# Stackelberg Model Essay

Custom Student Mr. Teacher ENG 1001-04 24 October 2016

## Stackelberg Model

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 the follower’s strategy of keeping its level of ouput low is that in that situation, only one firm can possibly act as a market leader. If both firms try to become leaders by increasing the quantity produced, there will be overproduction in the market leading to decrease in prices. The effect will be a decrease in profits for both firms.

III- Implications and applications:

Stackelberg model has been extended and modified to adjust a number of real market scenarios. The model has been empirically tested for more than two players in the oligopoly to fit the real complexities of the economic world. The extension to n-player model has been tested for different market conditions both, where the information is perfectly interracted amongst all players, and where there is uncertainty and incomplete information. Boyer and Moreaux (1987) developed a model will perfect information, while on the other hand, Gal-Or (1985à and Albaek have done research on Stackelberg Model of Oligopoly with incomplete information.

Gal-or argues that in opposite to the belief that first mover advantages result in a two-player Stackelberg model, the model can be extended to include multiple players. Similarly, the model has been tested for a market situation where there are multiple leaders. Sherali (1984) tried to consider the situation of multiple leader oligopolies with the assumption that each leader firm assumes that its actions do not precipitate responses from other leader firms. These variances of the model help practicioners indentity and understand the behavior of firms in their respective oligopolies.

IV- Empirical Examples:

This model is mostly used to analyze many industries where one firm acts as a leadern while others as followers. Economists and researchers use it to understand and evaluate their behavior in an oligopoly. For instance, Yu, Huanf and Liang (2009) have adopted this model to understand the supply chain of vendor managed invetory production. The manufacturer of the products is trated as the leader as it is responsible form amnaging the investories for all the retailers. The retailers on the other hand are treated as followers.

The leader knows the action of each retailer, and optimizes the investment on advertisements, cycles of raw materials and the finished products to maximize its profits. As a result of this move, the retailers sequantially follow the manufacturer’s decisionas input parameters so that they can determine the level of retail price and investments in advertisements to maximize the profit. Hence, an optimal supply chain solution is reached. In this case, the Stackelberg model helps in determining optimal spend by retailers and manufacturers to maximize their profits.

V- Implications:

These empiral examples reveal the usefulness of Stackelberg model in explaining the behavior of firms. It has been empirically tested and proved that the model provides realistic results in the short term. However, if we talk about the long term, every firm tries to become the first mover by accumulating experience and learning. This enables the firms to expand their capacities and technology to become the first mover. Hence, in the long run, the model does not significantly hold. Apart from that, the industry structure also has an important role.

The model can only be applied to the industries where one firm has significant edge over other firms in term of capacity and experience. In such a situation, other firms tend to follow the capacity and quantity values of the market leader. However, in a market where firms are more or less at the same size, the model doesn’t give realistic results, since in such a situation, each firm tries to become the market leader. In such an oligopoly, Cournot Model gives more realistic results.

VI- Limitations:

Like all economic models, Stackelberg Model has its own share of weaknesses and limitations. As opposed to Cournot and Bertrand Models, Stackelberg Model doesn’t hold when applied to multiple time periods. It assumes that every firm in a two player oligopoly can alternatively become leader and follower indifintely. The model ignores the fact that with time, each and every firm tries to acquire unique capabilities by moving up the learning curve. Thus, each firm will try to become first mover over a prolonged period of time, thus a symmetric pattern shouldn’t emerge.

VII- Conclusion:

Through analysis and careful investigation of the Stackelberg Model of Oligopoly, the following conclusions have been derived:

The significance and relevance of the model depends on the market situation and the characteristics of the oligopoly. Although the model gives higher profits to the firms as compared to Cournot-Nash Model, the appropriateness depends largerly in the industry structure (Boyer and Mareaux, 1987). If the industry structure includes firms of roughly similar size where no firm can enjoy leadership position, Cournot model is more suitable. However, for the industry where one firm has a signicant advantage over other firms, Stackelberg Model gives more realistic results. This can be seen in the industries that are dominated by a fewer huge firms that take lead in the introduction of a new idea or product concept.

For exmple, Apple can be considered a market leader due to its ability to come up with new technology before anyone else does. Moreover, it can also be concluded that Stackelberg Model is realistc as long as we keep in mind its limitations. The model has been increasingly used in many industries across the world to explain the behavior of the firms in oligopoly. However, there are constraints in the simple Stackelberg Model. These limitations and weaknesses are rectified by many alternative approached to the model through combining Stackelberg with other models explaining oligopolistic behavior of the firms.

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• Subject:

• University/College: University of Chicago

• Type of paper: Thesis/Dissertation Chapter

• Date: 24 October 2016

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