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Welcome to EC 209: Managerial Economics- Group A By: Dr. Jacqueline Khorassani. Week Ten. Managerial Economics- Group A. Week Ten- Class 1 Monday, November 5 11:10-12:00 Fottrell (AM) Aplia assignment is due tomorrow before 5 PM. Chapter 9 of Baye. Basic Oligopoly Models.
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Welcome to EC 209: Managerial Economics- Group ABy:Dr. Jacqueline Khorassani
Week Ten
Week Ten- Class 1
Monday, November 5
11:10-12:00Fottrell (AM)
Aplia assignment is due tomorrow before 5 PM
Chapter 9 of Baye
Basic Oligopoly Models
P0
QH1
QH2
QL2
QL1
Q0
D2 (demand for your cars when rival matches your price change)
P
PH
PL
D1 (demand for your cars when
rival holds its price constant)
Q
D2 (Rival matches your price change)
P
P0
D1
(Rival holds its
price constant)
Q
Q0
What if your rivals match your price reductions but not your price increases?
Your demand if rivals match price reductions but not price increases “Kinked Demand Curve”
P2
P1
D
Q1
Q2
PQ1 = aQ1 – bQ12 – bQ1Q2
PQ2 = aQ2 – bQ22 – bQ1Q2
TR1= PQ1 = aQ1 – bQ12 – bQ1Q2
TR2 = PQ2 = aQ2 – bQ22 – bQ1Q2
MC=MR
Firm 1’s MC = c1
And its MR = a- bQ2 -2bQ1
c1 =a- bQ2 -2bQ1
2bQ1= -c1+a-bQ2
Q1 = r1(Q2) = (a-c1)/2b - 0.5Q2
Q2
(a-c1)/b
If Q1 = 0 Q2 = (a-c1)/b
Q2
r1
(Firm 1’s Reaction Function)
Q1
Q1
(a-c1)/2b
If Firm 1 produces A Firm 2 produces B
If Firm 2 produces B Firm 1 produces C
If Firm 1 produces C Firm 2 produces D
Q2
(a-c1)/b
Cournot Equilibrium
Q2M
Q2*
D
B
r2
r1
Q1*
A
(a-c2)/b
Q1
C
Equilibrium Quantities are at intersection of the response curves
If Firm 1 produces A Firm 2 produces B
If Firm 2 produces B Firm 1 produces C
If Firm 1 produces C Firm 2 produces D
Q2
(a-c1)/b
Cournot Equilibrium
Q2M
Q2*
D
B
r2
r1
Q1*
A
(a-c2)/b
Q1
C
Equilibrium Quantities are at intersection of the response curves
Cournot equilibrium after
firm 1’s marginal cost increase
r1**
Q2**
Cournot equilibrium prior to
firm 1’s marginal cost increase
Q2*
r2
Q1**
Q1*
When c1 goes up vertical intercept of firm 1’s reaction curves goes down
Q2
r1*
(a-c1)/b
Q1
Firm 1’s production goes down
qA = Q – qB
qA = 339 – P - qB , or
P = 339 - qA – qB
= P qA = qA (339 - qA – qB)
= 339 qA- qA2 - qAqB
= 339 - 2 qA – qB
339 - 2 qA – qB = 147
or qA = 96 – 1/2 qB
Consider qB = 0; qA = 96
By the same reasoning qB = 96 – 1/2 qA
qA = 96 – 1/2 qB
qB = 96 – 1/2 qA
qA = 96 – 1/2 (96 – 1/2 qA )
Solve to find qA = 64
Similarly qB = 64
P = 339 - qA - qB
P = 339 - 64 - 64
P = 211
Remember that AC = 147
Each firm’s profit = q (P-AC)
Each firm’s profit = 64*(211-147) = 64 * 64 = 4096
QB
rA
After Collusion
48
rB
QA
48
qA = 96 – 1/2 qB
qA = 96 – 1/2 (48)
qA = 72
QB
rA
48
rB
QA
48
72
Q2 = (a – c2)/2b – 1/2Q1
Cournot equilibrium
Q2
r1
Stackelberg Equilibrium
Q2C
Q2S
r2
Q1M
Q1C
Q1S
Q1
Note: Firm 1 is producing on Frim 2’s reaction function (maximizes its profits given the reaction of Firm 2)
Q = 339 – P, and
AC = MC = 147
qA = Q – qB
qA= 339 – P - qB or
P = 339 - qA – qB
qB = 96 – 1/2 qA
P = 339 – qA - 96 + 1/2 qA
P = 243- 1/2 qA
Firm A’s revenue is
PqA = 243 qA– 1/2 qA2
MR = 243 – qA
Set this equal to MC
147 = 243- qA
qA = 96
Use B’s reaction function
qB = 96 – 1/2 qA,
qB = 96 – 1/2 (96),
qB = 48
Remember that
P = 339 - qA – qB
P = 339 – 96 – 48
P = 195, AC = 147
Firm A’s profit = 96 (195 - 147) = 4608
Firm B’s profit is 48 (195 – 147) = 2304
AC= MC = 10 , P1=15 , P2= 18
P1 – AC= 5