CCT1 Axioms of Consumer Theory Flashcards
How would you describe the Axioms of Consumer Theory?
A set of assumptions that in some circumstances are reasonable, which lead to the standard Neoclassical result of a tangency between budget line and indifference curve – yielding a consumer that maximises utility subject to a budget constraint
Does neoclassical consumer theory assume utility maximisation? Yes or no?
No, but the 5 axioms together give us an individual who behaves such that this tangency is as if they were maximising utility.
How is a binary relation, R, between items a and b, denoted?
aRb- i.e item a has a relationship (R) with item B
What are the 5 axioms?
- Completeness
- Transitivity
- Convexity
- Continuity
- Monotonicity
What does the Continuity axiom mean?
If there exists a bundle B1≻B2 then there must exist a bundle B3 sufficiently close to B1 where it is also true that B3≻B2.
What does the Completeness axiom mean?
This ensures that commodity spaces can be partitioned according to areas that are weakly preferred with continuous lines delineating those partition spaces. For all feasible bundles in the commodity space: B1≽B2, B2≽B1, or B1∼B2.
What does the Transitivity axiom mean?
Given any three bundles in the commodity space: B1,B2,B3:
If B1≽B2 and B2≽B3 then B1≽B3.
What does the Monotonicity axiom mean and what does this rule out?
More is better, and this rules out thick indifference curves as more of something cannot provide the same utility as less of it.
What does the Convexity axiom mean?
Convexity ensures that all partitioning lines have a convex shape, which implies that averages are preferred to extremes - the utility associated with an average bundle has a higher ranking than the utility associated with extreme bundles.
If... • a means Father • b means daughter • R means father of does aRb hold and why? does bRa hold and why?
- aRb holds as a is the father of b.
* bRa does’t hold, as b isn’t the father of a
If a relation doesn’t hold, what do we do to the R?
We put a strike through the R
If a is larger than b, and b is larger than c, with R denoting greater than, what is another way of writing aRb and bRc?
a>b>c
Which two binary relations are we most concerned with?
- weakly preferred ≽
* strictly preferred ≻
What is reflexivity?
Reflexivity requires that for each element, the binary relation works with respect to that element.
Which of these equations satisfy reflexivity and why?
• a≽b≽c
• a≻b≻c
- a≽b≽c satisfies reflexivity as a≽a holds.
* a≻b≻c doesn’t satisfy reflexivity as a≻a does not hold.
If B1∼B2, how would we generally think of these bundles?
As being on the same indifference curve.
If B1≽B2, how would we generally think of these bundles?
We would generally think of B1 being on a higher or the same indifference curve than B2 as B1 is weakly preferred.
Does the definition of completeness imply reflexivity? Why/why not?
Yes as all bundles can be compared with all bundles under the weakly preferred preference relation, and B1≽B1, thus implying reflexivity.
Why is transitivity important?
Transitivity is important as it ensures that we have a consistency in the ordering of the bundle’s rankings according to the preference relation.
Which two axioms imply rationality?
- Completeness
* Transitivity
What do we mean when we say preferences are well-behaved?
That they give rise to nice tangencies.
What happens when all axioms are satisfied?
We are going to have a nice tangency solution where the individuals indifference curve is going to be tangential to the budget constraint.
