Managerial Economics & Business Strategy. Chapter 9 Basic Oligopoly Models. Oligopoly. Relatively few firms, usually less than 10. Duopoly - two firms Triopoly - three firms The products firms offer can be either differentiated or homogeneous. Firms behave strategically
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Managerial Economics & Business Strategy
Chapter 9
Basic Oligopoly Models
Situation:
United Airlines and American Airlines fly passengers between Chicago and LA. Assume no other company can enter because they can’t get landing rights at both airports.
Facts:
Marginal Costs: MCAA = MCUA = $147/passenger.
Market Demand: Q = 339 – P or P = 339 – Q, where Q = QAA + QUA;
Thus, P = 339 – QAA – QUA
To maximize profits, each firm chooses Q at the level in which MR=MC. You can either find an expression for TR for firm i, then differentiate with respect to Qi. This will give each firm’s MR function. Alternatively, you can use the fact that MR has twice the slope of inverse demand function!
Marginal Costs: MCAA = MCUA = $147/passenger.
P = 339 – QAA – QUA, so
TRAA = 339QAA – QAA2 – QUAQAA
TRUA = 339QUA – QUA2 – QAAQUA
MRAA = 339 – 2QAA – QUA and MRUA = 339 – QAA – 2QUA
For AA: 339 – 2QAA – QUA = 147 and solve for QAA.
AA Rxn Func: QAA = 96 – 0.5QUA
UA Rxn Func: QUA = 96 – 0.5QAA
To find Cournot Equilibrium (also a Nash equilibrium), plug one firm’s rxn function into the other firm’s.
QAA = 96 – 0.5(96 - 0.5QAA), and solving for QAA = 64.
Plug QAA = 64 into UA rxn function. QUA = 64. This outcome is due to the fact that MC are the same for both firms.
QUA
rAA
96
48
rUA
96
QAA
192
Cournot Equilibrium
64
64
192
If UA and AA collude, then see monopoly outcome.
MR = 339 – 2Q.
Set MR=MC, 339 – 2Q = 147, Q = 96, where UA and AA split the passengers.
P = 339 – Q, P = $243 versus $211 if competing duopoly
QUA
rAA
96
48
rUA
96
QAA
Collusion: each produce 48 & each would earn greater profits, but likely not sustainable.
192
Cournot Equilibrium
64
64
192
QUA = 96 – 0.5QAA
243 – QAA = 147
QAA = 96
Therefore QUA = 48 and P = $195