Antonio has a utility function U = W, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stageof a game show, the host offers Antonio a choice between (A) $9 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $16million with probability 0.6.Use the blue curve (circle points) to graph Antonio's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million.?Utility (Thousands)5.04.54.03.53.0252.01.51.00.50+0246810 12 14Wealth (Millions of dollars)16 18True or False: Antonio is risk averse.2020Utility FunctionChoiceTrueO Falseoffers Antonio a higher expected prize. (Hint: The expected value of a random variable is the weighted average of the possible outcomes,where the probabilities are the weights.)Choice offers Antonio a higher expected utility.Antonio should pick choice,

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Answered: Antonio has a utility function U = W,…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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. 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?
Khalid has a utility function U = W1/2, where W is his wealth in millions of dollarsand U is the utility he obtains from the wealth. In a game show, the host offershim a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with probability 0.6 and $9 million with probability 0.4.i. Graph Khalid’s utility function with the help of above utility function. Ishe risk lover? Explain. ii. Does A or B choice offer Khalid a higher expected prize? Explain yourreasoning with appropriate calculations. iii. Does A or B offer Khalid a higher expected utility? Again, show yourcalculations. iv. Should Jamal pick A or B choice? Why?
At a different table, Juan wins $600 in a blackjack game. Similarly, he has to choose between $600 or the chance to play a new game. In this game, Juan has a 60% chance of winning nothing and a 40% of winning $1,000. The following graph presents the utility function of Juan with respect to money: U(w) U(w) U(1,000) U(700) U(600) U(400) 400 600 700 1,000 w 10.2.2 1.0 point possible (graded, results hidden) By how much money would his winnings need to increase or decrease so that Juan is indifferent between the $600 and the new game? (in case of an increase, insert a positive number; in case of a decrease, insert a negative number).
Suppose your friend Yvette offers you the following bet: She will flip a coin and pay you $3,000 if it lands heads up and collect $3,000 from you if it lands tails up. Currently, your level of wealth is $9,000. The graph shows your utility function from wealth. Use the graph to answer the following questions. UTILITY (Units of utility) 100 90 80 70 60 50 40 30 20 + 10 0 O 0 3 ** 6 с B 9 WEALTH (Thousands of dollars) 12 The shape of your utility function implies that you are a because the difference in utility between A and C is 15 ? individual, and, therefore, you the difference between C and accept the wager Which of the following best explain why the pain of losing $3,000 exceeds the pleasure of winning $3,000 for risk-averse people? Check all that apply. Risk-averse people overestimate the probability of losing money. Risk-averse people are relatively poor and cannot afford to lose any money. The more wealth that risk-averse people have, the less satisfaction they receive from an…
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?
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.
Suppose your classmate Shen offers you a wager: He will choose a playing card at random from a deck and pay you $1,000 if it is red, but you have to pay him $1,000 if it is black. Assume your wealth is currently $3,000. The graph shown below plots your utility as a function of wealth. Use the graph to answer the questions that follow. UTILITY (Units of utility) 100 90 80 70 60 50 40 30 20 10 0 0 1 B +++ A 2 * 3 WEALTH (Thousands of dollars) The shape of your utility function implies that you are a the difference in utility between C and A is less than 4 5 ? risk-averse individual, and, therefore, you would not the difference between A and B. accept the wager because Which of the following sentences most appropriately describe why the pain of losing $1,000 is greater than the joy of winning $1,000 for individuals who are risk averse? Check all that apply. Risk-averse people are relatively wealthy and simply do not need the additional money. ✔ The utility function of a risk-averse person…
Suppose the Super Bowl is this week, and Raphael is in need of a television to watch the big game. As a college student, Raphael knows that he can either buy his flat-screen television at the local electronics store, or he can shop online for a better deal but have to wait four days for the television to arrive. The following problem uses the economic concept of rate of time preference to help determine which decision is better for Raphael. Throughout the question, assume that Raphael pays for the good the day he buys it, so his wealth is affected in the initial time period no matter where he buys the good. Also, assume the shipping cost and cost to travel to the store are incorporated into their respective given prices. Finally, assume the goods are identical, and there's no cost to gaining information about prices-in other words, he knows the best price online and in the store without having to search. Suppose Raphael receives a utility of 35.11 utils once he actually receives his…
Consider two individuals, Dani and Tom. Dani's utility function is given by U(c)=In(c), where c is the amount of consumption in a given period. Tom's utility is U(c)=c^2 a) In two separate graphs, draw Dani and Tom's utility function (U in y-axis, c in x-axis). b) Both Dani and Tom can purchase a lottery that pays 5 with 75% probability, and 15 with 25% probability. Calculate and mark on the graphs the utility evaluated at the expected level of consumption for the lottery. Then calculate and mark on the graphs the expected utility for Dani and Tom. c) How do utilities at the expected level of consumption compare to the expected utility? What explains the difference between Dani and Tom? What implication does this difference have for their risk preferences?
Max is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $15,000. With probability p = 0.7 the palace will succeed and Max's wealth will grow from $15,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $10,000, so that his wealth will be just $5,000. What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $15,000 with certainty? (Please round your final answer to the whole dollar, if necessary)
Suppose your classmate Tim offers you a wager: He will choose a playing card at random from a deck and pay you $3,000 if it is red, but you have to pay him $3,000 if it is black. Assume your wealth is currently $9,000. The graph shown below plots your utility as a function of wealth. Use the graph to answer the questions that follow. UTILITY (Units of utility) 100 90 80 70 60 50 40 30 20 10 0 0 32 + 6 U + 9 B ?
Johnny owns a house that is worth $100,000. There is a O.1% chance that the house will be completely destroyed by fire, leaving Johnny with $0. Johnny's utility function is u(x) = vx, where x represents final wealth. Assuming that Johnny has no other wealth, what's the maximum amount that he would be willing to pay for an insurance policy that completely replaces his house if destroyed by fire? Make sure to answer with the dollar sign and then the number, i.e. $532.17. Be accurate up to the second decimal. You should not need to round. Hint: The hundredths place should be 0. Enter your answer here

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