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 with PINK.

You can see that the sea(profit) level denoted by the blue plane is coming up to and covering the first monument (Cournot equilibrium) and then the second monument (Stackelberg equilibrium).
The Cournot Equilibrium denoted by the black circled point in the figures is flooded at the 64 profit level, while the Stackelberg Equilibrium denoted by the blue circled point is covered by the 72 profit level.

Here is a showcase of the firm 1's reaction curve. You can assure the associate quantities pair (r₁(q₂),q₂).
Here is a showcase of firm 1's reaction curve.
Here is a showcase of firm 2's reaction curve, too.
The well-known reaction curve in the textbook is obtained by projection of 3-D graphics into plane. Namely, it is the looked down figure.
Here is a collection of figures including two firms' reaction curves and 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, 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.