Page 201 - DECO101_MICRO_ECONOMICS_ENGLISH

Micro Economics

Notes Hence, demand or output at zero price shows the competitive output.

∴ OD is competitive output.
Let the two duopolists be denoted by X and Y. Let Q and Q be their respective outputs.
x y

Suppose seller X enters the market first, followed by seller Y.
We analyse the behaviour of X and Y in stages.
In stage I, seller X acts as a monopolist. He faces demand curve CD so that CA is his marginal
revenue curve which must be situated halfway between the Y-axis and demand curve. CA cuts
OD at A, such that OA = AD = 1/2 OD. At output OA, marginal revenue = marginal cost = zero

and profits are at their maximum. Seller X charges price P and makes profi t = OARP .
1 1
Thus at stage I, we fi nd Q = 1/2 OD.
x
Now seller Y enters with the assumption that X will keep his output constant at 1/2 OD. In other
words, Y considers his demand curve to be RD which shows the leftover demand after X has
supplied OA output.

Hence at Stage I, seller Y finds his demand curve to be RD with RB as his marginal
revenue curve. RB cuts the X-axis at B. For seller Y, marginal revenue = marginal
cost = zero at output AB. Thus profit maximising output of Y at Stage I, is AB = 1/2

AD = 1/2 (1/2 OD) = 1/4 OD.
Thus in Stage I, Q = OA = 1/2 OD
x
and Q = AB = 1/2 AD = 1/2 (1/2 OD) = 1/4 OD
y
Seller Y charges price BT = OP and makes a maximum profi t = ABTK.
2
However, since X and Y are selling homogenous products, the price will decrease from OP to OP
2

for both of them. Profits of X will thus decline to OAKP .
2
Assuming seller Y will keep his output Q constant at 1/4 OD, seller X will have to reduce his
y
output so as to raise the price and his profi t.
In stage II, Seller X will produce profit maximising output on the basis of the demand leftover

after assuming Q to be = 1/4 OD. Therefore, in Stage II, X will produce output Q = 1/2
y
x
(OD – AB) = (OD – BD) and BD is 1/2 AD = 1/4 OD.

At stage II, Y decides his profit maximising output assuming Q will remain constant at
x
(1/2 – 1/8) OD. Hence, Q at Stage II will be = 1/2 [OD – (1/2 – 1/8) OD].
y
That is, Q = 1/2 (OD – 1/2 OD + 1/8 OD)
y
= (1/2 – 1/4 + 1/16) OD = (1/4 + 1/6) OD.
We can carry on this reasoning further, to Stage III, Stage IV, etc., to fi nd Q and Q at each
y
x
stage.

In short, we find that at each stage, seller X will decrease his output in such a way that it will be
equal to one-half of OD minus the output of Y in the previous stage (which is initially zero). On
the other hand, Y will increase his output Q at each stage so that it will be equal to one-half of
y
the difference between OD and Q at the same stage.
x
The stagewise changes in Q and Q are summarised in Table 13.1.
x y
We find that at each stage, Q declines by smaller and smaller quantities. In contrast, Q increases

x
y
by smaller and smaller amounts at each stage. Both Q and Q will, therefore, arrive at some fi nite
x
y
values which will give the equilibrium values of Q and Q .
x y
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