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Department of Economics
Econ 501a
Spring 2004
Prof. James Peck
Midterm Answers
Part I: Short Answer.
1.
(10 points)
goods
x
and
y
are represented by the utility function,
u
(
x;y
) =
xy
.
That
is, one bundle is preferred over a second bundle if and only if the amount of
good
x
multiplied by the amount of good
y
is greater in the ±rst bundle than
in the second bundle.
show that these preferences satisfy the ±rst
three axioms of consumer rationality. That is, show that these preferences are
complete, re²exive, and transitive (see the equation sheet).
Answer:
For any two bundles,
(
x
1
;y
1
)
and
(
x
2
;y
2
)
, exactly one of the following con
ditions will be true:
x
1
y
1
> x
2
y
2
;
x
1
y
1
=
x
2
y
2
;
or
x
1
y
1
< x
2
y
2
:
Therefore, preferences are complete. Preferences are re²exive, because
x
1
y
1
=
x
1
y
1
. Finally, if we have
x
1
y
1
> x
2
y
2
and
x
2
y
2
> x
3
y
3
, then it follows that we
have
x
1
y
1
> x
3
y
3
. Therefore, preferences are transitive.
2.
(10 points)
From January 1979 to January 1980, the price of gold
more than doubled. As the price of gold rose, the quantity of gold demanded
increased as well. Brie²y explain why it is
not
reasonable to say that this is
an example of the income e/ect swamping the substitution e/ect.
Answer:
The substitution e/ect of the price increase would be for the demand for
gold to decrease. The income e/ect is the change in the demand for gold, due
to the resulting reduction in purchasing power, holding relative prices constant.
For normal goods, the income e/ect will reinforce the substitution e/ect, so that
demand for gold should fall further. Unless you believe that gold is an inferior
good, where poor people have more gold than rich people, the explanation
cannot be due to the income e/ect swamping the substitution e/ect.
In case you are curious, what could be the explanation? The event causing
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This note was uploaded on 07/17/2008 for the course ECON 501.02 taught by Professor Yang during the Spring '08 term at Ohio State.
 Spring '08
 YANG
 Microeconomics, Utility

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