Page 202 - DECO101_MICRO_ECONOMICS_ENGLISH

Unit 13: Oligopoly

Notes
Table 13.1

The equilibrium values of Q and Q are found in the following way:
y
x
Q = [1/2–1/8–1/32 ...]OD
x
= [1/2–1/2 (1/4)–1/2(1/4) ...]OD
2
= [1/2–1/2 [(1/4+(1/4) +(1/4) ....]OD
2
3
= 1/2–1/2 [(1/4)/(1–1/4)]OD
= (1/2–1/6)OD
= (1/3)OD
\ Equilibrium Q = (1/3) OD
x
Q = 1/4+1/16+1/64 ....)OD
y
= [(1/4+(1/4) +(1/4) ....]OD
3
2
= [(1/4)/(1–1/4)]OD
= (1/3)OD
Equilibrium Q = (1/3)OD
y
Hence the total equilibrium output of the two duopolists X and Y is (Q + Q ) = 1/3 OD + 1/3
y
x
OD = 2/3 OD.
Since OD = competitive output, the duopoly equilibrium output is 2/3 of competitive output,
and the equilibrium output of each duopolist is = 1/3 of competitive output.
We can write 2/3 as = (2) / (2+1) and 1/3 as = 1/(2+1), where 2 is the number of sellers in
duopoly.

Extending this duopoly case to oligopoly with the number of firms (sellers) to be N, we can say
that according to the Curnot model, the equilibrium output of each of the N oligopolists is = 1/

(N+1) X competitive output. And total equilibrium output of N oligopolistic firms is = N / (N+1)
X competitive output
A Mathematical Version of Cournot’s Model

Assume that the market demand facing the duopolists is:
X = a*+b*P
or

P = a+bX b < 0

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