Bertrand and Cournot Competition Comparison

Topics: Game theory, Economics, Perfect competition Pages: 7 (1691 words) Published: August 25, 2013
Industrial Economics: Market Structure Individual Assignment 1

Student Name: Yibo, Shen Student ID: 1051698 Question Number: 1

Within the realm of industrial economics, a central focus is on equilibrium in oligopoly models, and the questions arise of how the firms would find the equilibrium and whether they will choose it. The efforts of this essay are devoted to a discussion of Cournot and Bertrand models of competition, two fundamental single-period models that form the basis for multi-period models (Friedman, 1977). Firstly the essay will give an introduction to the properties of the Cournot and Bertrand models of competition and examine their implications to the relationship between structure and performance. Then it will theoretically address the question that when and how we can choose either of these two models to better describe a market, and empirically distinguish between two models by giving example industries that behave according to each. Finally the essay will draw a conclusion.

Oligopoly theory abstracts from the complexity of real-life corporate strategy, and concentrates on just one or two strategic variables (Davies et al, 1991). Cournot (1838) takes the view tat the firm’s strategic variable is quatity or output. In contrast, Bertrand (1883) takes the viewe that the firm’s basic strategic variable is price. In order to capture the distinction between the Cournot and Bertrand framework, we will consider the simplest case of homogeneous products. Also due to word limitation, product differentation is out of scope of this essay.

In Cournot’s model of competition, each firm has a cost function, the industry has a demand function, firms compete with others just once and they make their production decisions simultaneously, and it is impossible for any new firm to enter or old firm to leave the industry. Most important, the only decision each firm is able to make is the choice of its output level (Friedman, 1977). being 𝑄𝑄 = ∑𝑛𝑛=1 𝑞𝑞𝑞𝑞. Also, we make the simplest possible assumption about demand and costs: 𝑞𝑞 Industry demand function: 𝑃𝑃 = 1 − ∑𝑛𝑛 𝑞𝑞𝑞𝑞 (where 𝑃𝑃 is the market price) (eq. 1) 𝑞𝑞=1 1

Assume there are n firms i=1, 2, …, n, where firm i produces output qi, with industry output

Firm’s cost function:

𝐶𝐶 (𝑞𝑞𝑞𝑞 ) = 𝑐𝑐𝑞𝑞 𝑞𝑞𝑞𝑞 (where 𝑐𝑐𝑞𝑞 is marginal cost of firm 𝑞𝑞) (eq.2) Given eq.1 and eq.2, we can derive firm i’s profit as a function of the output chosen: = 𝑞𝑞𝑞𝑞 �1 − � 𝑞𝑞𝑞𝑞 � − 𝑐𝑐𝑞𝑞 𝑞𝑞𝑞𝑞 𝑗𝑗 ≠𝑞𝑞 𝑗𝑗 =1 𝑛𝑛

𝜋𝜋𝑞𝑞 = 𝑃𝑃 𝑞𝑞𝑞𝑞 − 𝑐𝑐𝑞𝑞 𝑞𝑞𝑞𝑞

A Nash equilibrium for the Cournot competition is a bundle of strategies, qc and qc , such i j≠i that none of the firms can increase its profit by unilaterally deviating, given the Nash equilibrium output of its rivals (Church and Ware, 2000). This can be found using best reply functions, which gives firm i’s profit-maximising choice of output for any output produced by the other firms. The first-order condition for maximising with respect to qi is: 𝑗𝑗 ≠𝑞𝑞

= 𝑞𝑞𝑞𝑞 − 𝑞𝑞𝑞𝑞 2 − 𝑞𝑞𝑞𝑞 � 𝑞𝑞𝑗𝑗 − 𝑐𝑐𝑞𝑞 𝑞𝑞𝑞𝑞 (eq. 3)

𝜕𝜕𝜋𝜋𝑞𝑞 = 1 − � 𝑞𝑞𝑗𝑗 − 2𝑞𝑞𝑞𝑞 − 𝑐𝑐𝑞𝑞 = 0 𝜕𝜕𝑞𝑞𝑞𝑞 𝑞𝑞𝑞𝑞 =

1 − ∑𝑗𝑗 ≠𝑞𝑞 𝑞𝑞𝑗𝑗 − 𝑐𝑐𝑞𝑞 2 Which is the best reply function for firm i. This...
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