffs and corresponding payoffs are summarized in the accompanying table Project Red Orange Green Blue Multiple Choice The expected value of project Red is O OO $110. $50. $100. Boom (80%) $80 $ 70 $200. $90 $ 110 Recession (20%) $70 $80 $ 90 $ 110arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Managerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage Learning
Brief Principles of Macroeconomics (MindTap Cours...EconomicsISBN:9781337091985Author:N. Gregory MankiwPublisher:Cengage Learning
Essentials of Economics (MindTap Course List)EconomicsISBN:9781337091992Author:N. Gregory MankiwPublisher:Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning
Brief Principles of Macroeconomics (MindTap Cours...
Economics
ISBN:9781337091985
Author:N. Gregory Mankiw
Publisher:Cengage Learning
Essentials of Economics (MindTap Course List)
Economics
ISBN:9781337091992
Author:N. Gregory Mankiw
Publisher:Cengage Learning