Asked by Mauricio Davila on Jun 02, 2024
Verified
Mac Rowe doesn't sweat the petty stuff.In fact, he just cannot detect small differences.He consumes two goods, x and y.He prefers the bundle (x, y)to the bundle (x', y')if and only if (xy x'y' 1).Otherwise he is indifferent between the two bundles.
a.Show that the relation of indifference is not transitive for Mac.(Hint: Give an example.)
b.Show that the preferred relation is transitive for Mac.
Transitive
In economics and decision theory, referring to preferences that are consistent in their ranking: if option A is preferred over B, and B over C, then A is preferred over C.
Indifference
A state or condition of a consumer where different combinations of goods or outcomes are perceived as equally preferable.
Bundles
A collection of goods or services sold as a single package, often offered at a discount compared to buying each item separately.
- Analyze how consumer preferences relate in a sequential manner and its significance for decision-making strategies.
- Analyze consumer preferences for goods with special characteristics or constraints.
Verified Answer
ZK
Zybrea KnightJun 06, 2024
Final Answer :
a.Consider the bundles A (1, 1), B (1, 1.75), and C (1, 2.5).Then A is indifferent to B and B to C, but C is preferred to A.
b.To see that strict preference is transitive, suppose we have any three bundles, (x, y), (x', y')and (x'', y'').If the first is preferred to the second and the second to the third, then xy x'y' 1 and x'y' x''y'' 1.Simple algebra shows that xy x''y'' 1.Therefore the first must be preferred to the third.
b.To see that strict preference is transitive, suppose we have any three bundles, (x, y), (x', y')and (x'', y'').If the first is preferred to the second and the second to the third, then xy x'y' 1 and x'y' x''y'' 1.Simple algebra shows that xy x''y'' 1.Therefore the first must be preferred to the third.
Learning Objectives
- Analyze how consumer preferences relate in a sequential manner and its significance for decision-making strategies.
- Analyze consumer preferences for goods with special characteristics or constraints.