Price and output determination under Duopoly

If an industry is composed of only two giant firms, each selling identical products and having half of the total market, there is every likelihood of collusion between the two firms. The firms may agree on a price, or divide the market, or assign quota, or merge themselves into one unit and form a monopoly or try to differentiate their products or accept the price fixed by the leader firm, etc., etc.

In case the duopolists producing perfect substitute engage in price competition, the firm having lower costs, better goodwill and clientele will drive the rival firm out of the market and then establish a monopoly.

If the products of the duopolists are differentiate, each firm will have a close watch on the actions of its rival firms. The firms manufacturing good quality products with lesser cost will earn abnormal profits. Each firm will fix the price of the commodity and expand output in accordance with the demand of the commodity in the market.

Duopoly Models:

There are four main duopoly models which explain the price and quantity determinations in duopoly. These models are:

(i) Classical Model of Cournot and Edge Worth.

(ii) Hotellings Spatial Equilibrium Model.

(iii) Stackelberg’s Model.

(iv) Modern Game Theory Model.

(i) Cournot and Edgeworth Model:

Cournot approach is based, on the assumptions that rivals output remains the same and one duopolists plans to change in his output. Edgeworth model assumes that rival’s price of the good to remain unchanged as one duopolists plans a change in his price of the good.

(ii) Stackberg’s Approach:

It is based on the assumptions that one of the duopolists is a ‘Leader’ and the other is the follower.

(iii) Hotelling Spatial Equilibrium Model:

In this model, the products of the duopolists are differentiate in the eyes of the buyers by virtue of the location of the duopolists.

(iv) Game Theory Approach:

Whenever there are two or a few firms competing in an industry for profit, each firm can and dose react to the price, quantity, quality and product changes which other firm undertakes. The duopolists or oligopoly have a reaction function. As firms under duopoly are independent, they, therefore, employ strategies. The competing firm also make plans to contract and makes decisions about output and price of the good keeping in view the strategy of its rivals. The plans made by these firm, are known as game strategies. The game theory model describes the firms, interaction model. It is the analytical framework in which two or more firms compete for economics profits that depend on the strategy that the others employ.

All games theory models have at least three common elements:

(a) Players: Players in the game theory are the firms.

(b) Strategies: Strategies are the plans, the possible choices of the firms for production of output, prices of goods, changes in the quality of the product

(c) Pay offs (economic profit): These are the profits or losses realized by the firm.