21.4 Market Structure and Framework
Basic model utilizing aggregate demand
Bertrand Equilibrium: Firms compete on price
Cournot Market structure: Firm compete on quantity
Stackelberg Market structure: Leader-Follower model
Because we start with the quantity demand function, it is important to know where it’s derived from Richard and Martin (1980)
K. S. Moorthy (1988)
- studied how two firms compete on product quality and price (both simultaneous and sequential)
21.4.1 Cournot - Simultaneous Games
TCi=ciqi where i=1,2P(Q)=a−bQQ=q1+q2π1=price×quantity−cost=[a−b(q1+q2)]q1−c1q1π2=price×quantity−cost=[a−b(q1+q2)]q1−c2q2
dπ1dq1=a−2bq1−bq2−c1=0(1) dπ2dq2=a−2bq2−bq1−c2=0From (21.1)
q1=a−c12b−q22=R1(q2)is called reaction function, for best response function
From (21.2)
q2=a−c22b−q12=q1=a−c12b−a−c24b+q14
Hence,
q∗1=a−2c1+c23bq∗2=a−2c2+c13b
Total quantity is
Q=q1+q2=2a−c1−c23b
Price
a−bQ=a+c1+c23b
21.4.2 Stackelberg - Sequential games
also known as leader-follower games
Stage 1: Firm 1 chooses quantity
Stage 2: Firm 2 chooses quantity
c2=c1=c
Stage 2: reaction function of firm 2 given quantity firm 1
R2(q1)=a−c2b−q12
Stage 1:
π1=[a−b(q1+a−c2b−q12)]q1−cq1=[a−b(a−c2b+q12]q1+cq1
dπ1dq1=0
Hence,
a+c2−bq1−c=0
The Stackelberg equilibrium is
q∗1=a−c2bq∗2=a−c4b
Under same price (c), Cournot =
q1=q2=a−c3b
Leader produces more whereas the follower produces less compared to Cournot
dπ∗Wdβ<0
for the entire quantity range d<ˉd
As β increases in π∗W Firm W wants to reduce β.
Low β wants more independent
Firms W want more differentiated product
On the other hand,
dπ∗Sdβ<0
for a range of d<ˉd
Firm S profit increases as β decreases when d is small
Firm S profit increases as β increases when d is large
Firm S profit increases as as product are more substitute when d is large
Firm S profit increases as products are less differentiated when d is large