PROBLEM (1) (Rational Choice) Suppose your friend is about to buy a digital camera. A digital camera is identified with three dimensions; 1) resolution (in megapixels), 2) optical zoom (a real number) and 3) battery life (a number of hours). For example, A = (8, 4, 20) is a camera with 8mp resolution and x4 optical zoom and 20 hours of battery life. When he goes into a store, he faces a menu of cameras. When comparing two cameras if camera A is weakly better than B on at least 2 dimensions, it is weakly preferred to the other; written A ≥preferred B. a) Is this preference relation complete? Transitive? Prove it or show an example where the property doesn't hold. b) Suppose the agent chooses from any menu of cameras, a camera that is (weakly) preferred to all other cameras in the menu. Would this choice function be rational, given (a)? Briefly explain your reasoning.
PROBLEM (1) (Rational Choice) Suppose your friend is about to buy a digital camera. A digital camera is identified with three dimensions; 1) resolution (in megapixels), 2) optical zoom (a real number) and 3) battery life (a number of hours). For example, A = (8, 4, 20) is a camera with 8mp resolution and x4 optical zoom and 20 hours of battery life. When he goes into a store, he faces a menu of cameras. When comparing two cameras if camera A is weakly better than B on at least 2 dimensions, it is weakly preferred to the other; written A ≥preferred B. a) Is this preference relation complete? Transitive? Prove it or show an example where the property doesn't hold. b) Suppose the agent chooses from any menu of cameras, a camera that is (weakly) preferred to all other cameras in the menu. Would this choice function be rational, given (a)? Briefly explain your reasoning.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:PROBLEM (1) (Rational Choice) Suppose your friend is about to buy a digital camera. A digital camera is
identified with three dimensions; 1) resolution (in megapixels), 2) optical zoom (a real number) and 3) battery
life (a number of hours). For example, A = (8, 4, 20) is a camera with 8mp resolution and x4 optical zoom and 20
hours of battery life. When he goes into a store, he faces a menu of cameras. When comparing two cameras if
camera A is weakly better than B on at least 2 dimensions, it is weakly preferred to the other; written A ≥preferred B.
a) Is this preference relation complete? Transitive? Prove it or show an example where the property doesn't hold.
b) Suppose the agent chooses from any menu of cameras, a camera that is (weakly) preferred to all other cameras
in the menu. Would this choice function be rational, given (a)? Briefly explain your reasoning.
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