Oligopoly: Non-Collusive Models- Cournot, Stackelberg, Bertrand, Sweezy or Kinked Demand Curve

Models of Oligopoly

1. Collusive Models

• Cartel: Profit Sharing and Market Sharing
• Price Leadership

2. Non-Collusive Models

• Cournot Model
• Stackelberg Model
• Bertrand Model
• Sweezy Model or Kinked Demand Curve

Non-Collusive Models of Oligopoly

Cournot Duopoly Model

Augustin Cournot, a French Economist, published his Theory of Duopoly in 1938. We begin with a simple model of duopoly where two firms are competing with each other. It is assumed that the products produced by the two firms are homogeneous, and they are aware of the market demand curve.

The market demand curve is assumed to be linear, i.e. straight line. Each firm needs to decide how much to produce, and the two firms are taking their decisions at the same time. It is also assumed that the cost of production is taken as zero. It is only the demand side that is considered.

It is also assumed that each firm believes that the rival firm will keep its output constant regardless of its action and its effect on the market price of the product. In other words, each firm treats the output level of its competitors as fixed and then decides how much to produce. It is shown in Figure 1.

In Figure 1, price is measured on X-axis and quantity on Y-axis. We are taking a special case of duopoly where two firms are competing with each other. The demand curve faced by the two rival firms is the straight line DD1. The total output that both firms produce is OA+AD1=OD1. The maximum output produced by Firm 1 is OA, and by Firm 2 is AD1. When the total output OD1 is offered for sale in the market, then the market price is zero.

We are assuming that there is no cost of production. Let us suppose that firm 1 starts the business first and then is followed by firm 2. Firm 1 would behave like a monopolist as he is starting first. Firm 1 will produce maximum output OA to maximize profit. The price is OP which is charged by firm 1 to produce OA units of output. Firm 1 is facing no cost of production, so its entire revenue would be its profits. The profit that is earned by firm1 by producing OA units of output is OAEP.

Now suppose firm 2 also enters the market and starts operating its business. Firm 2 knows that Firm 1 is already operating in the market and producing OA units of output. Firm 2 believes that Firm 1 will continue to produce OA units of output irrespective of what output he decides to produce. So, firm 2 can take ED1 portion of the demand curve and produce half of AD1 units of output.

Firm 2 is now producing AB units of output. The total output that is produced by Firm 1 and Firm 2 is OA+AB=OB. The new price would be OP1 which is less than the price that is charged by firm 1 when he is the only firm that is operating in the market.

The total profits earned by both firms are OBCP1. This profit OBCP1 that is earned by both firms is less than OAEP. Out of OBCP1 total profits, profits earned by firm 1 are OAFP1 and profits earned by firm 2 are AFCB.

The profit earned by firm 1 is reduced from OAEP to OAFP1 as firm 2 is producing AB units of output. Now firm 1 assumes that firm 2 will continue to produce AB units of output. The best that Firm 1 can do is to produce half of (OD1-AB). Now that Firm 2 has been surprised by the reduction of output produced by Firm 1 and his reduced share of profits in comparison to Firm 1, he will reappraise his situation.

This process of adjustment and readjustment by each producer will continue, with firm 1 being forced gradually to reduce his output and firm 2 being able to increase his output gradually until each is producing the same amount of output equal to one-third of OD1 units of output. Throughout this process, each firm assumes that the other firm will keep its output constant irrespective of what it decides to produce.

Stackelberg Model

The Stackelberg Model is named after the German Economist Heinrich Freiherr von Stackelberg, who published Market Structure and Equilibrium in 1934, which described the model. The Stackelberg leadership model is a strategic game in economics in which the firm moves first, and then the follower firms move sequentially.

In this model, suppose firm 1 sets its output first, and then followed by firm 2, after observing firm1’s output, makes its output decision. Firm 1, before setting output, must consider how Firm 2 will react.

The Stackelberg model is different from the Cournot model, where neither firm has any opportunity to react. The Stackelberg and Cournot models are similar because, in both models, competition is based on quantity.

However, the first move gives the leader in Stackelberg a crucial advantage. The very important assumption in the Stackelberg model is perfect information. The follower must observe the quantity chosen by the leader; otherwise, the model would reduce to Cournot. The aggregate Stackelberg output and consumer surplus are greater than the aggregate Cournot output. And the Stackelberg price is lower than the Cournot price.

In Figure 4, BR1 and BR2 are the best response curves. The frown-shaped curves are firm1’s is o profits. Point N is the Nash equilibrium, where two reaction curves intersect each other. The Stackelberg equilibrium point is S, the point at which the highest is o profit for Firm 1 is reached on Firm 2’s best response function. At point S, firm 1’s o profit is tangent to firm 2’s best response function. If firm 1 cannot commit to its output, then the output function unravels, following the arrow from S back to C.

Bertrand Model

The Bertrand Model was formulated in 1883 by Bertrand in a review of Antoine Augustin Cournot’s (1838) book in which Cournot had put forward the Cournot Model.

According to Cournot, firms compete with each other and choose quantities, and the equilibrium outcome would result in prices which are more than the marginal cost. According to Bertrand, if firms choose prices rather than quantities, then the competitive outcome would occur with a price equal to marginal cost.

The Bertrand model assumes that products produced by firms are homogeneous. Suppose two duopoly firms compete by simultaneously choosing a price instead of quantities. We know that products produced by firms are homogeneous; then the consumer will only purchase from the lowest price seller.

If the two firms charge different prices, the lower-price firm will supply the entire market, and the higher-priced firm will sell nothing. The entire market is covered by the lowest-price seller.

If both firms charge the same price, then the consumers would be indifferent as to which firm they buy from. In this case, we may assume that each firm would supply the market equally.   The Nash equilibrium is the competitive output because of the incentive to cut prices.

Sweezy Model or Kinked Demand Curve

The two seminal papers on Kinked Demand were written nearly simultaneously in 1939 on both sides of the Atlantic. Paul Sweezy of Harvard College published “Demand under Conditions of Oligopoly”.

According to Sweezy, an ordinary demand curve does not apply to oligopoly markets and promotes a kinked demand curve. The price rigidity is the basis of the “kinked demand curve” model of oligopoly.

According to Sweezy, each firm faces a demand curve kinked at the currently prevailing price, say P*. For any price above (below) P*, the demand curve is elastic (inelastic). It implies that if the firm raises its price above P*, other firms would not follow him, and as a result, it would lose sales and market share.

On the other hand, if the firm lowers its price below P*, other firms would follow him else they would lose market share. Thus, an ordinary demand curve does not apply to oligopoly markets and promotes a kinked demand curve.

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