The Cournot equilibrium

"IIn a single-period model in which firms choose output levels independently, the Cournot Equlibrium is not only realistic ; it is the only plausible equilibrium" (Friedman, 1983)

The french mathematician Augustin Cournot presented the first - and probably still the most widely used - model of noncooperative oligopoly. He assumed that each firm acts independently and attempts to maximize its profits by choosing its output.

Let's consider a noncooperative duopoly with tow firms F1 & F2

What strategy should use F1 to choose its output level ? The answer depends on its belief about Firm F2's behevior. If F1 believes that F2 will sell q2, it can determine the q1 that will maximize its profit.

q₁ = q - q₂

Example

A Cournot duopoly : Two firms F1 and its rival F2.

Cost function of each of the two firms : C = 0,28q (no fixed costs, to simplify).

Market demande curve : q = 1000 – 1000p
Market Price function : p = 1- 0,001q

What strategy F1 must adopt to determine its output level ?

Answer of Cournot : it depends on its estimation of the output level (q2) of F2.

Let's suppose that F1 estimates the output level of F2 at 200 units. Then to calculate the output level of F1 use the "best-response function" or "reaction function" :

q₁= 360 – (q₂ / 2) - or - q₁= 360 – 0,5q₂

Response : q1 = 260 (quantity which maximizes the F1 profit)

Note : 360 is the optimal output in case of a monopoly (only one firm on this market)

Firms	Market Price	Output	Revenue	Cost	Profit
F1	0.54	260	140,4	72,8	67,6
F2	0.54	200	108,0	56,0	52,0
Industry	0.54	460	248.4	128.8	119.6

The Cournot equilibrium is reached when q1 = q2

q₁ = 360 – 0.5q₂ - and - q₂ = 360 – 0,5q₁

q₁ = 360 – 0.5(360 – 0,5q₁)

q₁ = 360 – 180 + 0,25 q₁

q₁– 0,25 q₁= 180

0,75 q₁= 180

q₁ = 240 and q₂ = 240

Comparaison between Monopoly, Noncooperative Oligopoly and Perfect Competition :

Market output	Market Price	Profit of industry
360	0.64	129.60	MR = MC	Monopoly
480	0.52	115.20	Cournot : q1= q2	Oligopoly
720	0.28	0.00	MC = Price	competition

Note : MR = marginal revenue ; MC = marginal cost

 

Sources :

Modern Industrial Organization, 2nd edition, Dennis .W. Carlton , Jeffrey .M. Peroloff, Addfison-Wesley, 1994

Economie Industrielle ( traduction de la 2ème édition par Fabrice Mazerolle), Dennis .W. Carlton , Jeffrey .M. Peroloff, de Boeck Université, 1998

Gaining and Soustaining Competitive Advantage, Jay. B. Barney, Addison-Wesley, 1997

Contemporary Strategic Analysis, Robert M. Grant, 3th edition, Blackwell, 1998

Strategic Management, Professor Raphael Amit, Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, B.C., Canada

Cours de Microéconomie, Bernard Jaquier, Ecole Hôtelière de Lausanne, 2003

 

Page publisher : Bernard Jaquier, Professor in Economics and Finance, Ecole Hôtelière de Lausanne, Switzerland, 2006