While spending the weekend in New York City, Sam, Teresa, and their son, Andrew, are lucky enough to hail the Cash Cab for their taxi ride. During their ride, they win $200 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 $300, and based on their understanding of the type of bonus question they'll be asked, they believe they have a 70% chance of getting the question right. As explained in the article, if they answer the video bonus question correctly, they will double their winnings, but if they miss the video bonus question, they will lose all of what they had previously won. Alternatively, they can choose not to play for the bonus and walk away with their winnings from the cab ride. 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 a family. Refer to the graph to answer the questions that follow. UTILITY (Utils) 10 9 8 7 2 1 0 0 100, 2.4 u(x) 100 200 300 400 500 600 700 800 900 1000 VACATION BUDGET (Dollars) (?) If the family chooses 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.
While spending the weekend in New York City, Sam, Teresa, and their son, Andrew, are lucky enough to hail the Cash Cab for their taxi ride. During their ride, they win $200 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 $300, and based on their understanding of the type of bonus question they'll be asked, they believe they have a 70% chance of getting the question right. As explained in the article, if they answer the video bonus question correctly, they will double their winnings, but if they miss the video bonus question, they will lose all of what they had previously won. Alternatively, they can choose not to play for the bonus and walk away with their winnings from the cab ride. 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 a family. Refer to the graph to answer the questions that follow. UTILITY (Utils) 10 9 8 7 2 1 0 0 100, 2.4 u(x) 100 200 300 400 500 600 700 800 900 1000 VACATION BUDGET (Dollars) (?) If the family chooses 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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Transcribed Image Text:2. Double or nothing
While spending the weekend in New York City, Sam, Teresa, and their son, Andrew, are lucky
enough to hail the Cash Cab for their taxi ride. During their ride, they win $200 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 $300, and based on their
understanding of the type of bonus question they'll be asked, they believe they have a 70%
chance of getting the question right. As explained in the article, if they answer the video bonus
question correctly, they will double their winnings, but if they miss the video bonus question, they
will lose all of what they had previously won. Alternatively, they can choose not to play for the
bonus and walk away with their winnings from the cab ride.
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 a family. Refer to the graph to answer the questions that follow.
UTILITY (Utils)
10
9
8
7
5
4
3
2
1
0
0
100, 2.4
u(x)
+-
100 200 300 400 500 600 700 800 900 1000
VACATION BUDGET (Dollars)
(?
If the family chooses 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.
Transcribed Image Text: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)
Answer correctly
Answer incorrectly
Utility
(Utils)
Because the passengers believe they have a 70% chance of getting the question correct, their
expected utility from taking the gamble is
utils. (Note: Enter all decimal places, and do
not round your answer.)
Because the expected utility from taking the gamble is
they do not do the video bonus question, Sam, Teresa, and Andrew
bonus question.
Suppose that the odds that passengers get the video bonus question right increase with the
number of people they have in the cab and decrease with the number of strikes they received
during their trip. If only Sam and Teresa had been in the cab, and they had received two strikes
during the trip, they would have estimated their chance of getting the video bonus question right
to be only 20%.
Scenario
20% chance of answering
correctly
$300 in winnings during the cab
ride
$100 initial vacation budget
than the utility they receive if
do the video
Complete the first row of the following table with the guaranteed utility the passengers will receive
if they walk away with their original winnings, the new expected utility from taking the gamble,
and the answer to whether they should do the video bonus question in this case.
Guaranteed
Utility
(Utils)
Expected
Utility
(Utils)
Do the Video
Bonus?
(Yes or No)
Now suppose that the chance that Sam, Teresa, and Andrew get the video bonus question right is
again 70%, but that instead of winning $200 during their ride, the family won $300. Taking this
new information into account, complete the second row of the previous table.
Again, suppose that the chance the passengers get the video bonus question right is 70%, and the
total winnings from the cab ride returns to $200. However, suppose the initial vacation budget
Sam, Teresa, and Andrew started with was only $100 instead of $300. Based on this information,
complete the final row of the previous table.
Expert Solution
Step 1
DISCLAIMER “Since you have asked multiple questions, we will solve the first three questions for you. If you want any specific question to be solved, then please specify the question number or post only that question.”
Utility implies the comprehensive benefits of consuming a product or service. This sums up the utility definition. Consumers would typically focus on maximising their utility and relying on rational choice based on economic models.
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