Bob is a decision-maker facing a set of outcomes X = {A new car, Caribbean cruise, Superbowl tickets}. Bob's choice rule for different menus or choice problems specifies the following: From the choice problem ?1,2=A1,2= {A new car, Caribbean cruise}, the choice rule specifies ?(?1,2)=C(A1,2)= {Caribbean cruise} From the choice problem ?1,3=A1,3= {A new car, Superbowl tickets}, the choice rule specifies ?(?1,3)=C(A1,3)= {A new car} From the choice problem ?2,3=A2,3= {Caribbean cruise, Superbowl tickets}, the choice rule specifies ?(?2,3)=C(A2,3)= {Caribbean cruise, Superbowl tickets} Explain why Bob's choices are not consistent with the Weak Axiom of Revealed Preference (WARP). Write down Bob's preference relation based on the choice rule information given above. Explain why the preference relation corresponding to Bob's stated choice rule is not rational.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 28PPS
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Bob is a decision-maker facing a set of outcomes = {A new car, Caribbean cruise, Superbowl tickets}. Bob's choice rule for different menus or choice problems specifies the following:

  • From the choice problem ?1,2=A1,2= {A new car, Caribbean cruise}, the choice rule specifies ?(?1,2)=C(A1,2)= {Caribbean cruise}
  • From the choice problem ?1,3=A1,3= {A new car, Superbowl tickets}, the choice rule specifies ?(?1,3)=C(A1,3)= {A new car}
  • From the choice problem ?2,3=A2,3= {Caribbean cruise, Superbowl tickets}, the choice rule specifies ?(?2,3)=C(A2,3)= {Caribbean cruise, Superbowl tickets}
  1. Explain why Bob's choices are not consistent with the Weak Axiom of Revealed Preference (WARP).
  2. Write down Bob's preference relation based on the choice rule information given above.
  3. Explain why the preference relation corresponding to Bob's stated choice rule is not rational.
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