Given this market demand curve and cost structure, we want to find the reaction curve for Firm
1. In the Cournot model, we assume
Q
i
is fixed for all firms
i
not equal to 1. Firm 1's reaction
curve will satisfy its profit maximizing condition,
MR
1 =
MC
1 . In order to find Firm 1's
marginal revenue, we first determine its total revenue, which can be described as follows
Total Revenue = P * Q1 = (100  Q) * Q1
= (100  (Q1 + Q2 +.
..+ Qn)) * Q1
= 100 * Q1  Q1 ^ 2  (Q2 +.
..+ Qn)* Q1
The marginal revenue is simply the first derivative of the total revenue with respect to
Q
1
(recall
that we assume
Q
i
for
i
not equal to 1 is fixed). The marginal revenue for firm 1 is thus:
MR1 = 100  2 * Q1  (Q2 +.
..+ Qn)
Imposing the profit maximizing condition of
MR
=
MC
, we conclude that Firm 1's reaction
curve is:
100  2 * Q1*  (Q2 +.
..+ Qn) = 10
=> Q1* = 45  (Q2 +.
..+ Qn)/2
Q
1
*
is Firm 1's optimal choice of output for all choices of
Q
2
to
Q
n
. We can perform analogous
analysis for Firms 2 through
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This note was uploaded on 12/13/2011 for the course ECO 1320 taught by Professor Staff during the Fall '11 term at Texas State.
 Fall '11
 staff

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