Econ 419 – Industrial Organization
Jura Liaukonyte
Homework 4 -
ANSWERS
Submit ONE version per study group. Write legibly.
I reserve a right not to grade messy or illegible answers.
Include a title page, listing the homework number and the names of all members of the study group.
PART I – Analytical Problems
CHAPTER 14
Problem 1
(a)
100
)
80
(
2
260
40
2
1
=
−
=
⇒
=
=
P
Q
Q
3200
)
40
)(
20
100
(
2
1
=
−
=
=
Cournot
Cournot
π
π
(b)
140
)
60
(
2
260
60
)
2
(
2
20
260
=
−
=
⇒
=
−
=
Monopoly
Monopoly
P
Q
Therefore, profit of each firm in a cartel is
3600
)
30
)(
20
140
(
2
1
=
−
=
=
Cartel
Cartel
π
π
(c)
Without loss of generality, suppose Firm 2 cheats, but Firm 1 maintains its cartel quantity of 30.
Then, the
optimal choice for Firm 2 can be found from its best response function.
(
)
45
)
30
(
2
20
260
4
1
2
=
−
−
=
Cheating
Q
Therefore, the market price is 260 – 2 (30+45) = 110.
As a result, the profit of the cheating firm is:
4050
)
45
)(
20
110
(
2
=
−
=
Cheating
π
If Firm 2 cheats, then it earns 4050 for one period, but earns its Cournot profit; 3200, for all periods afterwards.
On the other hand, if Firm 2 does not cheat, it can continue earning its cartel profit for ever. Hence, the collusive
outcome can be sustained if
δ
δ
δ
δ
δ
δ
δ
−
+
≥
−
⇒
+
+
≥
+
+
+
1
3200
4050
1
3600
)
3200
(
)
3200
(
4050
...
)
3600
(
)
3600
(
3600
2
2
53
.
0
≥
⇒
δ
, where
δ
is the probability adjusted discount factor.
Problem 4
(a)
Recall that for Cournot model with
n
identical firms, with marginal cost
c
, demand intercept
a
and slope
-b

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*