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# Cournot and Bertrand Models of Duopoly

Document Type:Coursework

Subject Area:Economics

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Two of the most popular and effective models in this category are the Cournot’s Duopoly Model and the Bertrand’s Duopoly Model. This essay will use these models to help differentiate actions as strategic complements and substitutes based on these two models. It will also explore the strengths and weaknesses of these models as well as their alternatives. Defining Strategic Complements and Substitutes Strategic complements and substitutes are common concepts in economics and the game theory. Actions of two firms are called strategic complements if they reinforce each other and strategic substitutes if they offset each other (Bulow et al. The firm assumes that firm A will not change its price or output since it is already making maximum profits.

Firm B sets its prices at P1 in a bid to make maximum profits, but it is only capable of supplying half of the available market – that is, ½ of ½, hence a quarter of the market, which is indicated by QN. As such, firm B’s maximum revenue is QRPN. Firm B’s entry into the market does not go unnoticed as it causes the price to fall to P1 from P2. Consequently, firm A’s profits fall from OP2PQ to OP1PQ, and this prompts it to adjust its price and output so as to adapt to the new changes. This reactionary process will continue until both firms get to an equilibrium whereby they can no longer decrease or increase supply without disrupting the market – eventually, both firms will supply 1/3 each of the market with the remaining 1/3 left up for grabs.

Actions as Strategic Complements According to Bertrand’s Duopoly Model Bertrand’s duopoly model considers prices to be strategic complements in a duopoly market (Vives, 1984) – that is, one firm’s decision to cut its prices in a bid to maximize profits will prompt the other firm to cut its prices too. Price war is one of the best and most popular strategies for competing companies producing closely similar and substitutable products and services. In response to price cuts, the other firms will always react by reducing their prices as customers will naturally go for the firm with the lowest price in a bid to save some money. This concept is explained in details in the graph below. this equilibrium price, however, doesn’t have to be the original price.

Limitations of Bertrand’s Duopoly Model and Viable Alternatives Bertrand’s duopoly model may be effective in understanding some concepts about price wars in a duopoly or oligopoly market, it comes with certain shortcomings that compromise its integrity. Following is a brief overview of the limitations of this model and viable alternatives to this model. Price Wars are Illogical In a duopoly market, and following the assumptions of Bertrand’s model, the market demand would exceed market supply. In such an atmosphere, companies would ideally increase the prices of their products and services instead of decreasing them. However, this model still holds this assumption dearly, thus making it self-contradictory. One or Two Firms Cannot Meet All Demand Duopoly markets do exist, but they are not capable of meeting all demand and, hence, do not last long unless in cases where they are reinforced by the law.

However, Bertrand’s duopoly model assumes that both firms are capable of meeting the market’s entire demand – it also assumes that the firm that wins the price war will get all the customers and meet all demand. This, however, is not true. Bertrand Duopoly Model’s Alternative: Bertrand-Edgeworth Model The Bertrand-Edgeworth model was developed by Francis Ysidro Edgeworth in response to the limitations of the Bertrand’s duopoly model. Eventually, prices will slowly rise again as both firms seek to increase their profits. Limitations of Cournot’s Duopoly Model and Viable Alternatives The Cournot’s duopoly model has been extremely useful in helping economists understand competition in duopoly markets based on output. However, it could not have taken all factors into consideration and, as such, has several shortcomings that have been widely criticized over the decades.