# ECMC41 Week 4 Oligopoly

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1 ECMC41 Week 4 Oligopoly Oligopoly An industry with a small number of firms (2-10?), where the firms make separate strategic decisions to maximize profit, but are aware of each other s actions in forming their strategies. Will compare to monopoly and perfect competition Many models of oligopoly: Cournot duopoly Cournot with n firms Stackelberg duopoly Bertrand Single-period games Multiple-period games

2 Cournot, Stackelberg and Bertrand developed a long time ago Modern oligopoly theory is game theory, and these older models can be expressed and analyzed as games. Cournot Cournot n Stackelberg Bertrand Joint monopoly Competitive (contestable?) Number of firms 2 Any # or more Many prob. Entry? No No No No No Yes Homogeneous product? Yes Yes Yes Yes Yes Yes Firm chooses? Output Output Output Price Output and price Output Simultaneous moves? Single period or multiple periods Yes Yes No Yes yes Single Single Single Single Single Single

3 Cournot duopoly Demand: Q = P Demand: P = Q q 1 + q 2 = Q Demand: P = q q 2 Firms do not communicate. Must make assumptions about their share of market in order to make strategic (i.e., profitmaximizing) decision about output. Each assumes the other s current output will remain constant, and each can therefore calculate its residual demand curve.

4 Graphically, Price q 2 Residual Demand Curve Industry Demand Curve q 2 Quantity If we start with P = q q 2

5 Then, the residual demand curve for Firm 1 (treating q2 as a constant) is : P = ( q 2 ) -.001q 1 So the expected MR 1 = ( q 2 ) -.002q 1 If TC = 0.28q, then MC = AC = 0.28 So MR = MC ( q 2 ) -.002q 1 = q 1 = q 2 q 1 = q 2 This is the profit-maximizing q In other words, the profit-maximizing value of q 1 is a function of whatever amount Firm 2 has decided to produce. We call this the reaction function, or bestresponse function for Firm 1

6 We assume that Firm 2 has the same beliefs, so Its residual demand curve is : P = ( q 1 ) -.001q 2 So the expected MR 2 = ( q 1 ) -.002q 2 If TC = 0.28q, then MC = AC = 0.28 So MR = MC ( q 1 ) -.002q 2 = q 2 = q 1 q 2 = q 1. We call this the reaction function, or bestresponse function for Firm 2

7 Solve for equilibrium by substituting one reaction function into the other (to find the values of q at which both are satisfied) Nash equilibrium q 1 = ( q 1 ) q 1 = q 1.75q 1 = 180 q 1 = 240 By a similar logic, q 2 = 240. This means that output in this Cournot industry is 480 units. Substituting into the demand function, we find that P = (480) = = \$0.52. Each firm earns profit of.52 x 240 (.28 x 240) = \$57.60 or profit of \$ as a whole. Consumer Surplus will be (1-.52) x 480/2 = \$115.20

8 Deadweight Loss (DWL) requires a comparison to results when P = MC (or Q =.28, so Q = 720 and P =.28). So DWL for Cournot is ( ) x ( )/2 = \$28.80 It is easy and useful to do a comparison with Joint Monopoly and Perfect Competition. Joint monopoly would be achieved if two producers colluded to act like a single monopolist Monopoly: P = Q MR = Q MC = Q =.28 or.72 =.002Q, so Q = 360 (split between two producers) and P = (360) = \$0.64

9 Profit would be.64 x 360 (.28 x 360) = \$ (split in two) Consumer Surplus = (1 -.64) x 360/2 = \$64.80 DWL = ( ) x ( )/2 = \$64.80

10 Competitive result (from calculations above) is at Q = 720, and P =.28 Profit = (.28 x 720) (.28 x 720) = \$0 Consumer Surplus = (1 -.28) x 720/2 = \$ DWL = \$0 Q P CS DWL Cournot Duopoly 480 \$0.52 \$ \$ \$28.80 Monopoly 360 \$0.64 \$ \$64.80 \$64.80 P. C. 720 \$0.28 \$0.00 \$ \$0.00

11 We could look at the output decision in a different framework game theory (a simultaneous single-period game). This is useful because it is not at all clear why every Cournot duopoly doesn t become a joint monopoly. Game theory will help us to understand. Game Theory Players Strategies Payoffs Rules of the game

12 Q 2 = 180 Q 2 = 240 Q 1 = 180 \$64.80, \$64.80 Q 1 = 240 \$72.00, \$54.00 \$54.00, \$72.00 \$57.60, \$57.60 What strategic move would Firm 1 make, if it can t negotiate with Firm 2? Why? What about Firm 2?

13 What is the equilibrium? Nash equilibrium concept: A pair of strategies is an equilibrium if neither player can make him/herself better off by changing strategy, given the strategy of the other player. i.e. neither player can make him/herself better off by changing the things he/she can control.

14 This is a type of game called the prisoners dilemma a very famous type of game. The players pursue their own self-interest. But, as a result, they can t reach the collectively-best payoff. It requires trust to achieve and maintain the joint-monopoly result (each produces 180). Either player can do better by cheating on the joint monopoly agreement. Helps us to understand why it is difficult to keep cartels together! (But things may be easier in a multi-period game). Also (to change the subject), why it is difficult to reduce pollution by exclusively voluntary measures!

15 Stackelberg leader-follower model Tweaking the Cournot model to see how a change in the behaviour of firms changes the equilibrium. Cournot: Each firm assumes the other will keep output constant. Choose best-response strategy. Stackelberg: One firm (the leader) assumes the other firm (the follower) will keep its best-response strategy constant, and uses that to manipulate the other firm. A more intelligent strategy. So, Firm 2 (the follower) follows the Cournot assumptions, and has a reaction function of q 2 = q 1 Firm 1 will incorporate this reaction into its strategic plan.

16 Demand is P = q q 1 But, incorporating Firm 2 s reaction function, this becomes P = ( q 1 ) -.001q 1 Simplifying, this is P = q 1 This is the residual demand curve for Firm 1, when it takes Firm 2 s output decisions into account. Now, Firm 1 can profit-maximize using this residual demand curve, so MR 1 = q 1 MC =.28 So,.001q 1 =.36 or q 1 = 360

17 Firm 2 will respond to this according to its reaction function (profit-maximization given its beliefs about the other player): q 2 = q 1 = (360) = 180. Total output in the industry will be 540 units. Equilibrium price will be P = = \$0.46

18 1 = (.46 x 360) (.28 x 360) = \$ = (.46 x 180) (.28 x 180) = \$32.40 Total profit in the industry is \$ Notice that the Stackelberg leader earns the same profit as each one of the joint monopolists! Consumer Surplus = (1 -.46) x 540/2 = \$ DWL = ( ) x ( )/2 = \$16.20 Q P CS DWL Monopoly 360 \$0.64 \$ \$64.80 \$64.80 Cournot Duopoly 480 \$0.52 \$ \$ \$28.80 Stackelberg 540 \$0.46 \$97.20 \$ \$16.20 P. C. 720 \$0.28 \$0.00 \$ \$0.00

19 Let s put the choice of output into a game framework again, but allow for one Firm to make a decision first, and the other second (leader-follower), instead of simultaneously. This is a sequential game (still a one-period game). Firms will have the choice of producing 180, 240 or 360 units of output, and there will be corresponding payoffs (profit). Firm 1 moves first and Firm 2 moves second. Firm 1 decides on its best strategy by looking forward, and reasoning back

20 The other model to look at is the Bertrand model with a homogeneous good. Bertrand producers choose price rather than quantity (choosing price is the strategic move). If we assume that they have the same kind of beliefs as Cournot producers (i.e., the other producer will keep its current price constant, while I choose a profit-maximizing price), we get an odd result.

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