EC3313: Industrial Economics
Maris Goldmanis
Autumn TakeHome Test (NonAssessed)
Due: Thursday, January 13, 2011
Instructions to candidates:
•
This is a takehome test. It is due
Thursday, January 13, 2011.
•
You may consult class notes, textbooks, the web and other resources; however,
you
may NOT consult with others
, in the class or outside.
•
Should you have any questions about the
instructions
to this exam, feel free to email
the instructor.
However,
hints to help you answer the questions will not be
given.
•
You must attempt to
answer all questions.
•
Please
write up your detailed derivations
neatly.
No credit will be given for
answers without proper derivations. You may either write your derivations by hand
and then scan these pages to a pdf file, or type the derivations up using L
A
T
E
X or a
word processor (such as MS Word).
•
Attach a
cover page
that gives short answers (without derivations) to all questions.
These answers
must be typed
(L
A
T
E
X or word processor).
•
Submit your complete answers (including both the cover sheet and the derivations)
using TURNITIN. The TURNITIN details for this class are as follows:
Course:
EC3313
Class ID:
222063
Password:
EC331310
•
Fill in the boxes in the Department’s standard nonassessed coursework submission
form (last page of this exam) and submit the form to the dropbox in Horton H209.
•
Good Luck and Happy Holidays!
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EC3313: Autumn 2010
Maris Goldmanis
TakeHome Test
1.
Homogeneous Cournot with Multiple Firms
This problem consists of multiple parts, which vary considerably in difficulty. Do not get dis
couraged if you get stuck at some point. Intermediate answers to several parts are given in the
text; you can use these in the latter parts even if you could not derive the previous answers
yourself.
Suppose that in a market there are
N
firms, all of which have the same constantreturns
toscale technology with marginal cost
c
≥
0, so that
C
i
(
q
i
) =
cq
i
for all
i.
The market demand is given by
P
(
Q
) =
A

BQ,
where
Q
=
∑
N
i
q
i
is the aggregate market output. Assume that
A > c
and
B >
0.
The firms compete in a Cournot game.
(a)
Warmup exercise: three firms
First, consider the case when there are three firms,
N
= 3.
In addition, assume
that the marginal cost is
c
= 0 and that
A
= 1 and
B
= 2.
i. Find the Cournot equilibrium. What are the quantities, prices, and profits in
this equilibrium?
ii. Suppose that two of the three firms merge. Solve for the new Cournot equilib
rium. Show that the joint profit of the two merging firms actually
decreases
as a result of the merger.
iii. What if all three firms merge? Does the joint profit of the merging firms increase
or decrease as a result of this merger?
(b)
The general case:
N
≥
2 firms
Now, let us solve for the Cournot equilibrium when there is an arbitrary number of
firms (
N
≥
2). We will also let
A
,
B
, and
c
take arbitrary values (with
A > c
≥
0
and
B >
0). This is slightly harder, so let us work it out stepbystep.
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 Spring '10
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 Economics, Game Theory, Cournot Competition, Stackelberg competition, takehome test, Maris Goldmanis

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