Question

In terms of expected output, price, consumer surplus, profits and societal welfare, compare the standard Cournot-Nash equilibrium (for the case of 2 firms), the monopoly equilibrium and the perfectly competitive equilibrium. What would happen to your results as the number of Cournot competitors increase? Explain your answer.

Would really appreciate help with this thanks. Its worth 50 marks so warrants a reasonably long answer.

Answer 1

Nash equilibrium is the outcome outcome where two players believe that they are doing the best they can, given the action of the other player. A game is said to be in equilibrium if neither player has an incentive to change his or her choice, unless the other player changes it.

Cournot competition is a model of imperfect competition in which two firms which has identical cost compete where there are homogeneous products in a static setting. The theory was developed by Antoine Cournot.

Cournot invented the concept of game theory almost 100 years before Nash when he looked at the case of how firms would behave in the situation of a duopoly. There are two firms operating in a limited market and their market production function is: P (Q) =a-bQ, where Q=q1+q2 for two firms.

Both companies look to maximize benefits. These benefits are derived from both maximum sales volume and higher prices leading to higher profitability. But increasing prices could damage revenue of the firm by losing market share but here Cournot suggested an approach which maximizes both market share and profitability by defining an optimum price level. This price will be the same for both the firms as otherwise the one with the lower price shall obtain full market share, which makes this Nash equilibrium, also known as the Cournot-Nash equilibrium model.

Now, for socially efficient levels of output that the two firms should produce and the price at which that output should be sold, it can be explained with the help of the following diagram:

In the diagram the marginal cost to the firm is denoted by the social marginal cost which includes all the social costs of producing the product which implies that there are no production externalities. And the demand curve is given by the DD in the Figure, which gives the amount that the public is willing to pay assuming that there are no externalities in consumption for additional units of output as they are received, also this amount equals to the value of other goods the public is willing to give up in order to obtain the last unit of the good consumed. So the demand curve here is considered the marginal social return. Equating marginal social cost with marginal social return leads to the optimum output at point e with the price of OP.

Social welfare does not change with new entry, but new entry would shift the surplus from producers to consumers. The equilibrium price falls with new entry, and therefore potential competition can limit market power.

Now, in the situation where Cournot competitors increases, which means that there are more than two firms in the market equilibrium of the game gets closer to the perfect competition outcome