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In pg. 509, of Hal Varian's Intermediate Microeconomics Ch. 27, writer discusses the Cournot equilibrium.

In the figure, the reaction curve of firm 1 f1(y2) was steeper than firm 2 f2(y1).

When we started from the point (y1t, y2t), we were able to reach the stable equilibrium. But what if f2(y1) was steeper than f1(y2)? I cannot find any adjustment process. Can such condition be viable? If not, then why?![Adjustment process when f1(y2) was steeper than f2(y1)]1

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  • $\begingroup$ I don't understand the adjustment process as explained by Varian. could you help me? $\endgroup$ – user7967 Apr 15 '16 at 10:40
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The trick is to draw the whole reaction function—including the part that coincides with the axis. Hopefully these figures make it clear:

enter image description here

enter image description here

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  • $\begingroup$ If we assume that both are producing positive outputs and f2(y1) is steeper than f1(y2), then this implies that the quantity leader, who chooses his/her output choice first, will be able to have the whole market? Should there be a relationship between producer 1 and 2, so that such situations shouldn't occur? Or, are these situations anomaly of the model? Is the model correct or I am missing some assumption? $\endgroup$ – Dhruv Goel Apr 10 '15 at 15:48
  • $\begingroup$ @DhruvGoel You are reading the model correctly. The thing to bear in mind is that the slope of the reaction function embodies a bunch of assumptions about the nature of the market. For example, if firms have large economies of scale (a "natural monopoly") then it is intuitive that a small firm will have higher costs that a big one and the small firm will tend to shrink relative to the large firm. In other words, the slopes of the reaction functions are an empirical consequence of conditions in the industry. It could also be true that the curves are non-linear and cross several times. $\endgroup$ – Ubiquitous Apr 10 '15 at 16:07

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