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.

Total Cost Function of each of the two firms : TC = 0.000001q³- 0.014q² + 69q + 128'000; Market demande curve : q = 19'500 - 100p ;
Market Price function : p = 195 - 0.01q

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 5000 units. Then to calculate the output level of F1 use the "best-response function" or "reaction function" :

q₁= 7950 – (q₂ / 2) - or - q₁= 7950 – 0,5q₂

Response : q1 = 5450 (quantity which maximizes the F1 profit)

Note : 7950 is the optimal output in case of a monopoly (only one firm on this market)

F	Output	P	R	TC	Profit
F1	5'450	90.50	493'225	250'094	243'131
F2	5'000	90.50	452'500	248'000	204'500
Market	10'450	90.50	945'725	498'094	447'631

The Cournot equilibrium is reached when q1 = q2

q₁ = 7950 – 0.5q₂ - and - q₂ = 7950 – 0,5q₁

q₁ = 7950 – 0.5(7950– 0,5q₁)

q₁ = 7950 – 3975 + 0,25 q₁

q₁– 0,25 q₁= 3975

0,75 q₁= 3975

q₁ = 5300 and q₂ = 5300

Comparaison between Monopoly, Noncooperative Oligopoly, Cartel and Perfect Competition :

Market output	Market Price	Profit of industry	Equilibrium	Markets
7'950	115.50	624'050	MR = MC	Monopoly
9'566	99.34	455'949	MR = MC	Cartel
10'600	89.00	444'766	Cournot : q1 = q2	Oligopoly
12'452	60.00	-	P = AC	Competition

Note : MR = marginal revenue ; MC = marginal cost ; AC = Average 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, 2008

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

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

Strategic Management, Raphael Amit, Professor at Wharton University of Pennsylvania, US

Cours de Microéconomie, Prof Bernard Jaquier, 2003

 

(c) ECOFINE.COM, Prof Bernard Jaquier, Switzerland, 2020