Econ 301 – F06
ANSWERS PROBLEM SET 2
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, the binary relation "is the half-brother of" is transitive.
1False, the relation "is the half-brother of" is
not necessarily
transitive.
Here’s an example.
Suppose Joe and
Mary beget Joey; Mary and Fred beget Freddy; and Fred and Jackie beget Jack.
Then, Joey is the ½ brother
of Freddy and Freddy is the ½ brother of Jack; but Joey is NOT the ½ brother of Jack.
b.
Over the set of people in New Jersey, the binary relation "is the mother of" is complete.
False, the relation "is the mother of" is not complete over.
For example suppose you and I both
come from NJ.
I am not your mother and you are not my mother and we are not each other's
mothers, so, the relation is not complete.
c.
If I am
always
willing to substitute six units of y for an additional unit of x, then my preferences
violate the monotonicity axiom.
No, they violate the STRICT CONVEXITY assumption.
Can’t refer to the notion of monotonicity
at all here since you are getting more of one good and less of the other.
2.
Draw indifference curve maps containing at least two indifference curves for the following
descriptions of preferences and indicate the direction in which happiness is increasing.
See last page.
3.
Coach Steroid likes his players to be big, fast, and obedient.
If player A is better than player B in
two of these three characteristics, then Coach Steroid prefers A to B, but if B is better than A in two of
these three characteristics, then Steroid prefers B to A.
Otherwise, Steroid is indifferent between them.
Wilbur Westinghouse weights 340 pounds, runs very slowly, and is fairly obedient.
Harold Hotpoint
weighs 240 pounds, runs very fast, and is very disobedient.
Jerry Jacuzzi weighs 150 pounds, runs at
average speed, and is extremely obedient.