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 2's profit surface is colored with GREEN.

How to get the firm 2's reaction curve.
For given firm 1's output (q₁), firm 2 wishes to produce output (q₂) which maximizes his or her profit. To help your understanding, we show the plane colored pink which is perpendicular to the plane including the given firm 1's output level. In this plane, the circled point shows the best Response for the firm 2. Namely, the firm 2 attains the maximum profit at the point and the locus of these points show the firm 2's reaction curve in 3-dimensional phase.
Here is another showcase of the firm 2's reaction curve.

Here is the firm 1'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 bird's-eye view of the figure.
Here is a collection of figures including two firms' reaction curves and the bird's-eye view of figures.
Here is a collection of figures including the firm 2's profit surface, reaction curve, and reactiion plane.
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.