ECON 5430: Industrial Organization
Bernard Lebrun
Notes on Chapter 0 in Tirole (1988)
The Theory of the Firm
1. Some theories of the ﬁrm
• 1.1 The ﬁrm as a loophole for the exercise of monopoly power
• 1.2 Technological view: the ﬁrm as a static synergy
—
ECON 5430 Industrial Organization
Bernard Lebrun
Exercises with suggestions of possible answers
Exercises 51 to 57
Exercise 51: Let a demand function D (p) that intersects the price
axis at p = p (0) > 0 and the quantity axis at Q > 0. Assume D (p) is,
wh
ECON 5430 Industrial Organization
Bernard Lebrun
Exercises with suggestions of answers
Exercises 31 to 50
Exercise 31: Consider the game above where every rms production
cost function is c (q ) = cq , the inverse demand curve is p (q ) = a bq, with
a > c
ECON 5430 Industrial Organization
Bernard Lebrun
Exercises with suggestions of possible answers
Exercise 24: (Amir and Lambson, 2000) Consider the Cournot oligopoly
with n identical rms and p (Q) = 2 Q and c (q) = log (q + 1).
(i) Does it satisfy or can i
ECON 5430 Industrial Organization
Bernard Lebrun
Exercises with suggestions of possible answers
Exercise 19: Under the assumptions of UT1 and when ci is linear, for
all i, and p (Q) is concave, show that (9) is satised only when n = 2.
Hint: When ci is li
ECON 5430 Industrial Organization
Bernard Lebrun
Exercises with suggestions of answers
Exercise 1P Show that rm 1s prot at its best response in Example 1
ab : q c 2
j 6=i j
max
,0
.
is
2
P
P
ab j 6=i qj c
Hint: If j 6=i qj < ac , substituting the solutio
Bernard Lebrun
ECON 5430: Industrial Organization
Review of the material in Tirole (1988): Part I
Additional Exercises
1. Two parties have to decide whether to trade and at what price. The
value of the good to the buyer is and the cost to the seller is .
ECON 5430
Bernard Lebrun
Two-Stage Models and Strategic Behavior
Strategic behavior: behavior, such as signalling or investing, aimed at
aecting future actions from potential or actual rivals.
I. Stackelberg model and limit pricing
Reading: 8.2.1 in Tirol
ECON 5430
Bernard Lebrun
Chapter 3: Betrand-Edgeworth Model
Reading: 5.3; 5.7.2 in Tirole (1988).
I. Exogeneous cost functions
Denitions:
Bertrand-Edgeworth Model: Let D (p) be a demand curve dened
for all p 0 and let there be n rmsrm 1,., rm nwith convex
ECON 5430 Industrial Organization
Bernard Lebrun
Chapter 1:
Cournot Model of OligopolySimultaneous Quantity Setting
VIII. Endogenous Entry
Consider the following two-stage game among M rms, where M is a
large number:
Stage 1: All rms simultaneously decide
ECON 5430 Industrial Organization
Bernard Lebrun
VI. Comparative Statics
Fixed number of rms
We rst look at the eects of changes of parameters, such as cost parameters, on an interior CE. Let q = (q1 , ., qn ) be a particular interior CE
(there may exist
ECON 5430
Bernard Lebrun
Chapter 1: Cournot Oligopoly
III. Uniqueness
Reading: 5.7.1.2 in Tirole (1988).
UT1Uniqueness Theorem 1 (from Szidarovsky and Yakowitz, 1977):
Hahn conditions imply uniqueness in the general asymmetric case
(1) Assume p is continu
ECON 5430 Industrial Organization
Bernard Lebrun
Chapter 1:
Cournot Model of OligopolySimultaneous Quantity Setting
I. Denition
Reading: 5.4 in Tirole (1988).
Denition: Let there be n rms, rm 1 to rm n, that produce the
same (homogeneous) good. For all i,
ECON 5430
Bernard Lebrun
Exercises with suggestions of answers
Part VII
Exercise 66: In Example 1 (in the section Cournot Model of Oligopoly),
nd the Stackelberg equilibrium in the duopoly case (n = 2). Compare
the leaders with the followers equilibrium p