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Unformatted text preview: can be shown to be unstable based on Cournot's behavioural assumptions. When B enters the market and takes one quarter, A takes B's production as given and thus believes that its own market has shrunk to of its previous size. Accordingly, A reduces their production from of 1 to of , or 3/8. In the next round, B takes A's output reduction as a sign to increase their production to of 5/8 (1 3/8 leaves 5/8), or 5/16. This process continues until A's output falls to 1/3 and B's output increases to 1/3, as we can see graphically below.
P D' D 0 QA = 0.5 QA = 3/8 QA = 11/32 A QB = 0.25 QB = 5/16 and so on... B 1 X 284 And so on. It can be proven that this process will stop when each of the two producers takes one third of the market since only at this point will there be no further reaction by either firm. For clarity, if B is taking 1/3 of the market then A will be happy to produce half of the remaining 2/3, or 1/3 of the market. The final (stable) equilibrium in our development of the simple Cournot Duopoly Model looks like this:
P PM PD A 1/3 QA = 0.3333 TR max B D 1/2 QB = 0.3333 2/3 1 X 0 The two firms A and B jointly sell 2/3 at PD and get a total revenue that is equal to the shaded area. We have noted that this is a stable equilibrium since each producer maximizes profits by taking of what it believes to be the available market. However, at this equilibrium joint profits are not maximized. The duopolists would be better off by colluding and acting as a monopoly, selling at PM and sharing the maximum total revenue at the midpoint of the demand curve. This analysis is FAR too simplistic, but most of its weaknesses can be overcome using more complex models (i.e. where MC 0 and/or is not equal for the two firms, etc.). We will consider an example that develops reaction functions for a more complex model soon, but before we do...we should be quite critical of the above model. Our criticisms would include the following: 1. The assumption of costless production is unrealistic in most, if not all, applications. 2. The model is limited...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.
 Spring '10
 sning
 Economics

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