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Lecture18-1

Lecture18-1 - Lecture#18 Recall from last class the Cournot...

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Lecture #18 Recall from last class, the Cournot Duopoly Model that we set up. You were asked to think about the stability of the situation that we described…to refresh your memory, here’s the graph. P This situation, where A takes half of the market and B takes one quarter of the market, can be shown to be unstable based on Cournot’s D’ behavioural assumptions. When B enters the market and takes one quarter, A takes B’s production as X MR A MR B A B D 0 1 takes B s production as given and thus believes that its own market has shrunk to ¾ of its previous size. Accordingly, A reduces their Q A = 0.5 Q B = 0.25 Accordingly, A reduces their production from ½ of 1 to ½ of ¾, or 3/8. In the next round, B takes A’s output reduction as a sign to increase their production to ½ 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 on the next slide.

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P And so on. It can be proven that this process will stop when each of the two producers takes one third of D’ 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 X A B D 0 1 Q A = 0.5 Q B = 0.25 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. Q A = 3/8 Q B = 5/16 Q A = 11/32 and so on… The final (stable) equilibrium in our development of the simple Cournot Duopoly Model looks like this: P The two firms A and B jointly sell 2/3 at P and TR max D 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 ½ of what it believes to be the P M P D A B profits by taking ½ 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 ½ X 1/2 2/3 D 0 1 Q A = 0.3333 Q B = 0.3333 1/3 by colluding and acting as a monopoly, selling ½ at P M 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 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 in scope because it does not consider the possibility of new firms entering the industry firms entering the industry.

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Lecture18-1 - Lecture#18 Recall from last class the Cournot...

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