3.1. Richard is an old-fashioned Englishman who likes his tea with milk and sugar. Though he prefers more sugar to less, he cannot always 58 Chapter 3 distinguish between two cups unless the difference in the amount of sugar is less than a third (< 1/3) or more than one teaspoon (> 1). If there are two cups of tea where the difference is between a third and one teaspoon of sugar, he is indifferent (~) between them. (a) Is Richard's strict preference relation (>) reflexive, total and tran- sitive? Explain why or why not for each property. (b) Is Richard's indifference relation (~) reflexive, total and transi- tive? Explain why or why not for each property. (c) Is Richard's weak preference relation () reflexive, total and tran- sitive? Explain why or why not for each property.
3.1. Richard is an old-fashioned Englishman who likes his tea with milk and sugar. Though he prefers more sugar to less, he cannot always 58 Chapter 3 distinguish between two cups unless the difference in the amount of sugar is less than a third (< 1/3) or more than one teaspoon (> 1). If there are two cups of tea where the difference is between a third and one teaspoon of sugar, he is indifferent (~) between them. (a) Is Richard's strict preference relation (>) reflexive, total and tran- sitive? Explain why or why not for each property. (b) Is Richard's indifference relation (~) reflexive, total and transi- tive? Explain why or why not for each property. (c) Is Richard's weak preference relation () reflexive, total and tran- sitive? Explain why or why not for each property.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:3.1. Richard is an old-fashioned Englishman who likes his tea with milk
and sugar. Though he prefers more sugar to less, he cannot always
58 Chapter 3
distinguish between two cups unless the difference in the amount of
sugar is less than a third (< 1/3) or more than one teaspoon (> 1). If
there are two cups of tea where the difference is between a third and
one teaspoon of sugar, he is indifferent (~) between them.
(a) Is Richard's strict preference relation (>) reflexive, total and tran-
sitive? Explain why or why not for each property.
(b) Is Richard's indifference relation (~) reflexive, total and transi-
tive? Explain why or why not for each property.
(c) Is Richard's weak preference relation () reflexive, total and tran-
sitive? Explain why or why not for each property.
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