Oligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry s output.

Topic 8 Chapter 13 Oligopoly and Monopolistic Competition Econ 203 Topic 8 page 1 Oligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry s output. Firms behave strategically -- Game Theory Focus on firm s behaviour -- pricing choice or quantity choice Competition model 1: the Cournot theory Competition model 2: Van Stackelberg duopoly theory Competition model 3: the Bertrand Theory

Monopolistic Competition Characterized by: The existence of numerous firms each producing a product that is a close, but imperfect substitute for the products of other firms free entry and exit of firms Econ 203 Topic 8 page 2

Oligopoly: Econ 203 Topic 8 page 3 In Chapter 12: the situation with a single firm (monopoly). The Monopolist: set price (market power) maintain an economic profit in the long run no entry of new firms Oligopoly: more than one firm in the market each firm has some market power to set price awareness of its competition in decision making process

Ther are many theories on how firms behave in an oligopolistic market. Econ 203 Topic 8 page 4 Behaviour will be determined by pricing and quantity choices. Such choices depend on the firms in the market and on how they compete. Main focus of this chapter will be on the duopoly: two firms in the market.

Econ 203 Topic 8 page 5 There is no single theory of oligopoly. In contrast to perfect competition or monopoly, where there is a single model, many types of oligopoly models exist. Depending on the circumstances each one of these theories may be appropriate. An oligopoly is a market structure with a limited or small number of firms.

An example in Canada, of an oligopoly is the Chartered Banks. Econ 203 Topic 8 page 6 Each of the major firms takes account of the reaction of the others when it determines its price and output policy, since its policy will affect the others. That is, when a firm increases its price, it must anticipate the reaction of other firms in the industry. If its competition decides against a price increase, it is likely that the price increase will have to be rescinded; otherwise, its rival will pull away a large number of its customers.

Five elements of a game: The players The timing of the game. The list of possible strategies for each player. The payoffs associated with each combination of strategies. The decision rule.

The Cournot Model: Econ 203 Topic 8 page 13 An industry in which firms produce identical goods and each firm determines its profit-maximizing output level, taking its rivals current output levels as given. firms maximize profits firms choose price and quantity assuming that the other firm(s) keeps their quantity fixed. Assume: two firms producing the same good. each duopolist treats the other s quantity of output as fixed.

Cournot s Water Example: MC =0 Econ 203 Topic 8 page 14 Let total market demand curve is given: P = a b( Q + Q ) 1 2, where a an b are positive numbers and Q 1 and Q 2 are outputs of the two firms. The profit maximizing problem facing firm 1, given the assumption that firm 2 s output is fixed at the current level: Max Π( Q, Q ) = PQ C ( Q ) Q 1 1 2 1 1 1.

The demand curve for firm 1 is therefore given by: Econ 203 Topic 8 page 15 P1 = ( a bq2) bq1. (Q 2 is assumed to be fixed.) We get the demand curve for firm 1 by subtracting bq 2 from the vertical intercept of the market demand curve. The idea is that firm 2 has already supplied the Q 2 units of market demand, leaving firm 1 the rest to work with.

Econ 203 Topic 8 page 16 Firm 1 s demand curve lies to the right of this new vertical axis. Often referred to as a residual demand curve. The firm s MR curve is labelled MR 1.

Econ 203 Topic 8 page 17 Since the profit maximizing level of output for firm 1 is found where MR 1 =MC and MC=0 in this case, they should supply at a point where MR 1 =0. P = ( a bq ) bq price 1 2 1 ( ) ) TR = PQ = a bq bq Q 2 TR = ( aq bq Q bq ) MR 1 1 1 2 1 1 1 1 2 1 1 1 TR = = a bq 2bQ Q 1 2 1 MR has twice the slope as demand so it intersects MC=0 at the half way point between Q 1 =0 on the horizontal intercept of the demand curve.

Econ 203 Topic 8 page 18 By symmetry, Q 2 =Q 1. Set MR = MC and solve for the output of firm 1 in terms of the output of firm 2. TR MR1 = = a bq2 2bQ1 = MC = 0 Q a bq 2bQ = 0 Q Q a bq 2bQ = 0 a = Q = 2 1 3bQ a = = 3b 1 2 1 1 1 1 Q 1 2

MR Q 1 1 = TR = = a bq2 2bQ1 = MC = 0 Q a 1 bq 2b 2 Econ 203 Topic 8 page 19 Reaction Function: a curve that tells the profit-maximizing level of output for one oligopolist for each amount to supplied by another. For the example where MC=0, the reaction function for firm 1 is : Q 1 = a bq 2b 2.

The function tells how firm 1 s quantity will react to the quantity level offered by firm 2. Econ 203 Topic 8 page 20 Since the Cournot duopoly problem is completely symmetric, firm 2 s reaction function has the same structure: Q 2 = a bq 2b 1.

Econ 203 Topic 8 page 21 The two reaction functions are illustrated above. There is a stable equilibrium at the intersection of the two reaction functions.

Here, both firms are producing 3 firm has any incentive to change. a b Econ 203 Topic 8 page 22 units of output, and neither Profit? Combined output Q=Q1+Q2= a a a 3 b + 3 b =2 3 b. Market price will be P = a b( Q + Q ) 1 2 a a a a a P = a b a = b 3 2 2 2 = = 3 3 3 3 3 Total revenue will equal: TR PQ a a 2 a = = =. 3 3b 9b.

Cournot Model of Quantity Competition Exercise: A market demand curve for a pair of duopolists is given as: P = 36 3Q where Q = Q1 + Q2. Each duopolist has a constant marginal cost equal to 18 (fixed cost is zero). Fill the below table. Model Q1 Q2 Q1+Q 2 P 1 2 1+ 2 Cournot

Bertrand Model of Price Competition Setting: Homogeneous product market with 2 firms Firm sets prices P1, P2 respectively and have unlimited capacity. Market demand given by P(q)=a bq Linear cost functions: Ci(qi)=ciqi where i = 1, 2. C1 = C2

Bertrand Model of Price Competition. The players: Firm 1 and Firm 2 The timing of the game: Simultaneous The list of possible strategies for each player: All possible choices of prices P1 and P2. The payoffs associated with each combination of strategies: profits The decision rule: maximize profit.

Bertrand Model of Price Competition Firm s problem: Firm faces the following demand schedule: Q = a bp1 if P1 < P2 Q = ½(a bp) if P1 = P2 = P Q = 0 if P1 >P2 Nash Equilibrium: With symmetric cost functions: P1 = P2 = MC and two firms split the market demand equally. With asymmetric cost functions: c1 < c2 then P2 = c2 and P1 = P2 - whole market. and firm 1 captures the Bertrand s Paradox: Only 2 firms but achieve the perfectly competitive market outcome.

Bertrand Model of Price Competion

Cournot Model of Quantity Competition Exercise: A market demand curve for a pair of duopolists is given as: P = 36 3Q where Q = Q1 + Q2. Each duopolist has a constant marginal cost equal to 18 (fixed cost is zero). Fill the below table. Model Q1 Q2 Q1+Q 2 P 1 2 1+ 2 Cournot 2 2 4 24 12 12 24 Bertrand

Econ 203 Topic 8 page 30 The Stackelberg Model: An industry in which one firm (the Stackelberg leader) sets its profit-maximizing level of output first, knowing that its rival (the Stackelberg follower) will behave as a Cournot duopolist. p. 402 In the Stackelberg model, a firm would want to choose its output level by taking into account the effect that choice would have on the output level of its rival. Suppose firm 1 knows that firm 2 will treat firm 1 s output as fixed. Can this knowledge be used to the advantage of firm 1?

Since firm 2 s reaction function is given by Econ 203 Topic 8 page 31 Q 2 = a bq 2b 1 reaction function. Knowing that firm 2 s output will depend on Q 1 in this manner, firm 1 can then substitute the reaction function for Q 2 into the equation for the market demand curve: P a b Q Q a b Q a bq a bq = + = 1 + 1 ( 1 2) 1 = 2b 2. This demand curve and MR curve are shown in figure 13.4.

Econ 203 Topic 8 page 32

Econ 203 Topic 8 page 33 With MC assumed to be zero in this example, firm 1 s profit maximizing output level will be the one for MR 1 is zero, at Q * 1 = a 2b. Firm 2 will produce: Q 2 4 ab Price: * P a b Q Q a b a * * a = ( + = + 1 2) 2b 4b a a 4a 2a a a P = a = =. 2 4 4 4 4 4 =.

Econ 203 Topic 8 page 37 The best output choice is a/2b for firm 1 once it takes into account that firm 2 will respond to its choice according to the reaction function for firm 2. Once firm 1 produces a/2b, firm 2 will consult its reaction function and product a/4b.

Econ 203 Topic 8 page 38 If firm 1 believes that firm 2 will fix the amount produced at a/4b, it should consult its own reaction function and produce the corresponding quantity 3a/8b. Firm 1 would earn more. However, firm 1 knows that if it cuts back, this will elicit a reaction from firm2. The best option is for firm 1 to remain at a/2b. Firm 1 earns more profit than at the intersection of the reaction curves, but does not give firm 2 any incentive to increase output.

Stackelberg Sequential Quantity Competition. Exercise: A market demand curve for a pair of duopolists is given as: P = 36 3Q where Q = Q1 + Q2. Each duopolist has a constant marginal cost equal to 18 (fixed cost is zero). Fill the below table. Model Q1 Q2 Q1+Q2 P 1 2 1+ 2 Cournot 2 2 4 24 12 12 24 Bertrand 3 3 6 18 0 0 0 Stackelberg

A Comparison across models. Model Q1 Q2 Q1+Q2 P 1 2 1+ 2 Cournot 2 2 4 24 12 12 24 Bertrand 3 3 6 18 0 0 0 Stackelberg 3 1.5 4.5 22.5 13.5 6.75 20.25 Shared Monopoly 1.5 1.5 3 27 13.5 13.5 27

Econ 203 Topic 8 page 39

Monopolistic Competition Econ 203 Topic 8 page 50 With monopolistic competition all firms sell a somewhat different product. Product differentiation is the primary defining difference with this market structure compared to perfect competition. With perfect competition, the product produced by all firms in the industry is identical. With monopolistic competition, each product within the industry is just a bit different.

Econ 203 Topic 8 page 51 Such differences can be in the product s physical make-up (Coke versus Pepsi), or in the amount of service each firm offers (Payless shoes versus Footlocker). Because of these differences, producers have a certain amount of control over the price of their product, although it is usually small because the products of other firms are very similar to their own. In addition to product differentiation, there are four other conditions that must be met for an industry to be considered to be part of the market structure known as monopolistic competition:

Econ 203 Topic 8 page 52 1) There must be a large number of firms in the industry. The good must be produced by at least 50 to 100 firms, with each firm s product a close substitute for the products of the other firms in the industry. 2) The number of firms in the industry must be large enough that each firm expects its actions to be of no real concern or ignored by its rivals, and it is not concerned with possible retaliatory moves by its rivals. With a large number of firms within the industry, this is usually met. The actions of the firm are not driven explicitly by the possible responses of its competitor.

Econ 203 Topic 8 page 53 3) There must be easy entry into the industry. No legal barriers. 4) There must be no collusion, such as price fixing or market sharing among firms in the industry.

Price and Output Decisions Under Monopolistic Competition Econ 203 Topic 8 page 54 Because each firm produces a slightly different product, the demand curve facing each firm slopes downward to the right. If the firm raises its price, the quantity demanded for its product will go down, but will no completely disappear. It will still retain some of its customers and not lose all of its customers to other firms. Conversely, if the firm decides to lower its price, it will gain some customers, but not all of its competitors customers. (Product loyality.)

Econ 203 Topic 8 page 55 Price profit MC P 0 C AC A B MC=MR Demand (d 0 ) MR q 0 Output Firm (Short-Run)

The diagram illustrates the short run equilibrium of a monopolistically competitive firm. Econ 203 Topic 8 page 56 The firm will set its price at P 0 and output rate at q 0, due to the fact that it will maximize its profits where MC=MR. Profit will be earned because P 0 is higher than average total cost at this output of q 0. (P 0 >A) Profit = AP 0 CB

Price MC Econ 203 Topic 8 page 57 P 0 LAC P 1 MR 1 Demand (d 1 ) MC=MR q 1 Output The next diagram illustrates the long run equilibrium. Profits are temporary since there are no barriers to entry. Other firms can enter and sell similar products.

Econ 203 Topic 8 page 58 As firms enter the industry, the firm s demand function shifts inward. In the long run, each firm must be making no profit and maximizing its profits. The zero profit condition is met at the combination of price=p 1 and output=q 1, since the firm s average cost at this output equals price P 1. Profit maximization is met, since MC=MR a t this output rate.

Econ 203 Topic 8 page 59 In monopolistically competitive industries, profits are competed away with entry of new firms, just like they are in competitive industries. Unlike competitive industries, each monopolistically competitive firm is a price maker, and therefore price exceeds marginal cost. Marginal cost equals price in a competitive industry. Under monopolistic competition each firm produces a smaller quantity than a competitive firm. Long run average cost is higher than minimum average cost.

Econ 203 Topic 8 page 60 But, consumers benefit from the variety of products and the ability of the industry to cater to particular demands of some consumers.

Game Theory Econ 203 Topic 8 page 41 Managers who must analyse and participate in oligopolistic decision making, are very likely to use modern game theory. Since a basic feature of oligopoly is that each firm must take account of its rivals reactions to its own decision making, oligopolistic decision making has many of the characteristics of a game. Game theory attempts to study decision making where, like an oligopoly, there is a mixture of conflict and cooperation.

Econ 203 Topic 8 page 42 A game is a competitive situation in which two more opponents pursue their own interests, and no one can dictate the outcome. Each player of the game is a decision making entity with a certain amount of allocated resources. The rules of the game describe how resources can be used. A strategy specifies what a player will do under each situation while playing the game. These are the actions that will be taken in response to a particular action taken by another player, or actions that reflect where the player wants to end up.

Econ 203 Topic 8 page 43 A player s payoff varies from game to game. For two-player games, the possible outcomes are illustrated with the aid of a payoff matrix. Possible Strategies 3 A s profit: $30 B s profit: $40 for Firm A 4 A s profit: $40 B s profit: $30 Possible Strategies for Firm B 1 2 A s profit: $20 B s profit: $30 A s profit: $30 B s profit: $20 Firm A can choose strategy 3 or 4 and Firm B can choose strategy 1 or 2.

The payoff, expressed in terms of profits for each firm, is shown above for each combination of strategies. Econ 203 Topic 8 page 44 In this game, there is a dominant strategy for each player. Regardless of whether Firm B chooses strategy 1 or 2, Firm A will make more profit if it chooses strategy 4 rather than 3. Strategy 4 is Firm A s dominant strategy. Similarly, regardless of whether Firm A adopts strategy 3 or 4, firm B will make more profit if it chooses strategy 1 rather than 2. Hence, strategy 1 is Firm B s dominant strategy. The solution to this game is that Firm A chooses strategy 4 and Firm B chooses strategy 1.

Nash Equilibrium Econ 203 Topic 8 page 45 Not all games have a dominant strategy for every player. Possible Strategies 3 A s profit: $30 B s profit: $40 for Firm A 4 A s profit: $40 B s profit: $30 Possible Strategies for Firm B 1 2 A s profit: $20 B s profit: $30 A s profit: $30 B s profit: $40 Suppose the pay off matrix for Firms A and B are as shown. Under these circumstances, Firm A still has a dominant strategy: 4. Regardless of which strategy firm B adopts, strategy 4 is firm A s best strategy.

Econ 203 Topic 8 page 46 But firm B no longer has a dominant strategy. Its optimal strategy depends on what firm A decides to do. If Firm A chooses strategy 3, firm B will make more profit if it chooses strategy 1 rather than strategy 2. If Firm A adopts strategy 4, Firm B will make more profit if it chooses strategy 2 rather than strategy 1. To determine what action should be taken, Firm B must try to anticipate what action Firm A will take. That is, Firm B must try to figure out what the best action it would take if it was Firm A.

Econ 203 Topic 8 page 47 Since we know from the table that Firm A s dominant strategy is strategy 4, Firm B can surmise that this strategy will occur. Firm A will most likely choose strategy 4, and hence, Firm B will choose strategy 2 because it is more profitable than strategy 1 if Firm A adopts strategy 4. Thus, Firm A is expected to adopt Strategy 4 and Firm B is expected to adopt strategy 2. This is the Nash equilibrium for this game.

Econ 203 Topic 8 page 48 A Nash equilibrium is a set of strategies such that each player believes that it is doing the best it can given the strategy of the other player. Neither player regrets its own decision or has any incentive to change it. If each player has a dominant strategy, this strategy is its best choice regardless of what other players do. This is a Nash equilibrium too. The next table is an example of a payoff matrix for a game with two Nash equilibria.

Econ 203 Topic 8 page 49 Possible Strategies 3 A s profit: $50 B s profit: $50 for Firm A 4 A s profit: $0 B s profit: $0 Possible Strategies for Firm B 1 2 A s profit: $0 B s profit: $0 A s profit: $50 B s profit: $50 If Firm A adopts strategy 3 and Firm B adopts strategy 1, each is doing the best it can given the other s choice of strategy. If Firm A adopts strategy 4 and B adopts strategy 2, each is doing the best it can given the other s choice of strategy. Hence, there are two Nash equilibria in this game.

Common Games. Prisoner s Dilemma PRISONER s DILEMMA. Prisoner 2 Stay Silent Prisoner 1 Stay Silent Each serves 1 year Betray Prisoner 1: Serves 20 years. Prisoner 2: Go free. Betray Prisoner 1: Go free. Prisoner 2: Serves 20 years Each serves 10 years.

Equilibrium of a Game Dominant Strategy Equilibrium. Dominant strategy equilibrium. Consider the following game: The players: Player 1 and Player 2 Timing of a game: Simultaneous. Information Availability: Perfect. Possible strategies: Player 1 (L;R) and Player 2(U;D) The payoffs associated with each combination of strategies (table below) Repetition: Non - repeated. The decision rule: Max own payoff. Equilibrium: (Player 1, Player 2) = (R;D) with payoff (6,3) Player 2 (U) (D) Player 1 L (2,2) (4,4) R (0,1) (6,3)

Equilibrium of a Game Nash Equilibrium. Dominant Strategy does not always exist. The Nash equilibrium (NE) Set of strategies (one for each player) such that no player wishes to change her strategy given the strategies of the other players The strategy of each player is a so-called best response to the given strategies of the other.

Equilibrium of a Game Nash Equilibrium. Nash equilibrium. Consider the following game: The players: Player 1 and Player 2 Timing of a game: Simultaneous. Information Availability: Perfect. Possible strategies: Player 1 (L;R) and Player 2(U;D) The payoffs associated with each combination of strategies (table below) Repetition: Non - repeated. The decision rule: Max own payoff. Nash Equilibria: (Player 1, Player 2) = (R;U) and (L;D) with payoff (3;6) and (6;3) Player 2 (U) (D) Player 1 L (0,2) (6,3) R (3,6) (0,2)