# Firm 1 s Output Decision

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1 Firm s Output Decision P D (0) Firm and market demand curve, D (0), if Firm 2 produces nothing. If Firm thinks Firm 2 will produce 50 units, its demand curve is shifted to the left by this amount. D (75) MR (0) If Firm thinks Firm 2 will produce 75 units, its demand curve is shifted to the left by this amount. MR (75) MC MR (50) D (50) Q Chapter 2

2 Oligopoly The Reaction Curve The relationship between a firm s profitmaximizing output and the amount it thinks its competitor will produce A firm s profit-maximizing output is a decreasing schedule of the expected output of Firm 2 Chapter 2 2

3 Reaction Curves and Cournot Equilibrium Q 00 Firm s reaction curve shows how much it will produce as a function of how much it thinks Firm 2 will produce. The x s correspond to the previous model. 75 Firm 2 s Reaction Curve Q* 2 (Q ) 50 x Firm 2 s reaction curve shows how much it will produce as a function of how much it thinks Firm will produce. 25 x Firm s Reaction Curve Q* (Q 2 ) x x Q 2 Chapter 2 3

4 Reaction Curves and Cournot Equilibrium Q Firm 2 s Reaction Curve Q* 2 (Q ) In Cournot equilibrium, each firm correctly assumes how much its competitors will produce and thereby maximizes its own profits. 50 x Cournot Equilibrium 25 x Firm s Reaction Curve Q* (Q 2 ) x x Q 2 Chapter 2 4

5 Cournot Equilibrium Each firm s reaction curve tells it how much to produce given the output of its competitor Equilibrium in the Cournot model, in which each firm correctly assumes how much its competitor will produce and sets its own production level accordingly Chapter 2 5

6 Oligopoly Cournot equilibrium is an example of a Nash equilibrium (Cournot-Nash Equilibrium) The Cournot equilibrium says nothing about the dynamics of the adjustment process Since both firms adjust their output, neither output would be fixed Chapter 2 6

7 The Linear Demand Curve An Example of the Cournot Equilibrium Two firms face linear market demand curve We can compare competitive equilibrium and the equilibrium resulting from collusion Market demand is P = 30 - Q Q is total production of both firms: Q = Q + Q 2 Both firms have MC = MC 2 = 0 Chapter 2 7

8 Oligopoly Example Firm s Reaction Curve MR = MC Total Revenue : R = PQ = 30 Q) ( Q = = 30Q 30Q ( Q Q 2 + Q 2 2 ) Q Q Q Chapter 2 8

9 Oligopoly Example An Example of the Cournot Equilibrium MR MR Q Q 2 = ΔR = 0 = = 5 = 5 ΔQ MC 2Q 2 2Q = 30 2Q Firm' s Reaction Curve Firm 2' s Reaction Curve Q 2 Chapter 2 9

10 Oligopoly Example An Example of the Cournot Equilibrium Cournot Equilibrium: Q = Q 2 Q =5 2 Q ; Q =0 Q = Q + Q 2 = 20 P = 30 Q =0 Chapter 2 0

11 Duopoly Example Q 30 Firm 2 s Reaction Curve The demand curve is P = 30 - Q and both firms have 0 marginal cost. 5 Cournot Equilibrium 0 Firm s Reaction Curve Q 2 Chapter 2

12 Oligopoly Example Profit Maximization with Collusion R = MR MR PQ = (30 Q) Q = 30Q = ΔR ΔQ = 30 2Q = 0 when Q = 5 and MR Q 2 = MC Chapter 2 2

13 Profit Maximization w/ Collusion Contract Curve Q + Q 2 = 5 Shows all pairs of output Q and Q 2 that maximize total profits Q = Q 2 = 7.5 Less output and higher profits than the Cournot equilibrium Chapter 2 3

14 Duopoly Example Q 30 Firm 2 s Reaction Curve For the firm, collusion is the best outcome followed by the Cournot Equilibrium and then the competitive equilibrium 5 0 Competitive Equilibrium (P = MC; Profit = 0) Cournot Equilibrium Collusive Equilibrium 7.5 Collusion Curve Firm s Reaction Curve Q 2 Chapter 2 4

15 First Mover Advantage The Stackelberg Model Oligopoly model in which one firm sets its output before other firms do Assumptions One firm can set output first MC = 0 Market demand is P = 30 - Q where Q is total output Firm sets output first and Firm 2 then makes an output decision seeing Firm s output Chapter 2 5

16 First Mover Advantage The Stackelberg Model Firm --leader Must consider the reaction of Firm 2 Firm 2--follower Takes Firm s output as fixed and therefore determines output with the Cournot reaction curve: Q 2 = 5 - /2(Q ) Chapter 2 6

17 First Mover Advantage The Stackelberg Model Firm Choose Q so that: MR = MC = 0 R = PQ = 30 Q Firm knows Firm 2 will choose output based on its reaction curve (behavioral pattern). We can use Firm 2 s reaction curve as Q 2. - Q 2 - Q Q 2 Chapter 2 7

18 First Mover Advantage The Stackelberg Model Using Firm 2 s Reaction Curve for Q 2 : R = 30Q Q 2 Q (5 2Q ) = 5Q 2Q 2 MR MR = ΔR = 0 : Q ΔQ = 5 = 5 Q and Q 2 = 7.5 Chapter 2 8

19 First Mover Advantage The Stackelberg Model Conclusion Going first gives Firm the advantage Firm s output is twice as large as Firm 2 s Firm s profit is twice as large as Firm 2 s Going first allows Firm to produce a large quantity. Firm 2 must take that into account and produce less unless it wants to reduce profits for everyone. Chapter 2 9

20 Price Competition Competition in an oligopolistic industry may occur with price instead of output The Bertrand Model is used Oligopoly model in which firms produce a homogeneous good, each firm treats the price of its competitors as fixed, and all firms decide simultaneously what price to charge Chapter 2 20

21 Price Competition Bertrand Model Assumptions Homogenous good Market demand is P = 30 - Q where Q = Q + Q 2 MC = MC 2 = \$3 Can show the Cournot equilibrium if Q = Q 2 = 9 and market price is \$2, giving each firm a profit of \$8. Verify yourself. Chapter 2 2

22 Price Competition Bertrand Model Assume here that the firms compete with price, not quantity Since good is homogeneous, consumers will buy from lowest price seller If firms charge different prices, consumers buy from lowest priced firm only If firms charge same price, consumers are indifferent who they buy from Chapter 2 22

23 Price Competition Bertrand Model Nash equilibrium is competitive output since have incentive to cut prices Both firms set price equal to MC P = MC; P = P 2 = \$3 Q = 27; Q & Q 2 = 3.5 Both firms earn zero profit Chapter 2 23

24 Price Competition Bertrand Model Why not charge a different price? If charge more, sell nothing If charge less, lose money on each unit sold The Bertrand model demonstrates the importance of the strategic variable Price versus output Chapter 2 24

25 Bertrand Model Criticisms When firms produce a homogenous good, it is more natural to compete by setting quantities rather than prices Even if the firms do set prices and choose the same price, what share of total sales will go to each one? It may not be equally divided Chapter 2 25

26 Price Competition Differentiated Products Market shares are now determined not just by prices, but by differences in the design, performance, and durability of each firm s product In these markets, more likely to compete using price instead of quantity Chapter 2 26

27 Price Competition Differentiated Products Example Duopoly with fixed costs of \$20 but zero variable costs Firms face the same demand curves Firm s demand: Q = 2-2P + P 2 Firm 2 s demand: Q 2 = 2-2P 2 + P Quantity that each firm can sell decreases when it raises its own price but increases when its competitor charges a higher price Chapter 2 27

28 Price Competition Differentiated Products Firms set prices at the same time Firm: π = = PQ P (2 = 2P \$20 2P 2-2P + + P 2 PP ) Chapter 2 28

29 Price Competition Differentiated Products If P 2 is fixed: Firm 's profit maximizing price = Δπ ΔP =2 4P + P 2 = 0 Firm 's reaction curve = P = 3 + 4P 2 Firm 2's reaction curve = P 2 = 3 + 4P P * = P 2 * = 4 Chapter 2 29

30 Nash Equilibrium in Prices What if both firms collude? They both decide to charge the same price that maximizes both of their profits Firms will charge \$6 and will be better off colluding since they will earn a profit of \$6 Chapter 2 30

31 Nash Equilibrium in Prices P Firm 2 s Reaction Curve Collusive Equilibrium Equilibrium at price of \$4 and profits of \$2 \$6 \$4 Firm s Reaction Curve Nash Equilibrium \$4 \$6 P 2 Chapter 2 3

32 Nash Equilibrium in Prices If Firm sets price first and then Firm 2 makes pricing decision: Firm would be at a distinct disadvantage by moving first The firm that moves second has an opportunity to undercut slightly and capture a larger market share Chapter 2 32

33 A Pricing Problem: Procter & Gamble Procter & Gamble had to consider competitors prices when setting their price P&G s demand curve was: Q = 3,375P -3.5 (P U ) 0.25 (P K ) 0.25 Where P, P U, P K are P&G s, Unilever s, and Kao s prices respectively Chapter 2 33

34 A Pricing Problem: Procter & Gamble What price should P&G choose and what is the expected profit? Can calculate profits by taking different possibilities of prices you and the other companies could charge Nash equilibrium is at \$.40 the point where competitors are doing the best they can as well Chapter 2 34

35 P&G s Profit (in thousands of \$ per month) Chapter 2 35

36 A Pricing Problem for Procter & Gamble Collusion with competitors will give larger profits If all agree to charge \$.50, each earn profit of \$20,000 Collusion agreements are hard to enforce Chapter 2 36

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