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Figure 1
Profit Maximizing Quantities
For Dominant Firm and Fringe
MC
p
MRd
q
qd
qf
Figure 2: Industry Evolution As Elasticity of Demand (εD) Varies; εS held fixed at 1
(b) m°next(m)
(a) m(m°)
ed=4
ed=1
ed=0
ed=100
1
1
0.9
0.9
Industry concentration at end of production phase
Industry concentration at end of merger phase
ed=100
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
ed=4
ed=1
ed=0
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
Industry concentration at start of merger phase
1
0
0.2
0.4
0.6
0.8
Industry concentration at start of production stage
1
Figure 3: Industry Evolution As Elasticity Of Supply (εS) Varies; εD held fixed at 2
(b) m°next(m)
(a) m(m°)
es=0.25
es=1
es=1000
es=0.01
1
1
0.9
0.9
Industry concentration at end of production phase
Industry concentration at end of merger phase
es=0.01
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
es=0.25
es=1
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0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
Industry concentration at start of merger phase
1
0
0.2
0.4
0.6
0.8
Industry concentration at start of production stage
1
Figure 4: Industry Transition F(m°)
As εD Varies; εS held fixed at 1
ed=4
ed=1.1
Figure 5: Industry Transition F(m°)
As β Varies; Elasticities εS=1, εD=0
ed=0
b=0
1
b=0.25
b=0.95
0.7
Industry concentration at start of next period
Industry concentration at start of next period
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0
0.2
0.4
0.6
0.8
Industry concentration at start of current period
1
0
0.1
0.2
0.3
0.4
0.5
0.6
Industry concentration at start of current period
0.7
Table 1: Steady State Concentration m o With Initial State m o = 0.5
Cost/demand
elasticity
εD=0.5
εD=1
εD=1.2
εD=1.5
εD=2
εs=2
0.353
0.462
0.515
0.615
1
εS=1
0.377
0.586
0.722
1
1
εS=2/3
0.396
0.692
1
1
1
εS=1/2
0.410
0.778
1
1
1
εS=2/5
0.421
0.845
1
1
1
Table 2: Critical Value βˆ (ε D , ε S )
(Perfect competition is stable if and only if β > βˆ (ε D , ε S ) .)
Cost/demand
elasticity
εD=0
εD=.1
εD=1
εD =10
εS=.1
.25
.42
.76
.94
εS=1
.25
.27
.40
.68
εS=10
.25
.25
.27
.38
εS=∞
.25
.25
.25
.25
Table 3: Critical Value β (ε D ,ε S )
(Monopoly is unstable if and only if β > β (ε D ,ε S ) .)
Cost/demand
elasticity
εD=2
εD=5
εD=10
εS=.1
.85
.92
.95
εS=1
.29
.55
.68
εS=10
.0004
.043
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