Cournot’s Model of Duopoly.
An Overview of Cournot’s Model
Cournot’s Model of Duopoly operates under the assumption that two competing firms produce similar products, and they maximize their profits based on the quantity of goods that they produce. Both firms tend to choose the quantity of goods at the same time. An increase in the quantity of goods translates into a decrease in the price (Dobbs 19). The resulting Nash equilibrium is called the Cournot (Nash) equilibrium, where the marginal cost is lower than the equilibrium price but higher than the monopoly price (Png 168). In instances where we drop the assumption of having two firms, a rise in the number of firms translates to a decrease in price to the level of the marginal cost.
Representation of the Cournot’s model of duopoly
Q1 & Q2 are the quantities of goods from both firms
P is the price of goods
D is the demand for goods
C is the marginal cost
Looking at the Cournot’s model, firms determine their output based on what their rival firms are producing. When a firm adjusts its quantity, it expects the rival firm to do the same and covers up for the adjustment, either by reducing or increasing its production. The equilibrium price is equal to the price of firm 1 and equal to the price of firm 2, which is equivalent to the price of the combined goods. Equilibrium prices will be: p 1 = p 2 = P (q 1 + q 2).
The outcome of Cournot’s model is of great significance to the industrial economists. In most cases, the price of goods and the marginal costs will not be equal, and the Pareto efficiency will not be achieved (Wilkinson 322). The difference between the marginal cost and the price of the firm is directly proportional to the market share of the firm and inversely proportional to the market elasticity of demand. In circumstances where the firms have similar goods and cost conditions, the difference between the price and the marginal cost is inversely related to the number of firms.
The Cournot’s model is based on several assumptions, some of which are arbitrary. These include:
- There are only two firms in this model
- The firms produce similar goods where their total output is a representation of the industry output.
- The firms engage in a single period of production and sales like the production of perishable goods like cabbages,
- The market and the inverse market demand are a linear function of price.
- Firms in this model do not cooperate. Hence, there is no collision,
- Both firms have a constant and equal marginal cost equal to c.
- The average cost is also constant and equal to c.
- Firms have excellent market power because their level of production affects the price of goods in the industry.
- The decision variable is the quantity of goods to produce and market.
Conjectural Variation
According to the oligopoly theory, conjectural variation is the belief that firms know how their rivals will behave if they change their output or prices (Png 249). Once a conjecture has been established, firms can as well adjust their output concerning the change exhibited by their competitors. For instance, in the classic Cournot model of oligopoly, there is the assumption that firms consider the output of their rival firms based on their choice of output (Png 250). This assumption is called the Nash conjecture as it is based on the Nash equilibrium concept. An example of such a scenario is when two firms produce the same good; thus, the industry price is determined by taking the output of the two firms. However, in the event of a Bertrand Conjecture, the total output and the price of goods in the industry does not change.
In a Bertrand Conjecture for a given scenario example scenario 1, if firm A records a rise in its output, then it assumes that firm B will reduce its output to create a balance with the already increased output of firm A so that the prices and the output remain constant. In a Bertrand Conjecture, firms believe that their output does not affect the market price. In case of any change in output, firms believe that their rival firms will adjust accordingly to maintain the market price. In extreme conditions of Joint Profit maximising conjecture, firms believe that their rivals will copy any changes they make in their output. This aspect makes the firms behave like a single monopoly supplier (Png 167).
Consistent Conjectures
The Conjecture Variation of the firms determines the slope of the reaction functions. For instance, the standard Cournot model has a conjecture of zero reaction, yet the actual reaction function for a Cournot model is negative. If an economist wants the conjecture and the real slope of the reaction function to be equal, he can introduce a consistency condition that equalises the scenario. An example of such a consistency condition is the Bresnehan’s consistency. However, many economists criticised the concept of consistent conjectures because it was not consistent with the principles of rationality employed by the Game Theory (Wilkinson 317). With time the game theory became popular among economists. As time moved on, it was evident that firms with consistent conjectures recorded higher profit margins and they were able to dominate the industry (Wilkinson 319).
Analysis of Conjectural Variation in Relation to Cournot’s Models
A Cournot model is an example of a conjectural variation model where assumptions are made on the behaviour of the rival firms in terms of their output production. Several criticisms have been brought forth regarding the conjectural variation model. Most of the conjectures held by most firms are arbitrary. They are not practical in real-life scenarios. This arbitrariness made some economists like Stigler to come up with theories like the cartel theory and the game theory to address this issue of arbitrariness (Wilkinson 318). However, this move did not solve the problem because these theories are based on some arbitrary assumptions like firms consider output over prices.
Another inconsistency with conjectures is that some of the occasional interpretations of conjectural variations are unbelievable. They are so exaggerated, and they do not apply in real life. They are based on unreliable beliefs and actions. These interpretations are different from those of the game theory model whose equilibrium is based on well-stipulated strategies that are consistent with the beliefs of the firm (Wilkinson 318). The model is based on a costless production scenario, which is not the case. Firms incur a lot of costs during production, which is always recovered through when they sell and make profits.
Another serious issue of multi-period interpretation of the Cournot model is that the assumptions of the firm become unrealistic. For instance, a firm may confirm that its changes in output have genuinely affected the behaviour of the rivals. However, despite this narrative changing over time, firms may continue holding on to the previous narrative, which does not apply anymore. This scenario is worse if the move by one firm was more of an experiment than the real strategy affirming that the Cournot assumption of no reaction is false (Wilkinson 319). Unfortunately, firms tend not to learn from their rival’s miscalculations in the past and act accordingly.
Most of these models imply that firms tend to maximize their profits in one period which is not true. Firms should engage in actions that will secure their future too and ensure that they get more profits in the coming days. Firms can increase their profits by changing their course of action over time. Another assumption is that the Cournot model is closed- no entry of other firms into the model(Dobbs 119). It is also assumed that the number of firms that were there, in the beginning, will not change even with the structural adjustments that come with the model.
This aspect is not true because, in every industry, firms have a free will of leaving and entering the industry. If firms face competition that will hinder them from making profits, then they will tend to leave the industry. The model can accommodate an infinite number of firms. The model does not also stipulate the length of the adjustment period. The Cournot model tries to depict a perfect situation in the market which is not always the case. Output tends to be greater in this model than in a monopoly model but tends to be lower than perfect competition. On the other hand, prices are lower in a Cournot model than the monopoly model but lower than the perfect competition. These variations do not yield the best reward for most firms making them strategize on different ways to reward themselves.
This model is based on the assumption that each firm’s conjectural variation is equal to zero. This assumption is not reasonable in reality because firms are always out to make profits. Firms will only produce at the level where they make the maximum profit (Wilkinson 317). Whenever forces of demand and supply require that they produce goods at a level where they are not making a good profit, firms will resort to illegal practices like cartels or collusions. When firms in a Cournot’s model resort to forming cartels, then the model changes to an illegal monopoly. Since cartels are illegal, firms engage in collisions so that they can reduce the output which will result in an increase in prices in the industry and the end the firms involved make the maximum profits.
Consequences of Abandoning the Assumptions of the Cournot’s Model
The ideal assumption in a Cournot model is that of “not conjecture” where each firm target to increase their profits, based on the expectation that its own production strategy will not affect the actions of its rivals. However, firms in a Cournot’s model tend to be a monopoly in the half of the industry they are supplying their goods (Png 170). If any of the firms decide to increase their output, then the assumption is that other firms will be expected to reduce their output to get to an equilibrium situation. If firms decide to abandon this assumption then the possible scenarios will include the second firm may decide not to respond to the actions of the first firm.
This may lead to great competition that may force one of the firms out of the market. Forcing one of the firms out of the market will lead to the creation of a monopoly (Png 169). Also, firms may find themselves in a situation where none of the firms changed as expected (Wilkinson 318)). This aspect may cause a situation of a Joint-Profit maximizing conjecture of +1 where the firms end up working like a single monopoly supplier (Png 169). When firms do not act as expected, then they may decide to come together and form cartels which are usually illegal. To go round this aspect, most firms end up colluding so that they can still be in control of the industry prices.
Conclusion
In summary, many economic models have been brought forth to explain the concept of demand and supply of goods. Firms in the industries employ all strategies to ensure they remain in the market including illegal practices like forming cartels and collusions. One of the economic models to explain this scenario is the Cournot’s model. This model is based on several assumptions including; firms in this industry are two, firms compete in quantities and not prices, this model does not factor in the cost of production, firms seek to make the most profits based on the decisions of their competitors, and firms produce only one product.
These assumptions are arbitrary and they do not always yield the expected results. Firms need to strategize how they are going to operate in the industry and maximise on their profits. They can come up with healthy mergers to ensure every firm remain in the industry and they still make their profits. Firms in this industry can adopt other realistic models like the Bertrand model and Stackelberg model and come up with policies that will be beneficial to them (Wilkinson 358). Firms can also choose not to base their actions or production on the actions of their rivals because the expected reaction may not always suffice.
Work Cited.
Dobbs, Ian M. Managerial economics. Oxford University Press, 2000
Png, Ivan. Managerial economics. Routledge, 2013.
Wilkinson, Nick. Managerial economics: a problem-solving approach. Cambridge University Press, 2005.