Chapter 13Chapter 13Oligopoly

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Objectives

Explain how managers of firms that operate in an oligopoly market can use strategic decision-making to maintain relatively high profitsUnderstand how the reactions of market rivals influence the effectiveness of decisions in an li l k toligopoly market

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4. Oligopoly

A market with a small number of firms (usually big)Oligopolists “know” each other Characterized by interdependence and the need for managers to explicitly consider the reactions of rivalsProtected by barriers to entry that result from government fiat, economies of scale, or control of strategically important resources

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Strategic interaction

Actions of one firm will trigger re-actions of othersOligopolist must take these possible re-actions into account before deciding on an actionTherefore, no single, unified model of oligopoly exists

CartelPrice leadershipBertrand competitionC t titiCournot competition

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Stages of evolutiong

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Market introduction and growth

New technology high uncertainty innovatorsNew technology, high uncertainty, innovators profit

Product is new, no close substitutes,Learning curve is steepTemporal monopoly in the market possiblep p y pBut high set-up costs What market is most receptive of the

dproduct?Strategic decisions about market introduction

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Maturity and decline

No more growth of the marketProduct gets more homogeneousPrice (and service) get more importantPrice (and service) get more importantPrice competition (oligopoly)p ( g p y)

O it j i di t fOvercapacity ==> major ingredient for price wars

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Cartels

The small number of firms in an oligopoly market tends to encourage cooperative behavior (collusion).behavior (collusion).

Increase profitsDecrease uncertaintyDecrease uncertaintyRaise barriers to entry

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Cartels

Adam Smith (1776): people of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the public, or in some contrivance to raise p y g p ,prices

Incentive to collude: recall the newspaper industry in DetroitChange in profits: each lost about 10 Mill. a year, afterwards profits were high as 150 Mill.

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Cooperative behavior

Cartel: A collusive arrangement made openly and formallyformally

Cartels, and collusion in general, are illegal in the US and EU.Cartels maximize profit by restricting the output of member firmsCartels maximize profit by restricting the output of member firms to a level that the marginal cost of production of every firm in the cartel is equal to the market's marginal revenue and then charging the market clearing pricecharging the market-clearing price.The need to allocate output among member firms results in an incentive for the firms to cheat by overproducing and thereby increase profit

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Cartel: A collusive agreementCartel: A collusive agreement made openly and formally

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CartelCartels act like multiplant monopolies.Profit of cartel is maximized if marginal costs among members of cartel are equalizedW ld th t hi h t fi d lWould mean that high-cost firms produce less

firms may still agree on equal quotasuse of side paymentsuse of side payments

ExamplesLysine (The informant!), DRAM industry, US school milk markets,Lysine (The informant!), DRAM industry, US school milk markets, elevators, Lombard clubOPEC, Coffee cartel

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Worker unions, Firm associations

Cartel as a multi-plant monopoly

PRICE

MC1 MC

MCSupplyD1 MC2

D

MR

Q1 Q2 TOTAL OUTPUT

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FIRM 1 FIRM 2

CartelInstability of cartel: incentive for members to cheat

I i bi f ll bIncentive biggest for small members

If a firm deviates it gets the total market at least for one periodperiod

Break down of the cartel

DeviatorDeviator compares profits from one-time deviating + profits from competition further after with profits from collusion

Decision whether to deviate

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Instability of Cartel: demand curve gets much flatter (D‘)demand curve gets much flatter (D )

We started at Price P0

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Problem 1The Bergen Company and the Gutenberg Company are the only two firms that produce and sell a particular kind of machinery. The demand curve for their

d t iproduct isP = 580 – 3Q

where P is the price of the products, and Q is the total amount demanded.

The total cost function of the Bergen Company isTCB = 410 QB.

The total cost function of the Gutenberg Company is TCG = 460 QG.

a) If these two firms collude, and if they want to maximize their combined profits, how much will the Bergen Company produce?

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b) How much will the Gutenberg Company produce?

Solution Problem 1a) Bergen’s marginal cost is always less than Gutenberg’s marginal cost. Therefore Bergen would produce all the combination’s output. Setting g p p gBergen’s marginal cost equal to the marginal revenue derived from the demand function, we get:410 = 580 – 6Q => QB = 28.33 and QG = 0.

b) If Gutenberg were to produce one unit and Bergen one unit less, it would reduce their combined profits by the difference in their marginal

tcosts.

If direct payments of output restrictions between the firms were legal, G tenbe g o ld a ept a e o o tp t q ota B t if ompetition e e toGutenberg would accept a zero output quota. But if competition were to break out, Gutenberg would make zero profits and Bergen would earn $2,000. Thus the most Bergen would pay for Gutenberg’s cooperation is $408.33 and the least Gutenberg would accept to not produce is $0.01.

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$408.33 and the least Gutenberg would accept to not produce is $0.01.

Price Leadership by a dominant firmPrice Leadership by a dominant firm

In oligopolistic industries managers at one firm mayIn oligopolistic industries, managers at one firm may have significant market power and can set their price.Industry is composed of a large dominant firm andIndustry is composed of a large, dominant firm and many small firms, big firm has cost-advantageBig firm can behave as a monopolist, small firms makeBig firm can behave as a monopolist, small firms make no super-normal profits

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AssumptionsAssumptions

One firm sets price and others followThere is a single firm, the price leader, that sets price in the market.There is a single firm, the price leader, that sets price in the market.There are also follower firms who behave as price takers, producing a quantity at which marginal cost is equal to price. Their supply curve is the horizontal summation of their marginal cost curvescurve is the horizontal summation of their marginal cost curves.The price leader faces a residual demand curve that is the horizontal difference between the market demand curve and the followers' supply curve.The price leader produces a quantity at which the residual marginal revenue is equal to marginal cost Price is then set to clear therevenue is equal to marginal cost. Price is then set to clear the market.

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ExamplesExample 1: Price cuts for breakfast

In April 1996 the Kraft Food Division of Philip Morris cut prices onIn April 1996, the Kraft Food Division of Philip Morris cut prices on its Post and Nabisco brands of breakfast cereal by 20 percent as demand stagnatedMarket shares: PM 16 20 Kellog: 36 32Market shares: PM 16 20, Kellog: 36 32

Example 2: CranberriesMarket is dominated by a giant growers’ cooperativeMarket is dominated by a giant growers cooperativeOcean Spray has 66 percent market share and sets prices each year in fall based on anticipated and actual supply and demand conditionsconditionsBased on this price other firms decide on how much they wish to harvest for sale, for inventory, but for use in other products or leave in the bogs

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leave in the bogs

How can a few firms compete pagainst each other?

Many different models

Some simplifying assumptions:

Identical product2 firms (can easily be extended to more)Same (constant) cost functionsK th (li ) d d f tiKnow the (linear) demand functionFirms act simultaneously

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Price (= Bertrand) Competition

Total costs: Market demand:

25 0 0 4 0 .5i i iT C q q= + +

100 100P +Market demand: 100 100 A BP q q q= − = − +

4M C q= +

WTP for first unit = 99, MC = 5If firm A would set price at 98, firm B would set price to 97 …

4i iM C q= +

If firms compete over prices, they would go down to marginal costsP = Q =Q =

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Example: Collusion (cartel)

Calculate price, quantity and profit for a collusion in this examplecollusion in this example

Add up marginal costs horizontally

4 4 8 2A B A BQ q q MC MC MC= + = − + − + = − +

42QMC = +

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Cournot-Nash Duopoly

Quantity (capacity) competitionTaking the other‘s output as given, what output is optimal for firm X?output is optimal for firm X?Series of “What if?” questions necessary

for each potential output of the rival you must have a potential answerpActual decision taken by assuming what rival will actually do

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will actually do

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Finding the reaction curves

Reaction curve: given the output of X, what output of Y is optimal?Of course, whatever Y does, will produceOf course, whatever Y does, will produce further reactions, i.e. X is not constant in general.general.Equilibrium only when both firms „sit“ on their reaction curves: no surprises and notheir reaction curves: no surprises and no incentive to alter the behavior

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Cournot-Nash DuopolyFirms are competing in quantitiesA th t fi t iAssume that firms are symmetric:

MC(A) = 4 + q(A) MC(B) = 4 + q(B)MC(B) 4 + q(B)

Industry demand: Q = 100 – P

Calculate reaction curves and optimal outputs and prices

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Cournot-Nash DuopolyP = 100 – Q = 100 – (q(A) + q(B))

TR(A) = P x q(A) = (100 – q(A) – q(B)) x q(A)MR(A) 100 2q(A) q(B) 4 + q(A) MC(A)MR(A) = 100 – 2q(A) – q(B) = 4 + q(A) = MC(A)96 – q(B) = 3 q(A)q(A) = 32 – 1/3 q(B) reaction curve of firm Aq(A) = 32 – 1/3 q(B) reaction curve of firm A

q(B) = 32 – 1/3 q(A) reaction curve of firm Bq(B) 32 1/3 q(A) reaction curve of firm B

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Cournot-Nash Duopoly

I t ti ti l t t f b th fiIntersection: optimal output for both firmsq(A) = 32 – 1/3 (32 – 1/3 q(A))q(A) 32 1/3 32 + 1/9 q(A)q(A) = 32 – 1/3 32 + 1/9 q(A)q(A) = 24q(B) = 24q(B) = 24Q = 48 and P = 100 – 48 = 52

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Example: comparison

2 fi th t i i th i fit (i) i A B2 firms that maximize their profits π(i), i=A,Bmarginal cost are constant: MC(i) = 4 and Demand is linear: P = 100 – QDemand is linear: P 100 Q

Bertrand: p = 4, Q = 96 and π(i) = 0Cournot: calculate reaction functions

MR(A) = 100 – 2q(A) – q(B) = 4 = MC(A)q(A) = q(B) = 32, Q = 64, P = 36 and π(i) = (36 - 4)32 = 1024

M l MR MCMonopoly: MR = MCQ = 48, P = 52 and π(i) = (52 - 4)48 = 2304

Cartel: firms divide profits π(i) = 1152

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Cartel: firms divide profits π(i) = 1152

Problem 2The International Air Transport Association (IATA) has been composed of 108 U S and European airlines thatbeen composed of 108 U.S. and European airlines that fly transatlantic routes. For many years, IATA acted as a cartel: it fixed and enforced uniform prices.

a) If IATA wanted to maximize the total profit of all b i li h t if i ld it h ?member airlines, what uniform price would it charge?

b) How would the total amount of traffic be allocated among the member airlines?among the member airlines?c) Would IATA set price equal to marginal cost? Why or why not?

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y

Solution Problem 2a) The IATA would charge the price that clears the

market at the level of output where marginal revenuemarket at the level of output where marginal revenue equals the horizontally summed marginal cost curves of each operator in the market.

b) The traffic should be allocated so that the marginal costs of all the members operating in the market

ld b l d th t b t tl iwould be equal and that no member not currently in the market would have a lower marginal cost.

c) No, the IATA would set a price equal to marginal cost multiplied by 1/(1+1/e) where e is the elasticity of demand in the market in question.

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q

Problem 3In Britain price competition among bookshops has been suppressed for over 90 years by the Net Book Agreement (of 1900), which was aimed at the prevention of price wars However in October 1991aimed at the prevention of price wars. However, in October 1991, Waterstone and Company began cutting book prices at its 85 British shops. According to Richard Barker, Waterstone’s operations director, the decision to reduce the price of about 40 titles by about 25% was d b ll ’ l ldue to price cuts by Dillons, Waterstone’s principal rival.

a) According to the president of Britain’s Publishers Association, the i i “ i ” h ill “dprice-cutting was “an enormous pity” that will “damage many

booksellers who operate on very slim margins. Does this mean that price-cutting of this sort is contrary to the public interest?

b) Why would Dillons want to cut price? Under what circumstances would this be a good strategy? Under what circumstances would it be a mistake?

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a mistake?

Solution Problem 3a) No. A price war, although always “an enormous pity”

for producers usually is very good news forfor producers, usually is very good news for consumers.

b) If demand is elastic at high prices, and if Dillons has a comparative advantage with respect to its rivals at high volumes it may prefer a low competitive pricehigh volumes, it may prefer a low competitive price to a high collusive one. If demand is inelastic, of if Dillons does not have a comparative advantage over it i l t hi h l it b i t k t tits rivals at high volumes, it may be a mistake to cut prices.

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Product Differentiation

Vertical differentiation: qualityconsumers have uniform preferences

Horizontal differentiation: design, g ,location,…

consumers have different preferences

by differentiation product gets uniqueby differentiation product gets uniquesmall monopoly can be constructed

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DUOPOLOLISTS AND PRICE COMPETITION WITH DIFFERENTIATED PRODUCTS

Bertrand model

Example: Two producers who sell differentiated but highly substitutable products

Assume MC 0 for both firmsAssume MC = 0 for both firmsDemand for firm 1's product: Q1 = 100 – 3P1 + 2P2

Demand for firm 2's product: Q2 = 100 – 3P2 + 2P12 2 1

Total revenue for firm 1: TR1 = P1(100 – 3P1 + 2P2) = 100P1 – 3P1

2 + 2P1P2TR1 = TR11 + TR12 where TR11 = 100P1 – 3P1

2 and TR12 = 2P1P2

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DUOPOLOLISTS AND PRICE COMPETITION WITH DIFFERENTIATED PRODUCTS

Example: Two producers who sell differentiated but highly substitutable products

Marginal revenue for firm 1: MR1 = ΔTR1/ΔP1 = (ΔTR11/ΔP1) + ( TR / P )(ΔTR11/ΔP1)MR1 = 100 – 6P1 + 2P2

Bertrand reaction function for firm 1: MR = MC1 = 0: 100 – 6P1 + a d a o u o o 1 0 00 6 12P2 = 0 => P1 = (50/3) + (1/3)P2

Bertrand reaction function for firm 2: MR = MC2 = 0: 100 – 6P2 + 2P = 0 => P = (50/3) + (1/3)P2P1 = 0 => P2 = (50/3) + (1/3)P1

Solving the two reaction functions simultaneously yields: P1 = P2= $25, q1 = q2 = 75, π1 = π2 = $1,875.

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DUOPOLOLISTS AND PRICE COMPETITION WITH DIFFERENTIATED PRODUCTS

Example: Two producers who sell differentiated but highly substitutable products (Continued)highly substitutable products (Continued)

Bertrand reaction function for firm 2: MR = MC2 = 0: 100 6P 2P 0 P (50/3) (1/3)P100 – 6P2 + 2P1 = 0 => P2 = (50/3) + (1/3)P1

Solving the two reaction functions simultaneously yields: P = P = $25 q = q = 75 π = π = $1 875yields: P1 = P2 = $25, q1 = q2 = 75, π1 = π2 = $1,875.

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Hotelling Model

consumers (and shops) located along a line (Linz - Landstrasse)consumers would like to shop at theconsumers would like to shop at the nearest shops (transport is costly)linear model:

here locationdifferentiation can often be analyzed using line segments

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Linear Model, prices are the , psame

L RR

These customers buy from L These customers buy from R

Firm L Firm R

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Setting Prices Icost of moving from L to R is csuppose a customer sits at a point that is the fraction x of the way from L to RpL, pR

customer pays: if shopping at L(1 ) if shopping at R

L

R

p xcp x c

++ −

and shops wherever cheaper

( ) pp gRp

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and shops wherever cheaper

Setting Prices IIMarginal customer x* who is indifferent

R * p (1 *) =>1

Lp x c x cp p

+ = + −1* 2 2

R Lp pxc−

= +

if pR = pL ... marginal customer in the middleif pR > pL ... L has more customers if c is small => small price change results in big sales gains, product hardly differentiated

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Setting Prices IIIdisregard production costsL maximizes pLx* (revenue): 1( )

2 2R L

Lp pp Max−

+ →

*

( )2 2

1 ( )2

LL p

L R

pc

p c p= +

if transport cost (differentiation) increases => pLif pR increases => pL

2L R

similarly for firm R: * 1 ( )2R Lp c p= +

Only partial response to price increase of competition

=>* *L Rp p c= =

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=> profits increase the higher differentiation is

L Rp p c

Choice of location Isimplify: hold prices constant

L R

by moving right market share increasesby moving right, market share increases

both firms will locate in centerboth firms will locate in center

analogy to political parties47

analogy to political parties

Choice of location II

if prices are flexible, it pays to be distant

by moving away prices can rise for Lby moving away prices can rise for Las a reaction competitor R will raise prices as wellis beneficial for firm Lis beneficial for firm L

t d ff diff ti titrade-off: more differentiation meansbeing close to customers is also close to competitors

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competitors