Econ 100b (Grossman) - Winter 2010 Final Exam - Version A Multiple Choice Test - University Of California Page 2
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45. Two coffee shops compete as Cournot duopolists. The inverse demand for coffee is p = 2
Q, where Q
2
is total amount produced by the two shops. Each shop has the same cost function c(q) = 2q
. What
is total equilibrium output?
(a) 4/7
(b) 4/9
(c) 3/8
(d) 6/15
6. An exchange economy has two consumers, named Jimmy and Sue, and two commodities, apples and
bananas. Jimmy’s initial endowment is 2 units of apples and 4 unit of bananas. Sue’s initial endowment
is 4 apples and 4 units of bananas. Jimmy’s utility function over apples and bananas is U (A
, B
) =
J
J
1/2
1/2
A
B
. Sue’s utility function is of the form U (A
, B
) = A
+ B
, where A
and B
are the
S
S
S
S
J
J
J
J
amounts of apples and bananas for Jimmy and A
and B
are amounts of apples and bananas for Sue.
S
S
The equation of the contract curve in terms of Jimmy’s coordinates is
(a) B
= A
J
J
A
(b) B
=
J
2
(c) B
= 2A
J
J
8A
(d) B
=
J
1+A
7. (continued from the previous question) In equilibrium, apples and bananas have the same price.
Jimmy’s consumption bundle must be
(a) 4 apples and 2 bananas
(b) 2 apples and 4 bananas
(c) 3 apples and 3 bananas
(d) 4 apples and 4 bananas
A
8. Ariel produces aluminum cubes, facing costs of C(A) =
, where A is the number of cubes produced,
10
and selling them on the competitive market for $30. Bjorn grows beets next to Ariel’s factory, facing
B
A
costs of C(B) = 5B +
+
, where B is the number of beets produced, and selling them for $15 on
100
20
the competitive market. Because aluminum pollution is harmful to beet production, the town council
decides to impose a tax on aluminum cubes. If the socially optimal production levels are A = 100
and B = 500, what is the tax (per aluminum cube) that would induce efficiency?
(a) $30
(b) $15
(c) $10
(d) $25
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9. Xavier makes xylophones next to Yasmin’s yak farm. Xavier’s profit function is π
(x) = 40x
x
and
x
2
Yasmin’s profits function is π
(y) = 50y y
xy. The loud noise from xylophone production interferes
y
with the yak breeding. There is no law against making noise (i.e. Xavier has the right to make noise),
so Yasmin offers to pay Xavier to cut back on his xylophone production. How many xylophones will
Xavier end up making after this negotiation?
(a) 4
(b) 10
(c) 20
(d) 15
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