Note: If they win the video, they double their winnings. If they lose, then they
ID: 3305072 • Letter: N
Question
Note: If they win the video, they double their winnings. If they lose, then they don't recieve any money.
2. Double or nothing Aa Aa While spending the weekend in New York City, Albert, Beth, and their son Zach are lucky enough to hail the Cash Cab for their taxi ride. During their ride they win $100 for correct answers and receive only one strike for a wrong answer, so at the end of the ride they are eligible for the Video Bonus question! Their vacation budget before entering the cab was $400, and based on their understanding of the type of question asked in the bonus question, they believe they have a 70% chance of getting the question right. The following graph shows the cab riders' utility as a function of their total vacation budget. For simplicity, assume that all three passengers have the same preferences, and they only care about their joint budget since they are family Utility (Units of utilityl 10 0 100 200 300 400 500 600 700 800 900 1000 VACATION BUDGET (Dollars] If they choose not to do the Video Bonus question, they will receive a utility of To determine whether they should attempt the Video Bonus question, you first have to examine the payoffs the family will receive, depending on whether they get the Video Bonus question correct or incorrect. Complete the following table with the total vacation budget they will have in each situation and the utilities corresponding to each outcome: Vacation Budget (Dollars) Utility (Units of utility) Correct IncorrectExplanation / Answer
To start with this question ,let me first breakdown the scenario to make it simpler to understand:
1.Let I be initial weath of the family ;2.Let X be the amount won by the family in the game cash cab
3.Let p be the probability that the family answers the video bonus question correctly.;4":Total budget=I+X
To begin with the question :
The utility function table can be interpreted as :
For the first part :
a)I=400;X=100;p=0.7
If they do not choose to opt for the video bonus question : T=500 ->U(T)=6 units of utility
b)(REMEMBER: On winning the video bonus ,the amount of win doubles -> hence amount =2*100=$200
Hence Expected Utility from the gamble =E(U(T))=0.7*6.2+0.3*5.5=4.34+1.65=5.99
c)Because expected utility from taking the gamble is less than the utility they recieve if they do not do the bonus,they DO NOT do the video bonus question.
FOR THE NEXT PART ;there are several cases given regarding values of I,X and p
Case 1: p=0.3,I=400,x=100,T=500;
Hence Guaranteed Utility U(500)=6;(given :it is the utility when he does not play the bonus)
For Expected Utility : E(U(T))=0.3*6.2+0.7*5.5=5.71
As E(U(T))<Guaranteed Utility ,they would not opt for the video bonus.
Similarly
CASE : p=0.7,X=300,I=400 ;
Guaranteed utility =U(700)=6.5
Expected Utility=E(U(T))=0.7*U(1000)+0.3*U(400)=6.41
As E(U(T))<Guaranteed Utility ,they would not opt for the video bonus.
Similarly
CASE 3 : p=0.7,X=100,I=300 ;T=400
Guaranteed utility =U(400)=5.5
Expected Utility=E(U(T))=0.7*U(500)+0.3*U(300)=6*0.7+0.3*5=5.7
As E(U(T))=5.7 > Guaranteed Utility(5.5) ,they would opt for the video bonus.
Vacation Budget(T) Utility(U(T)) 300 5 400 5.5 500 6 600 6.1 700 6.5 1000 6.8Related Questions
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