Stackelberg Model

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I- Introduction:

An oligopoly refers to the economic situation where there are several firms in the industry making a product whose price depends on the quantity (Examples can include large firms in computer, chemicals, automobile…) Cournot was the first economist to explore and explain the oligopolistic competition between the two firms in an oligopolu (Cournot and Fisher in 1897). He underlined the idea of duopoly problem and the non-cooperative behavior of the firms. In 1934, Heinrich F. von Stackelberg came up with another model that explains the strategic game through which the firms in an oligopoly decide the level of output in a sequential manner. The following essay evaluates the usefulness of the Stackelberg Model in explaining the behavior the firms in oligopolistic markets. Furthermore, it will be discussed that how realistic the model is in today’s world though economic diagrams and relevant theories.

II- Stackelberg Model of Oligopoly:

Oligopoly has been addressed through a number of models including Cournot Model, Bertrand Model and Stackelberg Model. The first one has made a great contribution towards explaining oligopoly as well as non-cooperative game theory. However the remaining two models have made contributions towards overcoming the limitations of the Cournot Model.

The Model basically explains the strategic game in which the market leader makes the first move, and the other follower firms in the oligopoly make sequential moves. The leader firm chooses the quantity first, and based on the leader firm’s quantity, the follower firms set the quantity. Once both quantities are chosen, the price is set to clear the market. The leader has the first mover advantage on the basis of better technology, higher production capacity, or the exisiting monopoly. Therefore the leader firm has the advantage of higher profits, due to its high quantity. The Stackelberg model has an irreversible nature, that is to say it involves permanent action or commitment of agents where later movers observe the moves or action of the first movers, and then acti in the game.

To explain how it works, lets consider two firms, A and B that produce homogenous products in an oligopoly. To make it simple, it’s assumed that A and B are the only firms in the oligopoly. Firm A is the leader firm, and B the follower one. QA represents the quantity decided and produced by firm 1 and QB the quantity the follower firm B will produce in sequence. The Sum of QA and QB will result in the market demand. RF(A) and RF(B) represent the reaction curves of both firms respectively. In this case, the model states that both firms decide on their output in sequence (due to the oligopoly). The leader chooses the output level due to its capacity of being the first mover. By setting this level, the leader makes a commitment that will be adjusted by the follower, then he will benefit by keeping the level of quantity high for itself. Besides, the follower has to keep its level relatively lower than the one of the leader. The equilibrium quantity is determined by the point of tangency between the reaction curve B and the lowest possible isoprofit of A. The point of intersection is also known as firm A’s bliss point as it maximizes the marginal utility for firm A. The equilibrium price is determined by inverse market demand, and since both firms seek to maximize their profits, they end up determining a quantity where their margninal costs equal the marginal revenue (MC=MR)

The Stackelberg model follows stages where in the first stage, firm A takes the action of setting the quanity, while firm B does nothing. This quantity is decided keeping in mind mind the expected answer of the follower. In the next statge, firm B knows the QA and then decides the quantity it wants to produce in respoonse to QA. In this stage, firm A does not take any action. The assumption here being that both firms know the quantity decided by each other. The logic of...
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