Oligopoly Master 2009-10 V2

AN INTRODUCTION TO OLIGOPOLY To p ic : O lig o p o ly tu to r2 u ; Mo Tanweer; [email protected]

Content W h a t is a n o lig o p o ly? K in ke d d e m a n d m o d e l Price - w a rs a n d ca rte ls Priso n e rs ’ d ile m m a E xte n sio n s : B e rtra n d / C o u rn o t/ S ta cke lb e rg co m p e titio n 

Oligopoly A

few large firms dominating an industry , with strategic One firm ’ s output and price decisions are A interdependence very high concentration ratio

influenced by

Intel/AMD duopoly

ist is likely to be aware of the actions of the others . The decisions Boeing/Airbus duopoly

UK Supermarkets (CR4 = 74%)

Possible examples

e Big Four accountancy firms

Fastfood restaurants (KFC, McD’s, Wimpy) Pizza chains: Pizza Hut, Dominos

eds to take into account the likely responses of the other market par P&G and Unilever (dominate detergent market)

Characteristics Price makers

Long run supernormal profits

“Few” number of dominant sellers

§The

Strategic interdependence

main key to behaviour in an oligopoly, is that companies must take into account what other companies will do. In perfect competition, firms are price-takers and can ignore other firms. In a (pure) monopoly, there is only one firm, and it does not take into account what competitors will do. Oligopolists are torn between: §cooperating to increase profits by obtaining the monopoly outcome, or; §competing to try to gain an advantage over competitors.

The Kinked-Demand curve model An

oligopolist faces a downward sloping demand curve but the elasticity may depend on the reaction of rivals to changes in price and output. (a) rivals will not follow a price increase by one firm, so the acting firm will lose market share - therefore demand will be relatively elastic and a rise in price would lead to a fall in  (b)the rivals more likely match a totalare revenue of the to firm price fall by one firm to avoid a loss of market share. If this Rev & happens demand will be more inelastic and a fall in price will Costs a .fall in total Rev &also lead to Rel Elastic Costs revenue.

P*

Rel . inelastic

AR2=D2

Discontinuity

AR=D MR

AR=D

MR2

Q*

q

MR

Price competition In oligopolistic markets, we tend not to see much price competition for the following reasons: This is because competitors will generally ignore price increases, with the hope of gaining a larger market share as a result of now having comparatively lower prices even a large price decrease will gain only a few customers because such an action will begin a price war with other firms. Rev & Costs

P* Furthermore, price stickiness occurs because there is a discontinuity which means a change in MC has no effect on profit-max P* or Q*

MR

AR=D

Non-price competition Due to undesirability of price competition, due to risk of price wars; firms in oligpolistic tend to undergo non-price competition: Mass media advertising and marketing ( informative vs Visual / Sound persuasive ) branding ; “ Every little helps ” ; “ Just Do It ”; “ The Worldcards ’ s Local Bank ” , Nectar points ) Store loyalty ( airmiles Home delivery Extension of opening hours Innovative use of tech . ( self - scanning machines ) Internet shopping ( some price discrimination here? ) Offering complementary g / s e . g . Tesco ’ s banking services Offering compli mentary g / s e . g . Amazon free delivery BOGOF ( price / non - price? ) BOGOFL In - store chemists / post offices / creches Promoting domestic ( nationalism ) g / s Celebrity Endorsements After - sales service / warranties / guarantees Corporate social responsibility / charitable work / / ethical values e . g . Starbucks Fairtrade Store layout



Cartels When there are only a few dominant firms in a market, they can cooperate to restrict output or fix e.g. higher OPEC prices Why might cartels break down? The more companies in the industry, the harder it is to form a cartel and enforce it (trust) The weaker the barriers to entry are, the harder it is to ensure a successful cartel Strong incentive to cheat: Firm’s output/prices cannot easily be checked

Whisteblowing legislation (OFT; Virgin-BA) When can collusion be good for con If demand is not inelastic enough (PED/YED) – too variable Different types of restrictive practices: Price fixing Information sharing SNPe.g. leads to Savings more non-price competition (benefits Stability in consumer?) prices StrategicHigher alliances Blu-Ray dvds on advertising/R&D (wasteful consumer) duplication?) (passed onto Tacit vs formal collusion Unwritten / unspoken agreements

for example, in some industries, there may be an acknowledged market lead which informally sets prices to which other producers respond, known as

Examples of collusion

Examples of anti-trust in action

Examples of anti-trust in action

Examples of anti-trust in action

Examples of anti-trust in action

Game theory is the study of how people behave in strategic situations (i.e. when they must consider the effect of other people’s responses to their own actions). In an oligopoly, each company knows that its profits depend on actions of other firms. This gives rise to the "prisoners’ dilemma". The prisoners' dilemma is a particular game that illustrated why it is difficult to cooperate, even when it is in the best interest of both parties. Both players select their own dominant strategies for shortsighted personal gain. Eventually, they reach an equilibrium in which they are both worse off than they would have been, if they could both agree to select an alternative (non-dominant) strategy. Oligopoly theory makes heavy use of game theory to model the behaviour of oligopolies: Bertrand’s oligopoly: In this model the firms simultaneously choose prices Cournot’s duopoly: In this model the firms simultaneously choose quantities Stackelberg’s duopoly: In this model the firms move sequentially

Game Theory Game theory is the study of how people behave in strategic situations (i.e. when they must consider the effect of other people’s responses to their own actions). In an oligopoly, each company knows that its profits depend on actions of other firms. This gives rise to the "prisoners’ dilemma". The prisoners' dilemma is a particular game that illustrated why it is difficult to cooperate, even when it is in the best interest of both parties. Both players select their own dominant strategies for shortsighted personal gain. Eventually, they reach an equilibrium in which they are both worse off than they would have been, if they could both agree to select an alternative (non-dominant) strategy. Oligopoly theory makes heavy use of game theory to model the behaviour of oligopolies: Bertrand’s oligopoly: In this model the firms simultaneously choose prices Cournot’s duopoly: In this model the firms simultaneously choose quantities Stackelberg’s duopoly: In this model the firms move sequentially

Pay - off matrix

Prisoners’ DilemmaNormal

sequential, is there first-mover or second-mover advantage?

form

The Nash equilibrium is (Betray, Betray); although it is Pareto-dominated by (S

B Silent A

Silent 6mths,6mths

Betray 10 years,0 years

Betray 0 years,10 years 5 years, 5 years

charge low price” advertise”; in R&D/don’t do R&D” R: The first number; “advertise/don’t always goes to the player on“invest the LEFT, and the second number always goes to the player

Cournot competition Cournot ’ s duopoly : In this model the firms simultaneo rnot ( 1801 - 1877 ) was a French economist , philosopher and mathematician .

Assume two firms that compete in quantities (q1, q2)  q 1 = f ( q 2 ); q 2 = f ( q 1 ) Linear ( inverse ) demand curve : P = a – bQ ( where Q = q 1 + q2) (1.1) For simplicity assume constant marginal costs TC i = cq i for i = 1,2 We are trying to find the optimal q1 and q2 that will be chosen , given the other firm ’ s output decisions , and thus the price that will be charged in the market in equilibrium 

Firm 1 chooses the best q1 given q2 and Firm 2 chooses the best q2 given q1

Cournot competition Firm 1 Profit for any firm is total revenue minus total costs ; ∏ = ( TR – TC )  ∏1 = p . q 1 - c . q 1 (1.2)



Recall from the previous slide , equation 1 . 1 , that P = a – bQ and Q = q 1 + q 2

 

So we get : P = a – b ( q 1 + q 2)  P = a – bq 1 - bq 2



(1.3)

If we then substitute 1 . 3 into 1 . 2 Then ∏ 1 = (a-bq1-bq2)q1 - c.q1



∏1 = aq1-bq12-bq2q1 - c.q1



(1.4)

Cournot competition Now that we have the profit function for Firm 1, as a function of its own output and the other firm’s output, we can now differentiate this function w.r.t. its own quantity, to find out at what quantity, q1, it should produce at to profit-maximise: Differentiate Equation (1.4) w.r.t q1

 

∂Π1 = a − 2bq1 − bq2 − c = 0 ∂q1

2bq1 + bq 2 = a − c

on ( q 2 ), the

2bq bq2 profit - maximising “ best 1 = a−c−

a − 2bq1 − bq2 − c = 0 − 2bq1 − bq2 = c − a a − c − bq2 response q1” =for firm is q 1 2b

This is known as Firm 1 ’ s REACTION FUNCTION

Cournot competition Since Firm 1 and Firm 2 are identical, both of the firm’s reaction functions can be found by differentiating their relevant profit functions, which gives:

a − c − bq2 q1 = 2b

a − c − bq1 q2 = 2b

his is known as Firm 1 ’ s REACTION FUNCTION This is known as Firm 2 ’ s REACTION FUNCTI

Cournot competition We can now plot these two functions on the same graph:

q2 If Firm 1

a − c − bq2 q1 = went for a different 2b

quantity ( say q1a ), Firm 2 ’ s best

If Firm 2 went for that q2a , Firm 1 ’ s best response

a − c − bq1 q2 = 2b

q 2a q 1b q 1a

q1

But if Firm 1 went for q1b , then Firm 2 ’ s best response is heatdefinition of athere Nash is equilibrium q * 1 , q * 2 that no tendency for change , given the other firm ’ s output decision

Cournot competition

eactions ; The pattern continues until a point is reached where neither firm de

We can now plot these two functions on the same graph:

q2

a − c − bq2This q1 = 2b

nition of a Nash equilibrium

point is the COURNOT EQUILIBRIU

Recall that these two functions are “ reac

ither firm has a profit icnentive to diverge from them q*2

a − c − bq1 q2 = 2b

q*1

q1

s the best response , given Firmshow 1 hasthe gone“ best for q * 1response ” given what the other They where they cross , implies that for Firm 1 , q * 1 , is the best response , given Firm 2 has gon

Cournot competition Solving algebraically, we have two equations with two unknowns, q1 and q2:

a − c − bq2 q1 = 2b

a − c − bq1 q2 = 2b

rating the component parts and cancel the “ b ”

q1 =

a c bq − − 2 2b 2b 2b

Factor out the 1 / 2

on function , q2

1a c  q1 =  − − q2  2 top b right b ), into  ( yellow box

here

1  a c  a − c − bq1   q1 =  − −    2b b  2b 

Cournot competition Continuing…:

1  a c  a − c − bq1   q1 =  − −    2b b  2b 

oss by 2 to get rid of the fraction

Simplify

 a c  a − c − bq1   2q1 = 1 − − 1   2b  b b 

Simplify

Multiply across by 2 to get rid of the fraction

a c a c q1 2q1 = − − + + b b 2b 2b 2

2a 2c 2a 2c 2q1 4q1 = − − + + b b 2b 2b 2

Cournot competition Continuing…:

2a 2c a c 4q1 = − − + + q1 b b b b

range so q1 is on one side

4q1 − q1 = Simplify

2a a 2c c − − + b b b b

a c 3q1 = − b b

a−c q1 = 3b

Cournot competition Since Firm 1 and Firm 2 are identical (whilst you could work it out again for Firm 2, you would get the same result) so:

a−c q1 = 3b

a−c q2 = 3b

resent the q * 1 and q * 2 that we showed on our diagram – i . e . the Cournot Nash equ Back (a while ago now!) we said that P = a – bQ (the inverse linear demand curve) We can now substitute the above two equations into the original demand curve to find the price that will be charged by the firms

a−c a−c P = a − b +  3b   3b

Cournot competition Simplifying these:

a−c a−c P = a − b +  3b   3b

 a−c a−c P = a − +  3   3

a c a c P = a − − + −   3 3 3 3

Cournot competition Simplifying these:

a c a c P = a − − + −   3 3 3 3

1 This1 is the 1 price 1 P =a− a− a+ c+ c 3 3 3 3

2 2 P =a− a+ c 3 3

that will be charged for the outputs th

1 2 P = a+ c 3 3

a + 2c P= 3

Cournot competition In terms of the industry output that will be produced, it is simply q1 + q2:

a−c q1 = 3b

a−c q2 = 3b

a−c a−c Q= + 3b 3b

2a−c Q=   3 b 

Cournot competition Using MC=MR Firm

1’s demand function is P = (60 - Q2) - Q1 where Q2 is the quantity produced by the other firm and Q1 is the amount produced by firm 1. Assume that marginal cost is 12. Firm 1 wants to know its maximizing quantity and price. Firm 1 begins the process by following the profit maximization rule of equating MC=MR. Firm 1’s total revenue function is PQ = Q1(60 - Q2 - Q1) = 60Q1- Q1Q2 Q12. The marginal revenue function is MR = 60 - Q2 - 2Q. Set MC = MR 12 = 60 - Q2 - 2Q 2Q = Q2 – 60 Q1 = 30 - 0.5Q2 [1.1] Q2 = 30 - 0.5Q1 [1.2] Equation 1.1 is the reaction function for firm 1. Equation 1.2 is the reaction function for firm 2. To determine the Cournot equilibrium you can solve the equations simultaneously. The equilibrium quantities can also be determined graphically. The equilibrium solution would be at the intersection of the two reaction functions.

Bertrand competition Bertand ’ s duopoly : In this model the firms simultan

thematician Joseph Louis François Bertrand ( 1822 – 1900 ) The

Bertrand model is essentially the Cournot model except the strategic variable is price rather than quantity. ‘Bertrand competition’ refers to a model of oligopoly in which two or more firms compete by simultaneously setting prices and in which each firm is committed to provide consumers with the quantity of the firm’s product they demand given these ‘posted prices’.  In

a Bertrand (Nash) equilibrium, firms compete in prices, i.e.Firm 1 chooses the best p1 given p2 and Firm 2 chooses the best p2 given p1

The

model assumptions are there are two firms in the market, producing a homogeneous product, at a constant marginal cost.

 Firms

choose prices PA and PB simultaneously

 The

only Nash equilibrium is PA = PB = MC.

 Neither

firm has any reason to change strategy. if the firm raises prices it will lose all its customers. If the firm lowers price P < MC then it will be losing money on every unit sold.

 The

Bertrand equilibrium is the same as the perfectly competitive outcome.

 Each

firm will produce where P = marginal costs and there will be zero supernormal profits.

Bertrand Paradox In

the ‘classic’ model of Bertrand competition, each of the firms produces an identical product at a constant unit cost Since their products are perfect substitutes, firms effectively compete for the total demand The firm setting the lowest price gets all of this demand; in the event of a tie, the firms charging the lowest price share total demand equally Consequently, all firms earn zero supernormal profits in equilibrium, a result that has come to be known as the Bertrand paradox The paradox stems from the fact that, while a monopolist would earn strictly positive profits by charging a price in excess of marginal cost, it takes only two firms to completely dissipate the monopoly profits and achieve the competitive outcome In a Bertrand equilibrium, all transactions take place at marginal cost, and all firms earn normal zero profits Another way of thinking about it, a simpler way, is to imagine if both firms set equal prices above marginal cost, firms would get half the market at a higher than MC price. However, by lowering prices just slightly, a firm could gain the whole market, so both firms are tempted to lower prices as much as they can. It would be irrational to price below marginal cost, because the firm would make a loss. Therefore, both firms will lower prices until they reach the MC limit  Note

that colluding to charge the monopoly price and supplying one half of the market each is the best that the firms could do in this set up. However not colluding and charging marginal cost , which is the non-cooperative outcome is the only Nash equilibrium of this model. If one firm has lower average cost (a superior production technology), it will charge the highest price that is lower than the average cost of the other one (i.e. a price just below the lowest price the other firm can manage) and take all the business. This is known as "limit pricing“.

Critique of Bertrand Since the Bertrand model assumes that firms compete on price and not output quantity, it predicts that a duopoly is enough to push prices down to marginal cost level, meaning that a duopoly will result in perfect competition; Whereas in Cournot the competition based on quantities leads to effectively acting as a cartel and restricting output The

most critical flaw of the model is the assumption that firms compete in one period, the price being chosen and set forever. However, as it is unreasonable to expect the other firm to indefinitely keep higher prices and sell nothing, each firm must expect that lowering the price will almost immediately be met with the same move by the other firm, thus no firm can expect to get bigger market share by cutting price, and the preferred strategy is keeping prices at monopoly price level. The situation is analogous to the prisoner's dilemma, single-period version of which has completely opposite implications than the iterated version. It assumes firms compete purely on price, ignoring non-price competition. Firms can differentiate their products and charge a higher price. For example, would someone travel twice as far to save 1% on the price of their vegetables? There are rarely just two firms in a market. If a firm does undercut a rival and get full market share, it now has to supply the whole market; many firms would not have the capacity to do this. In general, the greater the overall capacity constraints, the higher the price is than marginal cost.

Perfect competition (Bertrand) vs Monopoly vs Cournot Given the same cost structures:

P = a − bQ and TCi = cqi In Perfect Competition:

P = MC ⇒ P = C ⇒ Q pc =

a −c b

In Monopoly:

Π = TR − TC Π = PQ − CQ Π = ( a − bQ ) Q − CQ Π = aQ − bQ 2 − CQ

Π = aQ − bQ 2 − CQ ∂Π = a − 2bQ − C = 0 ∂Q

2bQ = a −c a −c Qm = 2b P = a −bQ  a −c  P = a −b   2b  a +c PM = 2

Perfect competition (Bertrand) vs Monopoly vs Cournot Recall that in Cournot the respective prices and quantities were:

Q

CO

2 a−c =   3 b 

P CO =

a + 2c 3

In Perfect Competition:

Q

pc

a −c = b

P =c

< Q PC

Therefore : P M > P CO > P PC

In Monopoly:

Qm =

Therefore : Q M < Q CO

a −c 2b

PM =

a +c 2

intuitive sense , since more competition should lead to more output and lower p

Stackelberg competition Stackelberg ’ s duopoly : In this model the fir

ch Freiherr von Stackelberg who published Market Structure and Equilibrium ( 1934 )

The firms adopt a leader-follower relationship and they compete on quantity. Firms

may engage in Stackelberg competition if one has some sort of advantage enabling it to move first. The leader must know ex ante that the follower observes his action. The leader must have commitment power. Moving observably first is the most obvious means of commitment: once the leader has made its move, it cannot undo it - it is committed to that action. Moving first may be possible if the leader was the incumbent monopoly of the industry and the follower is a new entrant. Holding excess capacity is another means of commitment.  The

principal difference between cournot and stackelberg competition lies on the order of actions. While in Cournot competition firms choose simultaneously the quantity they produce, in Stackelberg competition, firms are deciding sequentially. Thus the leader firm has a strategic advantage since she knows how will react the follower. It follows that in Stackelberg competition the leader gets higher profit than in Cournot while it is the reverse for the follower.

Stackelberg competition Stackelberg ’ s duopoly : In this model the fir

ch Freiherr von Stackelberg who published Market Structure and Equilibrium ( 1934 )

The Stackelberg model can be solved to find the subgame perfect Nash equilibrium or equilibria (SPNE), i.e. the strategy profile that serves best each player, given the strategies of the other player and that entails every player playing in a Nash equilibrium in every subgame. The model is solved by backward induction. The leader considers what the best response of the follower is, i.e. how it will respond once it has observed the quantity of the leader. The leader then picks a quantity that maximises its payoff, anticipating the predicted response of the follower. The follower actually observes this and in equilibrium picks the expected quantity as a response. To calculate the SPNE, the best response functions of the follower must first be calculated TO UNDERSTAND HOW TO SOLVE STACKELBERG GAMES IT WOULD HELP IF YOU WENT OVER THIS GAME THEORY LECTURE focusing on the backward induction extensive form idea 



Algebraic example Two

competing firms, selling a homogenous good The marginal cost of producing each unit of the good: c1 and c2 Firm 1 moves first and decides on the quantity to sell: q1 Firm 2 moves next and after seeing q1, decides on the quantity to sell: q2 Q = q1+q2 total market demand The market price, P is determined by (inverse) market demand: P = a-bQ Both firms are profit-maximisers

Algebraic example Suppose

firm 1 produces q1 Firm 2’s profits, if it produces q2 are: π2 = Total revenue – total costs: 

∏2 = P.q2 − c2 .q2

∏2 = [( a − b(q1 + q2 )] − c2 q2

∏2 = ( P − c2 )q2 

Maximising

to 0.

   

this profit function involves finding the FOC and setting it

∂ ∏2 = a − 2bq 2 − bq1 − c2 ∂q2

Which

is effectively setting MR – MC = 0

(a − c2 ) q1 q2 = − This 2b 2

(or MR = MC)

is firm 2 ’ s BEST RESPONSE ( REACTION ) FUNCT

Algebraic example Firm   We

1’s profits, if it produces q1 are:

∏1 = ( P − c)q1 = [a − b(q1 + q2 )]q1 − c1q1 know that from the best response of Firm 2:

   

(a − c2 ) q1 q2 = − 2b 2

Substitute

q2 into π1:

 

(a − c2 ) q1 ∏1 = [a − b(From q1 +FOC: − )]q1 − c1q1 2b 2  

∂ ∏1 (a + c2 ) = − bq1 − c1 = 0 ∂q1 2

(a + c2 ) bq1 ∏1 = [ − − c1 ]q1 2 2 (a − 2c1 + c2 ) q1 = 2b

Algebraic example So

we have Firm 1’s profits, if it produces q1:



q1 =

  And

(a − 2c1 + c2 ) 2b

firm 2’s best response:

 

q2 =

 Therefore:

(a − c2 ) q1 − 2b 2

   If

(a − c) q1 = 2b

c1 =

(a + 2c1 − 3c2 ) c2q2= = c 4b (a − c) q2 = 4b

Q=

3(a − c) 4b

Bertrand vs Cournot vs Stackelberg Recall that in Cournot the respective prices and quantities were:

Q

CO

2 a−c =   3 b 

P CO =

a + 2c 3

In Bertrand they were:

Q

pc

a −c = b

P =c

In Stackelberg:

Q

m

3( a −c ) ( a −c ) ( a −c ) = =( + ) 4b 2b 4b

PM =

( a +3c ) 4

Firm output / prices : Bertrand ≤ Stackelberg ≤ Cournot ≤ Monopoly

AN INTRODUCTION TO OLIGOPOLY

Topic : Oligopoly tutor2u ; Mo Tanweer; [email protected]