Question

Choose one of the four oligopoly models in Baye, and discuss an example

Answer 1

ANSWER :-

☆There is no single model describing the operation of an oligopolistic market. The variety and complexity of the models exist because you can have two to 10 firms competing on the basis of price, quantity, technological innovations, marketing, and reputation. However, there are a series of simplified models that attempt to describe market behavior by considering certain circumstances.

☆ Some of the better -known models are :

a). The dominant firm model

b). The Cournot-Nash model

c). The Bertrand model

d). The kinked demand model.

b) Cournot-Nash model :

☆ The Cournot-Nash model which is one of the four oligopoly models in baye and discussed with example .

● The Cournot–Nash model is the simplest oligopoly model. The model assumes that there are two "equally positioned firms"; the firms compete on the basis of quantity rather than price and each firm makes an "output of decision assuming that the other firm's behavior is fixed.

● The market demand curve is assumed to be linear and marginal costs are constant. To find the Cournot–Nash equilibrium one determines how each firm reacts to a change in the output of the other firm. The path to equilibrium is a series of actions and reactions. The pattern continues until a point is reached where neither firm desires "to change what it is doing, given how it believes the other firm will react to any change.

● The equilibrium is the intersection of the two firm's reaction functions. The reaction function shows how one firm reacts to the quantity choice of the other firm.

☆ For Example:

● Assume that the firm 1's demand function is P = (M − Q2) − Q1 where Q2 is the quantity produced by the other firm and Q1 is the amount produced by firm 1,[12] and M=60 is the market. Assume that marginal cost is CM=12. Firm 1 wants to know its maximizing quantity and price. Firm 1 begins the process by following the profit maximization rule of equating marginal revenue to marginal costs.

Firm 1's total revenue function :

●is RT = Q1 P = Q1(M − Q2 − Q1) = MQ1 − Q1 Q2 − Q12.

The marginal revenue function is :

● {\displaystyle R_{M}={\frac {\partial R_{T}}{\partial Q_{1}}}=M-Q_{2}-2Q_{1}}.

Note:

● RM = CM

● M − Q2 − 2Q1 = CM

● 2Q1 = (M − CM) − Q2

● Q1 = (M − CM)/2 − Q2/2 = 24 − 0.5 Q2 [1.1]

● Q2 = 2(M − CM) − 2Q1 = 96 − 2 Q1 [1.2]

● Equation 1.1 is the reaction function for firm 1. ● Equation 1.2 is the reaction function for firm 2.

● To determine the Cournot–Nash equilibrium you can solve the equations simultaneously. The equilibrium quantities can also be determined graphically.

● The equilibrium solution would be at the intersection of the two reaction functions. Note that if you graph the functions the axes represent quantities.The reaction functions are not necessarily symmetric.

● The firms may face differing cost functions in which case the reaction functions would not be identical nor would the equilibrium quantities.

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