Cournot, Bertrand and Stackelberg Models of Oligopoly - Essay Example

Critically Discuss the View that the Cournot, Bertrand and Stackelberg Models of Oligopoly are Fundamentally Flawed and are Unable to Explain Recent Events In the Markets and Industries Name: Professor: Course: Date:   Introduction In an oligopoly market a few number of sellers exists. In an oligopoly market, prices are since competition is not stiff. Since there are a few number of vendors in the market, price actions of a competitor influence the prices for the rest of the producers. Competition that arises from the form of market can lead to a number of outcomes or reactions. It is a common trend for trade barriers to be effected in an oligopoly market. In addition, cartels exist in an Oligopoly market. The cartels are responsible for setting the prices. Sometimes they form alliances that are responsible for dictating the prices of goods and services in the market (Hildenbrand, 2010). It is a common practice for firms in an oligopoly market to collude in setting up prices with an intention of mitigating the risks that arises in the particular market. However, most of the alliances formed are outlawed in most countries given that they short-change customers because of the less competition that they have unlike in other markets such a perfect competition environment (Vives, 1999). Models developed by three scholars try to explain the concept of an oligopoly market. The Cournot, Bertrand and Stacklerg models are used to explain the theory of oligopoly. The Game theory is widely applied by three models to analyse the market critically under consideration (Ginevičius and Krivka, 2008). Cournot oligopoly Main assumptions In a Cournot oligopoly, business entities compete on the basis of production levels. They determine the volume of products they are supposed to produce separately within a specified period. The main assumption made in a Cournot oligopoly is that the core business activity of a business entity is profit maximization. It assumes that the decision of determining the volume level is independent. Furthermore, it is assumed that all players in the market are aware of the cost function and the number of players that exist in the market. However, the cost function may vary from one organization to another (Giocoli, 2003). Cournot’s equilibrium The Cournot equilibrium is also referred to as the Nash equilibrium. It indicates a point where the cost function equals the demand function in the model (Yue et al., 2006). Example In an industry, two companies have a cost function of Total Cost(y) =20y.On the other hand, the demand function is represented by p=100-Q. Q-Total output p-prices Nash equilibrium Company A profit=y1 (100-y1-y2)-20y1 =100-2y1-y2-20=0; Thus equilibrium= (80-y2)/2 y2 y1=a1 (y2) 0 y1 Source: Bulletin of Economic Research Company B A1 (y1) = (80-y1) 90 45 y2 45 90 y1 Source: Bulletin of Economic Research Some of the implication of the assumptions made in Cournot model is that the production level in the market is likely to be less compared to that of other markets such as the perfect competition market (Kopel and Löffler, 2008). Additionally, the prices in a Cournot oligopoly are lower compared to those of other markets. Conversely, given the nature of the market, formation of firms are likely to form cartels. Consequently, the model can be transformed to become similar to that of a monopoly market (Day et al., 2002). q2 Reaction function R2 (q1) q1 R1 (q2) Source: Bulletin of Economic Research Cournot models assume firms do not rectify the mistakes that they had done in previous transactions. In addition, the model may not be applicable to other forms of market such as a monopoly (Schipper, 2002) Cournot model has been applied in the telecommunication industry in Colombia. The evidence of a study conducted in the country indicated that majority of organizations that are in the industry according to the theories that were suggested by Cournot, who developed the model. The firms operated like cartels since they have less competition in comparison to those in a perfect market. According to the model the market has a few numbers of sellers who dictate the prices in the market. Consequently, consumers are left with no options but to buy the goods or services are the set prices. Similarly, cell phone users in Columbia have a few mobile service providers. Consumers in the country have few alternatives hence they experience high tariffs (Schipper, 2002). Bertrand’s model The Bertrand model assumes that on a lower side, two firms that produce similar products can form a strategic alliance to succeed in the market (Yang et al., 2002). The two business entities charge uniform prices whereas the expectations of customers are that they will pay affordable prices. Uniform pricing of products slits customers equally between the two firms (Puu, 2011). Bertrand equilibrium The competitive prices in a Cournot equilibrium are also applicable to the Bertrand model. In Bertrand equilibrium, the unit cost for two companies is equivalent to the rates. In such scenarios, no business entity is in a position to make profits. Consequently, if one company fixes a price that is equal to the unit cost than another company does an opposite decision, the market will remain indifferent (Tremblay and Tremblay, 2011). p P (q) Q (p) Source: Bulletin of Economic Research In a Bertrand model, one firm monitors how the competing firm fixes its prices. Firm will set its prices based on what it predicts their rival will set up the prices. Prices for company A Prices for company B Source: Bulletin of Economic Research In the model, the two firms are competing on the basis of prices rather than quantity The main weaknesses associated with the model are that it assumes that firms have the ability to meet the demand in the market (Puu and Sushko, 2002). Bertrand’s equilibrium with differentiated products P2 P1 Source: Bulletin of Economic Research Example The Bertrand model is applicable to Coca-Cola and Pepsi. The two are the largest soda producers in the world that mainly rely on price to set up their prices. Stackelberg’s models - "Price Leadership." The price leadership model is similar to the Cournot model. The firms in this type of model have the opportunity of determining the quantity of output they want to produce. However, the decision of deciding the quantity of output is not made during a given period. Under the model, the assumptions made are: 1. Firms are at liberty to decide their output 2. Firms monitor pricing activity of their rivals 3. Firms have an opportunity to choose their capacity once Leaders demand curve q2 q2 q2 π1 π2 π3 q1 q1 Source: Bulletin of Economic Research Model with equations Equation Assume MC=30 P=100-0.5Qd Qd=market quantity demand P=Prices 1.The total quantity demanded of two companies Qd=q1+q2 When q1 and q2 are substituted in the price function P=100-0.5(q1+q2)=100-0.5q1-0.5q2 Prediction of reaction of firms of one firm when the other changes prices Total Revenue2=q2XP=(100-0.5q1-0.5q2)Xq2=100q2-0.5q1q2-0.5q22 In a Stackelberg model, the unit cost of firm 2 is equal to the total revenue Maximum profit is attained when MR=MC MR2=100-0.5q1-q2=30=MC2 100-30-0.5q1=80-0.5q1=Quantity demanded The total revenue for company 1 Total Revenue1=PXq1=(70-0.25q1)q1=70q1-0.25q12 MR1=70-0.5q1=10=MC1 70-10=60=q1 Q2=70-0.5q1=70-0.5(60)=40 Weaknesses The Stackelberg has a number of weaknesses. For example, it assumes that all industry players are rational. However, that may not be the case. Sometimes a market leader may make any irrational pricing decision momentarily to lure competitors to follow suit. The decision might have been made without any tangible reason because a market leader may want to appear to be unique in terms of their prices (Yao and Hobbs, 2006). In addition, the model assumes that the market leaders have symmetrical information about the market. The assumption is impractical in a real business world and can only be taken as a matter of theory. Similar assumption exists in the perfect market. However, practically, there is no single market that can have complete information. Many markets are characterised by informational asymmetry (Colciago and Etro, 2010). Another shortcoming that the model has is that market leaders are aware that their rivals do incapable of coming up with stiff competition in the near future. However, in as much a firm that is an industry leader may be employing certain strategies that are uncommon to their followers, some of the rival firms may improve their game plans with time (Lo and Kiang, 2005).The premise that suggests followers may not be in a position to counter strategies in the future is unfounded. In fact; some followers are very proactive and may investigate some of the game plans that the market leaders are using to succeed in the market (Poddar and Sasaki, 2002). The characteristic feature of the three types of market is that all assume that the cost function is known to all firms. Secondly, it also assumed that all companies in the market produce similar products. Additionally, all the three market believe that industry players rarely meet to make agreements. Finally, all the three markets strive to make profits (Dastidar, 2004). Conclusion The three Cournot, Stackelberg and Bertrands model, are important concepts that were developed by the economist. The three concepts try to explain the behaviour of firms in an oligopoly market. In a market where there is a few number of sellers, firms sometimes behave as if they are monopolies (Yu et al., 2000). They decide on the volume of products that they produce and the prices. In such a market, consumers are the ones that suffer given the fact that they have limited options. Unlike other markets that offers customers a variety of choices such in perfect competition, in an oligopoly market, the customers have limited alternatives (Ledvina, and Sircar, 2011).On the other hand, and producers sometimes have an opportunity of forming cartels and fix desired prices. However, the practice is illegal in most countries. Despite the immense contribution that were made by the developers of the models, the models are fundamentally flawed and are unable to explain recent events in the markets and industry more especially during the recent global financial meltdown that the whole world experienced (Breitmoser, 2012). Reference List Breitmoser, Y. (2012). On the endogeneity of Cournot, Bertrand, and Stackelberg competition in oligopolies. International Journal of Industrial Organization, 30(1), 16-29. Colciago, A., and Etro, F. (2010). Real business cycles with Cournot competition and endogenous entry. Journal of Macroeconomics, 32(4), 1101-1117. Dastidar, K. G. (2004). On Stackelberg games in a homogeneous product market. European Economic Review, 48(3), 549-562. Day, C. J., Hobbs, B. F., and Pang, J. S. (2002). Oligopolistic competition in power networks: a conjectured supply function approach. Power Systems, IEEE Transactions on, 17(3), 597-607. Ginevičius, R., and Krivka, A. (2008). 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Puu, T. (2011). Oligopoly old ends - new means. Berlin Heidelberg: Springer. Schipper, B. C. (2002). Imitators and optimizers in symmetric firm Cournot oligopoly. Bonn Econ Discussion Papers, (29). Tremblay, C. H., and Tremblay, V. J. (2011). The Cournot–Bertrand model and the degree of product differentiation. Economics Letters, 111(3), 233-235. Vives, X. (1999). Oligopoly pricing: old ideas and new tools. Cambridge, Mass: MIT Press. Yang, C. W., Hwang, M. J., and Sohng, S. N. (2002). The Cournot competition in the spatial equilibrium model. Energy Economics, 24(2), 139-154. Yao, J., Oren, S. S., and Hobbs, B. F. (2006). A hybrid Bertrand-Cournot model of electricity markets with multiple sub networks. Berkley, University of California. Yu, Z., Sparrow, F. T., Morin, T. L., and Nderitu, G. (2000). A stackelberg price leadership model with application to deregulated electricity markets. In Power Engineering Society Winter Meeting, 2000. IEEE (Vol. 3, pp. 1814-1819). IEEE. Yue, X., Mukhopadhyay, S. K., and Zhu, X. (2006). A Bertrand model of pricing of complementary goods under information asymmetry. Journal of Business Research, 59(10), 1182-1192. Read More