UNCWilmington
ECN321
Department of Economics and Finance
Dr. Chris Dumas
Cournot Model of Duopoly
Example Problem:
Suppose there are only two producers of product Q, firm 1 and firm 2.
The producers make
production decisions at the same time / simultaneously (or, equivalently, they are myopic).
Firm
1 produces Q
1
units of output at a cost of $c
1
per unit.
Firm 2 produces Q
2
units of output at a
cost of $c
2
per unit.
Consumer demand for product Q is given by P
Q
= a  bQ, where a and b are
constants, and Q = Q
1
+Q
2
is total quantity sold to consumers.
Determine each firm's reaction
function, then determine each firm's profitmaximizing output level Q
1
*
and Q
2
*
(the superscript
"*" is used to denote the "Cournot model solution").
Next, determine the resulting market price,
P
Q
*
.
Finally, determine each firm's profit level (Profit
1
*
and Profit
2
*
).
Solution:
Let's solve firm 1's problem first.
Firm 1 wants to maximize profit, taking into account his per
unit cost of production, c, the level of demand in the market P
Q
= a  bQ, and the fact that the total
supply on the market will be the total of firm 1's production plus firm 2's production, Q = Q
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '08
 Dumas
 Microeconomics, Monopoly

Click to edit the document details