Cournot Model: Concept, Assumption, Solution, and Criticism

What’s it: A Cournot model is one of the economic models to explain the oligopoly market. This model assumes that the firm independently decides the profit-maximizing level of production. I mean, they don’t depend on how many competitors are producing.

The name of this term is taken from its originator, Augustin Cournot, a French mathematician.

Basic assumptions of the Cournot model

In this model, the company produces a homogeneous product. They seek to maximize profits by choosing how much to make.

Since the product is homogeneous, in this market structure, competition is based on the quantity of output produced. All firms decide output simultaneously. They assume competitors’ output will not change.

Another assumption is that companies cannot collude or form cartels. They also have the same view of market demand and are familiar with competitors’ operating costs.

Cournot duopoly solution

The Cournot model produces logical results. In the long run, prices and output are stable; that is, there is no possibility that changes in output or prices will make the firm better off.

In a duopoly market structure, Cournot’s solution falls between competitive and monopolistic equilibrium. Perfect competition produces the lowest prices and the highest output. Meanwhile, the monopoly imposes the highest price and produces the lowest output.

Furthermore, when the number of firms in the industry increases, equilibrium points will close to the competitive equilibrium.

To answer why Cournot’s solution is between perfectly competitive and monopolistic markets, let’s take a simple example.

Say, market demand is:  Q_d = 200 – P, where P is the market price.

The market consists of only two companies. The supply curve for each firm is represented by marginal cost (MC), which is constant at CU20.

Let’s solve the case.

Since there are only two, the quantity of market supply (Q_s) equals the sum of the quantity of output of the first firm (Q_s1) and the quantity of output of the second firm (Q_s2).

Q_s = Q_s1 + Q_s2

Remember, market equilibrium occurs when market demand equals market supply (Qd = Qs). So we can convert the above-market demand equation to:

Q_d = Q_s <—> 200 – P = Q_s1 + Q_s2

From this equation, we get the equation for the market price, which is as follows:

 P = 200 – Q_s1 – Q_s2

Next, we’ll find the revenue for each firm using the market price equation above. Revenue is the market price times the quantity of output.

• Total revenue of the first firm (TR1) = P x Q_s1 = (200 – Q_s1 – Q_s2) x Q_s1= 200Q_s1 – (Q_s1 x Q_s1) – (Q_s2 x Q_s1) = 200Q_s1 – Q_s1² – (Q_s2 x Q_s1)
• Total revenue of the 2nd firm (TR2) = P x Q_s2 = (200 – Q_s1 – Q_s2) x Q_s2= 200Q_s2 – (Q_s2 x Q_s1) – (Q_s2 x Q_s2) = 200Q_s2 – (Q_s2 x Q_s1 )– Q_s2² 

In the long run, the company produces at the profit-maximizing level of output. It occurs when marginal revenue (MR) equals marginal cost (MC). Since we already know the value of MC ($20), our next task is to find marginal revenue.

Marginal revenue equals the first differential of total revenue concerning the quantity produced by each firm. For the first firm, we must find the first differential TR1 against Q_s1. As for the second firm, we must find the first differential TR2 against  Q_s2. The result:

Marginal revenue of 1st firm (MR₁) = 200 – 2Q_s1 – Q_s2

Marginal revenue of 2nd firm (MR₂) = 200 – 2Q_s2 – Q_s1

Since both companies have the same marginal cost of $20, we can finally calculate Q_s2 and Q_s1.

To maximize profit, the firm will operate at a rate where MR = MC. So, for the two companies we get the following equation:

•  1st firm: MR₁ = MC <—> 200 – 2Q_s1 – Q_s2 = 20
• 2nd firm: MR₂ = MC <—> 200 – 2Q_s2 – Q_s1 = 20

 First, let’s solve for firm 1 and get the equation for Q_s2.

200 – 2Q_s1 – Q_s2 = 20 <—> Q_s2 = (200-20) – 2Q_s1 <—> Q_s2 = 180 – 2Q_s1 

 Now, we substitute the equation Q_s2 to firm 2. The goal is to get the value of Q_s1.

200 – 2Q_s2 – Q_s1 = 20 <—> 200 – 2(180 – 2Q_s1) – Q_s1 = 20 <—> 200 – 360 + 4Q_s1 – Q_s1 = 20 <—> -160 + 3Q_s1 = 20

So, the value of Q_s1 = (20+160)/3 = 60.

After getting the Q_s1 value, the next task is to get the Q_s2 value.

Q_s2 = 180 – 2Q_s1 = 180 – (2 x 60) = 60

Thus, in Cournot strategic pricing, the equilibrium price and quantity will equal:

• P = 200 – Q_s1 – Q_s2 = 200 – 60 – 60 = 80
• Q_d = 200 – P = 200 – 80 = 120

Let us compare the results with perfectly competitive and monopolistic markets.

Under perfectly competitive markets, profit maximization occurs when price equals marginal cost and equals marginal revenue: P = MR = MC = $20. And for the quantity:  Q_d = 200 – P = 200 – 20 = 180.

Under monopoly, equilibrium occurs when marginal revenue equals marginal cost (MR = MC). Since there is only one firm, the total revenue will be equal to TR = P × Q_d = (200 – Q_d ) Q_d = 200Q_d – Q_d². 

In this case, the marginal revenue (first differential of Qd) is 200 – 2Q_d..

Since MR = MC, we get the price and quantity in the monopoly market as follows:

• MR = MC <—> 200 – 2Q_d = 20 <—> Q_d= 90 
• P = 200 – Q_d = 200 – 90 = 110 

In summary, I present the quantities and prices in the three markets in the table below.

Criticism of the Cournot model

The Cournot model’s assumptions are unrealistic in the real world. 

In Cournot’s classic duopoly model, the two players set their quantity independently. It is unrealistic. Since there are only two players, they would tend to be highly responsive to competitors’ strategies.

Quantity is not the only basis for competition. In the oligopoly industry, competition is not only based on price but also through differentiation.

Differentiation allows firms to maximize profits without having to get involved in price competition. Thus, as quantity rises, prices may not necessarily fall if the product is unique. It isn’t easy to find the perfect substitute.