500359 – MICROECONOMICS – 2019/20
Class Exercises
Problem Set 3
1
The following questions relate to the axioms of consumer theory:
(i)
If a consumer chooses bundle (X
1
, Y
1
) when bundle (X
2
, Y
2
) is available, is it
right to conclude that (X
1
, Y
1
)
(X
2
, Y
2
)?
[Hint: Are the two bundles necessarily on different indifference curves?]
(ii)
When it comes to dessert, given two options B
1
and B
2
, Calvin always prefers
the largest dessert with the most ice cream.
Is this preference relation
(a) transitive? (b) complete?
[Hint: Can you represent all possible bundles with indifference curves that
satisfy the axioms?]
(iii)
Can an indifference curve that satisfies all the axioms cross itself?
See Figure
1.
[Hint: Compare bundles A and B.]
(iv)
Prove, using a diagram, that if preferences are monotonic a diagonal line
though the origin will intersect each indifference curve exactly once.
[Hint: Proof by contradiction helps i.e. what shape must indifference curves
be for the line from the origin to cross them more than once?
Do these
indifference curves represent monotonic preferences?]
Figure 1
Y
X
A
B

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- Fall '19