Economics 101
Problem Set 2
January 19, 2011
George J. Mailath
Due Thursday, January 27, 2011
Please indicate your recitation time/number and recitation instructor on
your answer.
1. Andrew consumes positive amounts of goods 1 and 2. He thinks that
3 units of good 1 is always a perfect substitute for 1 unit of good
2. Which of the following utility functions represent Andrew’s prefer
ences?
(a)
U
(
x
1
,x
2
) = min
{
x
1
,
3
x
2
}
.
(b)
U
(
x
1
,x
2
) = 9
x
2
1
+ 6
x
1
x
2
+
x
2
2
.
(c)
U
(
x
1
,x
2
) =
√
5
x
1
+ 15
x
2
+ 100.
(d)
U
(
x
1
,x
2
) =
x
1
+ 3
x
2
+ 500.
2. Bruce has preferences,
±
, that are complete and transitive. Suppose
there are four bundles
x
1
,
x
2
,
x
3
, and
x
4
, with the property that
(a)
x
1
±
x
2
,
(b)
x
3
±
x
4
, and
(c)
x
1
²
x
3
.
How do Bruce’s preferences rank
x
2
and
x
4
?
3. Anthony’s utility function for good 1 and good 2 is given as the fol
lowing. Graph his indiﬀerence curves for diﬀerent utility functions in
the commodity space,
R
2
+
, and discuss whether these preferences are
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 Spring '08
 DANNICATAMBAY
 Economics, Microeconomics, Utility, Substitute good

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