While spending the weekend in New York City, Raphael, Susan, and their son, Alex, 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 $400, and based on their understanding of the type of bonus question they’ll be asked, they believe they have a 80% 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. ### Understanding Expected Utility in Decision Making: An Example**Concept Overview:** In decision-making, especially under uncertainty, expected utility is a key concept. It helps individuals decide whether to take a gamble based on the potential outcomes and their probabilities.In this example, passengers must decide whether to take a video bonus question. They estimate their chance of getting the question correct and calculate the expected utility from taking the risk.#### Setting the Scene:- Passengers believe they have an 80% chance of answering the question correctly.- They need to decide whether to take the video bonus question or walk away with their current winnings.#### Key Calculation Elements:1. **Expected Utility Calculation:** - Expected Utility = Probability of Success * (Utility if Correct) + Probability of Failure * (Utility if Incorrect)**Scenario Analysis:**1. **Passengers believe their chances of getting the question correct are 80%:** - Expected utility from taking the gamble is **____** utils. - *Note:* Enter all decimal places and don't round your answer.2. **Comparison of Utilities:** - Expected utility from gambling is ___ utils. - Utility if no video bonus = ___ utils. - Result: Raphael, Susan, and Alex **should/should not** take the video bonus.3. **Changes in Number of Strikes and Passengers:** - If only Raphael and Susan were in the cab and received two strikes, their estimate drops to a 40% chance of getting the video bonus question correct.#### Table of Estimated Utilities and Decisions:| Scenario | Guaranteed Utility (Utils) | Expected Utility (Utils) | Do the Video Bonus? (Yes/No) ||-----------------------------|-----------------------------|---------------------------|------------------------------|| 40% chance of answering correctly | | | || $300 in winnings | | | || $200 initial vacation budget| | | |**Further Adjustments Based on New Information:**4. **Suppose their chance returns to 80% with $300 winnings:** - Complete the second row of the table based on this information.5. **Adjustments with Different Initial Budgets:** - If the initial budget starts at only $200, recalculate using a total cab ride winning of $200 and an 80% chance of correct response.| Scenario | Guaranteed Utility (Utils) | Expected Utility ( ---**Utility and Decision Making: Understanding Vacation Budgets**In this module, we will analyze how varying vacation budgets impact a family's utility. The graph provided illustrates the relationship between the vacation budget (in dollars) and the corresponding utility.### Graph ExplanationThe graph plots vacation budgets on the x-axis (ranging from $0 to $1000) and utility values on the y-axis (ranging from 0 to 10 utils). Utility represents the satisfaction or happiness a family derives from their vacation budget. The curve depicted is denoted as $ u(x) $, which shows the increasing utility as the vacation budget increases, although at a diminishing rate.- **Data Points**: Black crosses (+) along the purple curve represent specific data points where utility has been measured or estimated.- **Example Data Point**: At a vacation budget of $1000, the utility is 6.7 utils.### Utility Without Attempting the Bonus QuestionIf the family decides not to participate in the video bonus question, they will achieve a utility of 5.9 utils.### Decision Analysis: Attempting the Bonus QuestionTo decide whether to attempt the video bonus question, the family must consider the utilities associated with each potential outcome - answering the question correctly or incorrectly. Below, you will complete the table based on the provided instructions.---#### Complete the Following TableFill in the total vacation budget and the corresponding utilities for both correct and incorrect answers to the video bonus question.| Answer Correctly | Answer Incorrectly ||------------------|--------------------|| **Vacation Budget (Dollars)** | [Fill in] | [Fill in] || **Utility (Utils)** | [Fill in] | [Fill in] |### Guided Example1. **Assessing Outcomes**: - Evaluate how an increase or decrease in the vacation budget (due to the quiz result) affects the family's total utility.2. **Decision Making**: - Compare the utility of 5.9 utils (not attempting the question) against the expected utilities from either getting the video bonus question correct or incorrect.By understanding these elements, the family can make an informed decision aimed at maximizing their vacation satisfaction.---This exercise teaches essential concepts in decision theory and utility analysis, helping illustrate real-world applications of economic principles in everyday decisions.For more advanced modules, please refer to our [Advanced Decision Making](#) section.---

In economics, utility refers to the amount of satisfaction that a consumer gets from the consumption…

Answered: While spending the weekend in New York…

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC