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ECONOMICS 3200BLecture 6Ch. 6, 7

October 22, 2013

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Oligopoly

Cournot competition

• Duopoly case

• Homogeneous products, single instrument – Qi (quantity produced by each firm)

• Demand function: P(Q) = 1 – Q = 1- Q1 – Q2

• Ci (Qi) = Ci Qi (constant returns), where C1 C2

• Firm 1:– Max 1 (Q1, Q2) = Q1 (1- Q1 – Q2) – C1 Q1

– d 1 /d Q1 = 1- 2 Q1 - Q2 - C1 = 0

– Reaction function for firm 1: Q1 = [1- Q2 - C1]/2 = R1 (Q2)

– Strategic substitutes since d Q1/d Q2 < 0

– Reaction function for firm 2: Q2 = [1- Q1 – C2]/2 = R2 (Q1)

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Oligopoly

Cournot competition• Nash equilibrium: solve by equating reaction functions:

– R1 (Q2) = R2 (Q1)– Q1* = [1 + C2 – 2C1 ]/3

– Q2* = [1 + C1 – 2C2 ]/3

• P* = [1 + C1 + C2 ]/3 1* = [1 + C2 – 2C1 ]2/9 2* = [1 + C1 – 2C2 ]2/9

• If C1 < C2 1 > 2

• With symmetric costs and N firms [Ci = C]– Qi* = [1 - C]/(N+1)– P* = [1+ NC]/(N+1)– As N increases, Qi* decreases, P decreases towards C and the profit for each firm

decreases towards 0

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Q1

Q2

1

Q2 = R2 (Q1, C2)

Q1 = R1 (Q2, C1)

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Oligopoly

• In monopoly (if no X-inefficiency), Bertrand competition and perfect competition models, production occurs at lowest cost– Higher cost producer cannot survive

• With Cournot competition, higher cost producer can survive

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Oligopoly

Stackelberg competition

• Firm 1 is the leader and firm 2 is the follower – why?

• Firm 1 knows firm 2’s reaction function – assume same demand and cost conditions as in Cournot example

• Firm 1:

– Max 1 (Q1, Q2) = Q1 (1- Q1 – Q2) – C1 Q1

– Q2 = [1- Q1 – C2]/2 = R2 (Q1)

Max 1 (Q1) = Q1 (1- Q1 + C2)/2 – C1 Q1

– d 1 /d Q1 = 0.5- Q1 + 0.5C2 - C1 = 0

– Q1* = [1 + C2 – 2C1 ]/2 > Q1* (Cournot) = [1 + C2 – 2C1 ]/3

– Q1* (follower) < Q2* (Cournot)

– Leader has higher profits than in Cournot game – Firm 1 a leader most likely because it ahs lower costs

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Q1

Q2

N

Q2 = R2 (Q1, C2)

Q1 = R1 (Q2, C1)

S

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Oligopoly

• Equilibrium prices (highest to lowest)– Monopoly/Infinite period repeated duopoly

– Cournot duopoly

– Stackelberg duopoly

– Competition/Bertrand duopoly/Single game duopoly

• Extensions:

• (1) Bertrand with sunk costs, firm 1 incumbent, firm 2 potential entrant– Unless potential entrant has a cost advantage, firm 2 anticipates that

incumbent will lower price to eliminate economic profits (firm 1 will ignore its sunk costs in setting price in response to entry: P < AC where AC includes sunk costs), so firm 2 will not invest ex ante in what will become sunk costs ex post because it will not be able to earn competitive return on investment

– First mover advantage with sunk costs

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Oligopoly

• Extensions:

• (2) Stackelberg with capacity constrain for leader

– If leader (firm 1) does not have capacity to produce Q1* = [1 + C2 – 2C1]/2, firm 1 will produce up to its capacity

– Resulting equilibrium: pt. 2 in following

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Q1

Q2

N

Q2 = R2 (Q1, C2)

Q1 = R1 (Q2, C1)

S

2

SQ1

2Q1

NQ1

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Oligopoly

• Extensions:

• (3) Repeated game Bertrand– Cooperation with P=PM , and monopoly profits shared

– Competition shifts away from prices to other strategies involving instruments that cannot be easily detected or imitated

• Research

• Marketing, sales

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Oligopoly

Examples of non-cooperation• Overcapacity

• Price wars

• Advertising

– Fixed end-point – financially weak competitor• Lobbying to change bankruptcy laws to make it more difficult to exit

• Aggressive pricing

• Rumors

• Banks unwilling to lend to weak financial institutions

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Oligopoly

Factors facilitating cooperation• Competition law

• No leader

• Low costs for detecting cheating– Small numbers, homogeneous product, transparency in pricing

• Expected benefits

• MAD strategy

• Contracts– Most favored nation clause

– Meet the competition

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Oligopoly

Competition shifts to difficult to detect, time-consuming to respond strategies

• Product innovations/introductions

• Marketing

• Lobbying

• Production technology innovations

• Exclusive contracts – suppliers, distributors

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Oligopoly

• Oligopoly markets generally consist of one to three dominant firms and several smaller firms– Wireless market in Canada

– Rail transportation

• Dominant position may not survive over time

• How does a firm become dominant – see discussion regarding how a monopoly develops

• Why doesn’t dominance survive?– Consider case of Canadian steel companies (Dofasco, Stelco,

Ipsco, Algoma) and Arcelor Mittal

– RIM, Blockbuster, Nokia, GM, PanAm, Sears, Groupon, Merrill Lynch, Xerox, Kodak, Nortel, etc.

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Hollowing Out

• Canadian companies acquired by foreign companies:– Inco; Falconbridge; Dofasco; Ipsco; Stelco; Algoma; Masonite;

ATI; Moore; Four Seasons; Fairmont Hotels; The Bay; Domtar; Alcan; Molson’s; Labatt’s; Vincor; Future Shop; Nexen

• Definition of hollowing out:– As Canadian-owned, Canadian-headquartered companies are

bought up by foreigners, head-office jobs, capital markets listings, corporate tax revenues, and charitable donations are disappearing potentially resulting in the hollowing out of Canada’s economic sovereignty

– Not a Canadian phenomenon alone

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Hollowing Out

• Debate– Causes – government policies or management?

• In a spiky world, firms either globalize or eventually get swallowed up by a globalizing corporation, typically headquartered elsewhere

• Canadian managers that ignore this reality are fooling themselves and selling Canada short (Roger Martin and Gordon Nixon)

– Good or bad for Canada – employment, productivity, standard of living

– Policies: corporate taxation; screening foreign takeovers; regulations; inter-provincial trade barriers; human capital; infrastructure; subsidies

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Hollowing Out

• Michael Porter: explained why entire global industries were often headquartered in a single country if not a single region within a single country

• Set of conditions in local market creates a cluster of competitive companies that pressure each other to innovate and upgrade, teach local customers to be ever-more demanding, draw in and develop human resources, and attract co-location of helpful related and supporting industries – external economies of scale

• Result: cluster that keeps getting better and better and, on the basis of that beneficial local competition, helps its members succeed internationally against competitors from elsewhere who don't have the power of a strong local cluster behind them

• Porter's theory predicts a spiky world in which most of the successful competitors in a global industry come from very few places and export to the rest of the world

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Hollowing Out

• Increasing favorable trade conditions and falling transportation and communications costs combine to make globalizing more of a reality as leading national firms find themselves pressured by capital markets to expand globally rather than stay at home

• Research and development-intensive firms find that the only way they can afford to invest in competitive technological solutions is to utilize the scale economies of a global market

• Transformation proceeding in one direction only – to a spikier world in which all the globally competitive firms in all industries are headquartered in a limited number of locations

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Monopolistic Competition

• Product differentiation– Product consists of bundle of characteristics – quality, location, color,

time of availability, etc.

– Computers, laptops, clothing, air travel

• Firms have some degree of market power

• Standard model

– Free entry may drive profits to 0, at least for marginal firms in market

– Definition of industry/market?

– Critical value for cross-price elasticity of demand?

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Monopolistic Competition

• Vertical differentiation model – characteristic: quality

• Quality (S): S [0, 1]– Consumers agree over most preferred mix of characteristics and over

preference ordering: S1 > S2 implies that quality S1 exceeds quality S2 and higher quality preferred over lower quality

– Consumers have perfect information regarding quality

– Value (utility – U) to consumer: U = S – P

• Model:– Consumer buys if U > 0 S > P

– Does not buy if U 0 S P

– Distribution of tastes ( ) across all consumers: F(), where F(min) = 0 and F(max) = 1

– F(0): proportion of all consumers with taste parameter [0, 0]

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Monopolistic Competition

Case 1

• 2 products with qualities S1 > S2 and P1 > P2

• Assume:– S1/P1 > S2/P2 S1/P1 > S2/P2

• Consumers will prefer the higher quality product if: S1 – P1 > S2 – P2 and

S1 – P1 > 0

• Since S1/P1 > S2/P2 then:

– [ S1/P1 – 1] > [ S2/P2 – 1]

– P1[ S1 – P1] > P2[ S2 – P2]

– Since P1 > P2 , consumers prefer higher quality product

– Product differentiation, but only high quality variety of product is produced and sold

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Monopolistic Competition

Case 2

• 2 products with qualities S1 > S2 and P1 > P2

• Assume:– S1/P1 < S2/P2 S1/P1 < S2/P2

• Consumers will prefer the higher quality product if: S1 – P1 > S2 – P2 and

S1 – P1 > 0

• Since S1/P1 < S2/P2 then:

– [ S1/P1 – 1] < [ S2/P2 – 1]

– P1[ S1 – P1] < P2[ S2 – P2]

– Since P1 > P2 , consumer preference indeterminate

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Monopolistic Competition

Case 2

• Critical value for separates consumers into two groups: one group prefers S1 { S1 – P1 > S2 – P2} and the other prefers S2 { S1 – P1 < S2 – P2}

• Critical value (*):– Consumers indifferent when: S1 – P1 = S2 – P2

– * = [P2 – P1]/[S1 – S2]

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Monopolistic Competition

Case 2

• When > *, consumer prefers higher quality variety (S1)

– Demand for high quality product: consumers with [(P2 – P1)/(S1 – S2), max]

– Aggregate demand: D(S1, S2, P1, P2) = N[1-F((P2 – P1)/(S1 – S2))]

– D(S1, S2, P1, P2) increases if S1 increases, S2 decreases, P1 decreases and/or P2 increases

• When < *, consumer prefers lower quality variety (S2)

– Demand for low quality product: consumers with [P2/ S2, (P2 – P1)/(S1 – S2)]

– Aggregate demand: D(S2, S1, P1, P2) = N[F((P2 – P1)/(S1 – S2)) – F(P2/ S2)]

– D(S2, S1, P1, P2) increases if S1 decreases, S2 increases, P1 increases and/or P2 decreases

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Monopolistic Competition

• Location model – example of differentiation

• Different locations represent different varieties of a product– Varieties differentiated by geographic location or other characteristics

• Consumers have preferred location/characteristics for a product– For given price, utility maximized at preferred location

– Utility declines as actual product location differs (moves farther away) from preferred location

• To make problem manageable, focus on one characteristic

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Monopolistic Competition

Hotelling model

• Horizontal differentiation – location (nearness in terms of product characteristics other than quality) matters

• Transportation cost – disutility of choice/location different from preferred choice/location: T per unit of “distance”

• Competition drives two firms to locate at same place/location if consumers uniformly distributed (tastes regarding preferred locations) along product/geographic space– No product differentiation

• Identical location result reinforced if consumers normally distributed along product/geographic space– Largest concentration of consumers around mean of distribution

• Identical location – homogeneous products, Bertrand price competition

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Monopolistic Competition

Hotelling model

• Assume two firms locate at end-points (maximize product differentiation) to minimize price competition/maximize market power

• Product differentiation establishes clienteles (market niches) and allows firm to enjoy some market power over clientele

• 2-stage game: firms choose location (anticipating outcome of price competition), then firms simultaneously chooses prices– Optimal location at end-point of 2-dimensional geographic space (straight

line)

– Consumers located at X [0, 1] – total cost to each consumer of two products located at respective end-points

• Product at 0: P0 + TX

• Product at 1: P1 + T(1-X)