Econ 301 – F07
ANSWERS to PROBLEM SET 2 - due in class on Thursday September 20
Wissink
1.
Critically evaluate the following statements and explain why or in what way are they true, false, or
uncertain.
a.
Over the set of people in New York State, the binary relation "is the Facebook Friend of" is complete
and transitive.
[ANSWER]
False, the binary relation “is the Facebook Friend of” is
not complete and not
transitive
.
Completeness: For example, take Jane and Mike who both live in NY and are not Facebook Friends
(FBF).
So Jane is NOT Mike’s FBF and Mike is not Jane’s FBF, or both, so the relation is NOT
complete.
Transitivity: for example, Jane is the Facebook Friend of Mike.
Mike is the Facebook
Friend of Carol.
To be transitive, Jane MUST BE the Facebook Friend of Carol.
But, in reality,
Jane may not be the Facebook Friend of Carol.
b.
Assuming a 2 good commodity space and an agent with well behaved preferences, the binary
relation “is strictly preferred to” is complete.
[ANSWER]
False, the binary relation “is strictly preferred to” is
not complete
.
Suppose Bundle A
and Bundle B are indifferent to each other. Then A is not strictly preferred to B and B is not strictly
preferred to A, or both, so the relation “is strictly preferred to” it not complete.
c.
Unlike Prof. Wissink, an indifference curve can never be “thick.”
[ANSWER]
True, a well behaved indifference curve can never be “thick.” A thick indifference
curve violates the monotonicity assumption, which means that more is better.
Suppose that (x1, y1)
is a bundle of goods and (x2, y2) is a bundle of goods with strictly more of both goods x and y.
By
the monotonicity assumption, (x2, y2) is strictly preferred to (x1, y1).
But if two bundles are on the
same thick indifference curve, (x2, y2) is indifferent to (x1, y1).
(x1,y1)
(x2,y2)
x
y
IC