Transitivity assumption

In microeconomics , the assumption of transitivity ( assumption of transferability) is mostly postulated in relation to the preferences of economic subjects, according to which (in simplified terms) a household that prefers alternative A to alternative B and B in turn prefers alternative C must also prefer A to C. . In principle, however, the assumption can be applied to any binary relations , so that it can also be used in other contexts of microeconomic theory.

Formal: Be three alternatives and be the preference-indifference relation ("is as good as or better than"). Then the following must apply: ${\displaystyle x,y,z}$ ${\displaystyle R}$

${\displaystyle \forall x,y,z\in X:xRy\wedge yRz\implies xRz}$

Transitivity is a necessary prerequisite for an actor's preferences to be represented by means of a representative utility function . See the article on preference relation . Graphically, the transitivity assumption ensures that indifference curves can never intersect.

See also

• Preference relation
• Transitive relation
• Household theory

literature

• Wayne Shafer: Transitivity. In: Steven N. Durlauf and Lawrence E. Blume (Eds.): The New Palgrave Dictionary of Economics. 2nd edition Palgrave Macmillan ( online edition , not freely accessible).

Individual evidence

1. ↑ Dictionary_articles - The New Palgrave Dictionary of Economics, 2nd Edition | Macroeconomics | Economic inequality. Accessed April 20, 2019 . 
2. ↑ Edwin von Böventer, Gerhard Illing: Introduction to microeconomics . Ed .: Edward Duae, Jonas Regul, Antoine Frambach. 1997, ISBN 3-486-24248-2 .