You can imagine the duopoly model in which two firms compete each other strategically in quantity-setting.
Each firm's profit depends on both firms' quantities (q1 and q2).
You can see the 3-D graphics to show these relations.

These figures are produced by Mathematica 4.0.
The firm 1's profit surface is colored according to the profit levels ,i.e., lower class of profit with BLUE, middle class of profit with RED,and upper class of profit with YELLOW.
The firm 2's profit surface is colored with GREEN.

The figure shows both firms' profit surfaces truncated by profit level at 64.
Firm 1's reaction curve is marked by RED bold line.
Firm 2's reaction curve is marke by BLUE bold line.
You can see both firms' reaction curves intersect at profit level of 64 (circled BLACK point).
We call it the Cournot Equilibrium.
The tide (profit level) is out at the start. But the tide comes up gradually to the profit level at 64. What happens in the Oligopoly Island? Is the Cournot Equilibrium point in the sea?

Here is a showcase of the firm 1's reaction curve. You can assure the associated quantity level in the figure.
Here is another showcase of the firm 1's reaction curve.
Here is another showcase of the firm 1's reaction curve.
Here is a showcase of the firm 2's reaction curve.
The well known reaction curve in the textbook is obtained by projection of the 3-D graphics into plane. Namely, it is the looked down figure.
Here is a collection of figures including two firms' reaction curves and the looked down figures.

Parameters of market demand curve and both firms' cost functions affect shapes of 3-D graphics, directly.
JavaScript1.1 can be used for changing figures for animation.

Masaru UZAWA,,/A> Professor
Otaru University of Commerce Department of Economics
CAL(Computer Assisted Learning) in Economics programs for Windows 95/98

Tel & FAX: +81-134-27-5310
uzawa@res.otaru-uc.ac.jp
Please send me your comments on my page.

Acknowlegement:
I thank the following software group and books: Wolfram Research, Inc. for MATHEMATICA 3.0 and 4.0
OKAZAKI, HASEGAWA, and HANBA, Handbook of HTML & JavaScript,(in Japanese),(Shuwa System, 1997)
MIYASAKA, JavaScript Handbook,(in Japanese),(Softbank, 1998)

Copyright © 2001 by Uzawa, Otaru University or Commerce.