# How to Calculate Cournot Equilibrium

by Gerald Hanks; Updated September 26, 2017Economists use the Cournot equilibrium equation to determine the most profitable output in an industry with only two producers, also called a duopoly. Each member of the duopoly must produce a homogenous good, control the market over the production of that good and not collude for the Cournot equilibrium to apply in their case. The Cournot equilibrium is used to calculate the peak profit point for one member of the duopoly based on the expected production of the other member.

### Theory of Cournot Equilibrium

The Cournot equilibrium equation assumes that at least two firms are participating in an industry, these firms control the means of production and do not engage in collusive behavior. Each firm chooses its output levels independently from its competitors, and the market, not the firms, determine the sale price. Instead of a competitive environment, in which the firm's output does not directly affect its competitor, the Cournot equilibrium examines a duopoly, in which one company's revenue depends on both its own output and the other firm's output.

### Calculation of Cournot Equilibrium

To calculate the Cournot equilibrium point, you must know the demand equation of your entire market and adjust that equation for the two participants in the duopoly. Determine the total revenue function for your company by multiplying the price by the total amount your company produces from the demand equation. The derivative of the total revenue function gives you the marginal revenue function, or the amount of revenue you earn with each additional unit produced. Set the marginal revenue function equal to the marginal cost to determine the maximum profit point. The function will be in terms of both your company's production and that of your competitor in the duopoly.

### Cournot Equilibrium and Costs

The production levels of each company in a Cournot duopoly depend not only on the expected production of the other participant, but also on the cost functions of both firms. If both participants must pay the same costs for their raw materials, they will each produce half the goods in their markets. If one firm pays higher costs for their production materials than the other, the one that pays the higher costs will produce less, while the one that pays less will produce the remainder and have higher profits.

### Reality of Cournot Equilibrium

While the Cournot Equilibrium describes the conditions under which two companies in a duopoly can reach their maximum profits, it does not describe how each company arrives at that point. Each company would need perfect information on its opponent's demand curve to make the proper calculations. Also, prices are lower and output is higher in a Cournot duopoly than in a monopoly, so the incentives are there for the duopoly to become a cartel, in which both parties cooperate for maximum profits in the industry rather than compete against each other.

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