Econ 51: Midterm Answer Key
Answers are in bullets, following the questions.
1 True/False questions (36 points)
(a)
Let
x
and
y
be the consumption in two states of the world.
The utility function
u
(
x, y
) = 10 + 2
x
2
+ 6
y
2
+ 21
y
3
+ 7
x
3
does not represent vNM preferences.
•
False. We can rewrite
u
(
x, y
) =
1
4
v
(
x
) +
3
4
v
(
y
) with
v
(
x
) = 10 + 8
x
2
+ 28
x
3
, which is
of the vNM form.
(b)
An individual with vNM utility
v
(
x
) =
e
7
x
is risk averse.
•
False.
v
00
(
x
) = 49
e
7
x
is positive, so the individual is not risk averse.
(c)
There are apples (
a
) and bananas (
b
).
Tom and Rob have identical utility function
u
(
a, b
) = max(
a,
15). There are 20 apples and 20 bananas on the island. Any point in
the Edgeworth box is Pareto e
ﬃ
cient.
•
False. For example, giving 17 apples and 10 bananas to Rob is not Pareto e
ﬃ
cient: by
taking one apple from Tom and giving it to Rob, Rob is better o
ff
while Tom is not
worse o
ff
(his utility remains 15).
(d)
There are apples (
a
) and bananas (
b
).
Tom and Rob have identical utility function
u
(
a, b
) = log(
a
). A
fi
rm can transform one apple to 3 bananas. In equilibrium it must
be that
p
a
= 3
p
b
.
•
False.
Nobody in this market wants bananas, so in equilibrium the
fi
rm will not
produce and the equilibrium price for bananas will be zero.
(e)
There are apples (
a
), bananas (
b
), and cucumbers (
c
).
Y
=
{
(
a, b, c
) :
a
≤
0
, b
= 2
a, c
=
−
3
b
}
is a
fi
rm’s production set. This
fi
rm can transform apples into both bananas and cu
cumbers.
•
False. Both apples and bananas are inputs. The
fi
rm transforms apples and bananas
into cucumbers.
(f)
Country A can produce 2 apples or 5 bananas with one unit of labor. Country B can
produce 3 apples or 6 bananas with one unit of labor. This means that country B has
a comparative advantage in the production of both apples and bananas.
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 Winter '07
 Tendall,M
 Utility, Kobe, Shaq

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