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.

How to get the firm 1's reaction curve.
For given firm 2's quantity (q₂), you have to find the firm 1's best Response quantity (q₁=r₁(q₂)) in the sense that it maximizes her or his profit. In the figure, the firm 1's profit surface is truncated by the firm 2's quantity plane that goes through (0,q₂) and is perpendicular to the q₁-q₂ plane.
You can easily find out the point (circled BLACK point in the figure) that have a highest profit.
We often call this point as the best Response for the firm 1.
The locus of the best Response is the firm 1's reaction curve (q₁=r₁(q₂)) in the 3-D graphics.
Here is another showcase of the firm 1's reaction curve.
Here is a showcase of the firm 2's reaction curve.
Here is another showcase of the firm 2's reaction curve.
The well known reaction curve in the textbook is obtained by projection of 3-D graphics into plane.
Namely, it is the bird's-eye view of the figure.
Here is a collection of figures including two firms' reaction planes and the bird's-eye view of the figures.
Here is another collection of figures including two firms' reaction curves and the bird's-eye view of the 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, 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.