CCT1 Axioms of Consumer Theory

Question 1

How would you describe the Axioms of Consumer Theory?

Answer 1

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

Question 2

Does neoclassical consumer theory assume utility maximisation? Yes or no?

Answer 2

No, but the 5 axioms together give us an individual who behaves such that this tangency is as if they were maximising utility.

Question 3

How is a binary relation, R, between items a and b, denoted?

Answer 3

aRb- i.e item a has a relationship (R) with item B

Question 4

What are the 5 axioms?

Answer 4

• Completeness
• Transitivity
• Convexity
• Continuity
• Monotonicity

Question 5

What does the Continuity axiom mean?

Answer 5

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.

Question 6

What does the Completeness axiom mean?

Answer 6

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.

Question 7

What does the Transitivity axiom mean?

Answer 7

Given any three bundles in the commodity space: B1,B2,B3:

If B1≽B2 and B2≽B3 then B1≽B3.

Question 8

What does the Monotonicity axiom mean and what does this rule out?

Answer 8

More is better, and this rules out thick indifference curves as more of something cannot provide the same utility as less of it.

Question 9

What does the Convexity axiom mean?

Answer 9

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.

Question 10

If...
• a means Father
• b means daughter
• R means father of
does aRb hold and why?
does bRa hold and why?

Answer 10

• aRb holds as a is the father of b.

* bRa does’t hold, as b isn’t the father of a

Question 11

If a relation doesn’t hold, what do we do to the R?

Answer 11

We put a strike through the R

Question 12

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?

Answer 12

a>b>c

Question 13

Which two binary relations are we most concerned with?

Answer 13

• weakly preferred ≽

* strictly preferred ≻

Question 14

What is reflexivity?

Answer 14

Reflexivity requires that for each element, the binary relation works with respect to that element.

Question 15

Which of these equations satisfy reflexivity and why?
• a≽b≽c
• a≻b≻c

Answer 15

• a≽b≽c satisfies reflexivity as a≽a holds.

* a≻b≻c doesn’t satisfy reflexivity as a≻a does not hold.

Question 16

If B1∼B2, how would we generally think of these bundles?

Answer 16

As being on the same indifference curve.

Question 17

If B1≽B2, how would we generally think of these bundles?

Answer 17

We would generally think of B1 being on a higher or the same indifference curve than B2 as B1 is weakly preferred.

Question 18

Does the definition of completeness imply reflexivity? Why/why not?

Answer 18

Yes as all bundles can be compared with all bundles under the weakly preferred preference relation, and B1≽B1, thus implying reflexivity.

Question 19

Why is transitivity important?

Answer 19

Transitivity is important as it ensures that we have a consistency in the ordering of the bundle’s rankings according to the preference relation.

Question 20

Which two axioms imply rationality?

Answer 20

• Completeness

* Transitivity

Question 21

What do we mean when we say preferences are well-behaved?

Answer 21

That they give rise to nice tangencies.

Question 22

What happens when all axioms are satisfied?

Answer 22

We are going to have a nice tangency solution where the individuals indifference curve is going to be tangential to the budget constraint.