Case for Instructiecollege 4, Economics 1.2, Bedrijfskunde. Oligopoly.
In this case we study the oligopolistic behaviour of two airline companies, American
airlines and United airlines. They are the only airline companies that obtained the right to
operate on the route Chicago-LA. We assume that the services of the two airline
companies are homogenous to the customers and we have the following market demand
function for flights on this route
Q 339 p
with Q expressed in units of 1000 passengers, and p the price per passenger. The airline
companies have the same production technology and therefore have the same cost
function
c(q) 147q
with q the number of passengers in units of 1000 of the firm.
The Cournot model
Now assume that the airline companies in this market behave according to the Cournot
model.
A. Determine the Best-response, or, reaction function, of American airlines.
B. Also determine the Best-response function for United airlines.
C. Draw these two functions in the same graph.
D. How is the Cournot equilibrium determined according to this graph? Show which
output level each firm produces in the Cournot equilibrium, and compute the
equilibrium price and profit levels for both firms.
E. Compute the Cournot equilibrium values.
The Stackelberg model
We assume that American airlines can choose its output before United airlines. Thus, we
now assume that the two airline companies behave according to the Stackelberg model,
with American airlines as the leader and United airlines as the follower.
F. What will be the best strategy of the follower, United airlines?
G. What choice is made by American airlines? Compute the Stackelberg output
values for both airline companies and the price level in the equilibrium.
H. Compute the Stackelberg profit values for both companies.
The Bertrand model
Suppose that American airlines and United airlines choose their price level, rather than
their output level, according to the Bertrand model.
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In this case we study the oligopolistic behaviour of two airline companies, American
airlines and United airlines. They are the only airline companies that obtained the right to
operate on the route Chicago-LA. We assume that the services of the two airline
companies are homogenous to the customers and we have the following market demand
function for flights on this route
Q 339 p
with Q expressed in units of 1000 passengers, and p the price per passenger. The airline
companies have the same production technology and therefore have the same cost
function
c(q) 147q
with q the number of passengers in units of 1000 of the firm.
The Cournot model
Now assume that the airline companies in this market behave according to the Cournot
model.
A. Determine the Best-response, or, reaction function, of American airlines.
B. Also determine the Best-response function for United airlines.
C. Draw these two functions in the same graph.
D. How is the Cournot equilibrium determined according to this graph? Show which
output level each firm produces in the Cournot equilibrium, and compute the
equilibrium price and profit levels for both firms.
E. Compute the Cournot equilibrium values.
The Stackelberg model
We assume that American airlines can choose its output before United airlines. Thus, we
now assume that the two airline companies behave according to the Stackelberg model,
with American airlines as the leader and United airlines as the follower.
F. What will be the best strategy of the follower, United airlines?
G. What choice is made by American airlines? Compute the Stackelberg output
values for both airline companies and the price level in the equilibrium.
H. Compute the Stackelberg profit values for both companies.
The Bertrand model
Suppose that American airlines and United airlines choose their price level, rather than
their output level, according to the Bertrand model.
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