kilpailu- ja yhtiöoikeuden taloustiede

Markku Stenborg: Kilpailu- ja yhtiöoikeuden taloustiede 1

Joensuu 2004

Kilpailu- ja yhtiöoikeuden taloustiede

• Teacher: Markku Stenborg, PhD (Penn State)– Research Fellow, ETLA, http://www.etla.fi/

• Innovation, regulation, and the changing terms of competition in wireless telecommunications funded by Nokia and Tekes, http://brie-etla.org/

• Economics of OSS– Senior Research Scientist, HIIT, http://www.hiit.fi

• Managing Privacy and Trust in Mobile P2P– Consultant at CEA– Previously

• Assistant Prof with Turku Business School• Senior Adviser at Finnish Competition Authority• Senior Manager at KPMG Transaction Services

– email: [email protected]– During this week: room M 12 (3rd floor, “Optimi”)


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• Course homepage: http://www.cea.fi/joe.htm• This course covers theoretical and empirical issues related to

Economics of strategic competition and competition policy:– Price and non-price competition– Strategies to affect competition– Market delineation– Dominance– Mergers– Cartels and coordination of market conduct– Vertical restrictions

• Focus more on Economics, less on Law



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• No textbook, but we will look at some papers and EU and Finnish notices and cases

• Some useful reading:– Aalto-Setälä et al. (2003) Kilpailulait ja laki julkisista

hankinnoista, 3rd ed. (or 2nd ed., 2001)– Besanko, Dranove,& Shanley (2000) Economics of Strategy– Cabral (2000) Introduction to Industrial Organization– Carlton & Perloff (2000) Modern Industrial Organization– Church & Ware (2000) Industrial Organization: Strategic

Approach– Motta (2004) Competition Policy: Theory and Practice– Whinston (2003) Lectures on Antitrust Economics, draft at

http://www.csio.econ.nwu.edu/• I assume you have grasp of basic Economics concepts such as

demand, marginal benefit and cost, supply, efficiency, surplus, …



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Luennot• ma 13.9. klo 16-20, sali B6• ti 14.9. klo 10-14, sali MA155• ke 15.9. klo 14-18, sali MA155• to 16.9. klo 10-14, sali B6• pe 17.9. klo 10-14, sali MA155Final exams• Ke 29.9. klo 12-16, sali K4• Ti 12.10. klo 14-18, sali K4• 2+2 questions, 1+1 answers• One case, one more technical question• Two straightforward explanations• Prize: best student receives Aalto-Setälä et al. Kilpailulait ja laki

julkisista hankinnoista, 3rd ed, Tietosanoma 2003.



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1. History and objectives of competition policy• Introduction and objectives for competition policy

– Suggested reading: Motta, Ch 1, Kovacic and Shapiro (1999) “Antitrust Policy: A Century of Economic and Legal Thinking”, UC Berkeley, Working Paper No. CPC99-09

2. Market power and welfare• Market power, allocative and productive efficiency• Competition policy and innovation• Market power and entry

– Aalto-Setälä et al. Ch 8.1-23. Market delineation and market power • Product and geographic market definition• How to measure market power

– Aalto-Setälä Ch 7; US Merger Guidelines, http://www.usdoj.gov/atr/public/guidelines/hmg.htm, Section 1 "Market Definition"

– Case: Commission's Volvo/Scania decision

Course Outline


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4. Oligopoly, cartels and tacit collusion• How oligopolists compete• What is collusion• Factors that facilitate collusion• Ex-ante and ex-post measures to fight collusion

– Aalto-Setälä Ch 5.1-2; Stenborg (2004) “Forest for the Trees: Economics of Joint Dominance”; Europe Economics (2001) “Distinguishing between Competitive and Dominant Oligopolies in Merger Control”

5. Horizontal mergers• Incentives to merge• Competitive and welfare effects of mergers• Which variables matter? How to deal with merger cases?

– Aalto-Setälä Ch 15; Epstein and Rubinfeld (2001), “Merger Simulation: A Simplified Approach with New Applications”, Antitrust Law Journal;

– Case: Commission's UPM/Haindl and Volvo/Scania decisions

Course Outline


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6. Vertical restraints• Vertical externalities: double marginalization• Vertical restraints to internalize externalities• Welfare effects of vertical restraints• Foreclosure: exclusive dealing and other instruments

– Aalto-Setälä Ch 9.1-2; Dobson & Waterson (1996) “Vertical Restraints and Competition Policy”, OFT Research Paper 12

– Case: 7. Predatory practices• Predatory prices: long-purse, reputation, financial market effects• Tests of anti-competitive behavior

– Aalto-Setälä Ch 8.1-2, 8.4.7;– Grout (2001) “Recent Developments in the Definition of

Abusive Pricing in European Competition Policy”, http://www.bris.ac.uk/Depts/CMPO/workingpapers/wp23.pdf

– Case:

Course Outline


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1. Intro: Competition Law and Policy

• Why do we need competition law and policy?– Economic competition is self-steering process that guides

production, distribution, pricing, etc. decisions– Competition is an efficient way to organize many activities in

society• Efficient ≈ Pareto optimal: maximize well-being or surplus

generated by production and exchange, from assets possessed in society

– Allocative efficiency– Productive or X-efficiency– Dynamic efficiency

– Market power and restraints on competition• reduce efficiency and/or• restrict and disturb self-guiding process on markets


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Goals of competition laws• Promote efficiency?

– Obviously, …– … but with nonprice competition simple formulas for

efficiency (consumer surplus + producer surplus) are deceptive and misleading

• What is efficiency?– Do not strive for perfect competition but promote ”workable

competition”– With non-price competition, consumer welfare becomes multi-

dimensional • Customers have preferences over quality, speed and

security of supply, introduction of new products and services, etc.

• These may not be measurable• And even if they are measurable, value judgments are

necessary for efficiency analysis


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• Protect economic freedom and opportunity by promoting competition, so that competition can create– lower prices– better quality– greater choice– more innovation

• Sometimes competition laws have also other goals:– In EU, competition laws are used to promote single market

within EU– Competition laws also protect SMEs in some cases– These other goals can conflict with the main goal of protecting

economic freedom and opportunity


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1.1 Competition Laws

1. Restrictions on Competition• Article 81(1) of EU Treaty states that

”agreements between undertakings, decisions by associations of undertakings and concerted practices […] which have as their object or effect the prevention, restriction or distortion of competition within the Common Market” [shall be prohibited]

– Article 81 covers much more than formal cartel arrangements

– Not only collusion, but also many beneficial forms of horizontal and vertical cooperation are prohibited

• Browse (http://www.europa.eu.int/comm/competition/):

– Guidelines on the applicability of Article 81 of the EC Treaty to horizontal cooperation agreements

– The Competition rules for supply and distribution agreements – Guidelines on Vertical Restraints


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2. Abuse of Market Power• Article 82 states that

”Any abuse […] of a dominant position […] shall be prohibited […]. Such abuse may, in particular, consist in:

imposing unfair purchase or selling prices or other unfair trading conditions;limiting production, markets or technical development to the prejudice of consumers;applying dissimilar conditions to equivalent transactions with other trading parties, thereby placing them at a competitive disadvantage;making the conclusion of contracts subject to acceptance by the other parties of supplementary obligations which, by their nature or according to commercial usage, have no connection with the subject of such contracts.”

• Read “määräävän markkina-aseman väärinkäyttö” at http://www.kilpailuvirasto.fi/


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Per se and rule of reason• Per se: conduct is prohibited if it fulfills the legal test regardless

of other issues• Rule of reason: conduct is prohibited if its negative consequences

outweigh the positive• Articles 81 and 82 of EU Treaty seem to be per se• But to prove that firm has abused its dominant position,

authorities must– show that the firm has dominant position– conduct was abusive– In practice, Article 82 has flavor of rule of reason analysis

• Article 81(1) does not apply to insignificant restrictions• Article 81(3) and Commission Notices exempt various restrictions

– Article 81(1) also has flavor of rule of reason


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• In some legal systems, many vertical restraints are dealt with rule of reason– Eg. previous Finnish law

• A priori, effects of vertical restraints to competition and efficiency are ambiguous– Many vertical restraints are solutions to problems, not

problems for competition• Vertical restraints can align private incentives in supply

and distribution• Double marginalization (two vertical monopolies)

– Hence the Block exemptions


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3. Merger review

• Transactions that lead to increase in market power or to some other competition problems may be prohibited

– Illegal to monopolize markets by M&As

• In EU”A concentration which would significantly impede effective competition […] in particular as a result of the creation or strengthening of a dominant position, shall be declared incompatible with the common market.”

– EU previously had pure dominance-test

• US: ”the effect of such acquisition may be substantially to lessen competition, or to tend to create a monopoly”

– Usually, SLC-test poses lower threshold for intervention

– Monopoly is US legal jargon dominant position monopoly in Economics textbooks


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1.2 Market Power in Case Law

• Read Motta, Ch 2 & 3, and Volvo/Scania decision, Market Definition section pp 5-21

Assessment of market power in abuse and merger cases

1. Define relevant antitrust markets

2. Evaluate market power within the relevant markets

• Relevant markets are defined basically by demand substitution

– Only those goods that provide immediate and intense competitive constraints to each other belong to the same relevant market

– In some instances, also supply substitution and entry by potential competitors are taken into account in market delineation


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1.2 Market Power in Case Law

• Market power on relevant markets is analyzed:

– calculate market shares

– analyze competitive strengths of firms

– evaluating degree of actual competitive pressure firm faces

– entry barriers and other supply substitution

• In abuse cases, analyze whether conduct of dominant firm was misuse of market power

– In EU, dominant firms have special obligations

– Dominant firms cannot use their market power to impair conditions of competition

– Idea is to protect competition, not competitors


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2. Economics of Market Definition

• Read EU and US Guidelines on relevant markets– http://www.europa.eu.int/comm/competition/antitrust/

relevma_en.html– http://www.usdoj.gov/atr/public/guidelines/hmg.htm

• Why we need to define relevant antitrust markets in case law?– To calculate meaningful market shares– Market shares tell us something about market power

• Market shares do not need to imply or correlate with market power– More on this in Oligopoly and Merger sections

– Identify main competitors and competitive constraints– We are interested in market definition only to extent it helps

in analyzing market power– Sometimes we can identify and measure market power w/o

defining markets• More on this will follow (Merger section)


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2.1 How to define markets? — SSNIP

• On which set of goods market power can be exercised? Which goods compete immediately with each other– Market for cars? Separate markets for minivans, luxury sedans,

large family cars, compacts, subcompacts…?• Relevant antitrust market is something that can be monopolized

– If it cannot be monopolized, it is too narrow– Then important competitive pressures are left out of candidate

market• Test: Small but Significant Non-temporary Increase in Price

– Take a small set of substitute goods and a geographic area– Assume all goods produced by hypothetical monopoly– Incentive to permanently increase prices by 5-10 %?– Yes: candidate market = relevant market

• Proceed to analyze market power etc– No: candidate market < relevant market

• Include more goods and repeat


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• Logic: Goods on relevant market create intense competition to each other– Once this competition is removed, incentive to increase price– If strong competition remains, price increase is not possible,

and goods do not constitute relevant market• Leave out significant constraints on market power,

candidate market is too small• Keep in firms and products that are not significant

constraints, market is too large• Price increase leads to

– Consumers substitute away– Outside producers increase output or enter

• SSNIP asks: how much demand shifts away for a price increase and does this make price increase non-profitable?


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• SSNIP in Economics jargon: What is demand elasticity for this set of goods?– Basically: elastic demand market too narrow, inelastic

demand relevant antitrust market – But recall effects from costs and supply subsitituition

Digression on demand• Individual demand is ultimately derived from customer

preferences– Hold everything else constant and vary the price of the good

customer’s demand curve– Demand as function of own price vs shifts in demand function– Sum up all customer demand’s market demand

• Note: economics textbooks (sort of) assume relevant market has been defined when discussing demand


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• Market demand vs firm demand– Demand for colas vs demand for Coca-Cola, say?– What happens after ”market-wide” price increase?

• Marshallian demand based on ceteris paribus assumption and measures effect of price change by keeping all other prices constant– Merger Guidelines assume that “the terms of sale of all other

products are held constant” = Marshallian demand– Direct demands are hard to estimate

• Suppose condidate for relevant market has n goods and their demand depend on each others’ prices

• Need to estimate at least n2 parameters to get any info on Marshallian demand

• Price change in some goods do not leave all other prices constant


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• Residual demand curve is the demand curve faced by an individual firm– Residual demand = total market demand curve - supply of all

other firms in marketqi = Q(p) - qj

– Residual demand curve incorporates effects of changes in prices of other products in response to changes in this product’s price

– Residual demand is good tool for market definition to as it is relatively easy to estimate from data available

• We do not observe demand curves, but price-output pairs, determined jointly in equilibrium

• Can one identify demand and supply?• Need econometrics to get from data to demand curve


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2.2 Critical Elasticity of Demand and Loss

• SSNIP-test should be applied by estimating own elasticity of demand

• What value of elasticity is large enough for concluding that given set of goods comprise relevant market?

• Notation:P0 = Current observed priceP1 = P0 plus some specified price increase tC = Marginal costL = (P – C)/P price-cost margin or Lerner-index: T = Price increase deemed significant (eg. 0.05 or 0.1)T = (P1 – P0)/P0

elasticity of demand• Assume C is constant, profits are then (P-C)Q - F• For profitable price increase, profits with higher price must at

least equal profits from selling more at lower price

/( )

/dQ P dQ Q

e PdP Q dP P


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• Break-even condition is Q(P0)(P0 – C) = Q(P1)(P1 – C)where P1 = break-even price

• Rearranging: Q(P1)/Q(P0) = (P0 – C)/(P1 – C)

• Using definitions of T and L:

• For linear demand Q = (A - P)/B:

– Recall elasticity of demand here is e(P0) = P0/(A - P0), which gives Q(P1)/Q(P0) = 1 - Le(P0)

• Break-even requires Q(P1)/Q(P0) = L/(L+T) so this gives usL/(M+T) = 1 – Te(P0), and solving gives us critical elasticitye(P0) = 1/(L+T)

0 0

1 1

( - ) /

( - ) /

P C P LL TP C P

1 1 1 0 0

0 0 0 0

( )1

( )

Q P A P P P P

Q P A P P A P


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– When demand is isoelastic, break-even elasticity ise(P0) = [log(L+T) – log(L)]/log(1+T)

• Critical sales loss for a price increase = proportionate decrease in quantity sold as a result of the price increase large enough to make price increase unprofitable

• Sales loss resulting from price P0 P1 is1 - Q(P1)/Q(P0)

• For linear demand Q = (A–P)/B we can write this as1 – Q(P1)/Q(P0) = 1 – (A – P1)/(A – P0)= [(P1 – P0)/P0][P0/(A – P0)] = Te(P0)

• Applying break-even value of e(P0) derived above gives value for break even critical sales loss Y = T/(L+T)

• If actual sales-loss after price increase is less than Y, it is profitable to increase price– The break-even value of the critical sales loss is the same for

both linear and isoelastic demand curves


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• Relationship between market power index L, and critical e and Y for 5 % price increase:

L % e Y %50 1.82 9.140 2.22 11.130 2.86 14.320 4.00 20.010 6.67 33.3

Cross-Price Elasticity• Sometimes in case law market definition is based on cross-price

elasticity of demand

• Cross price elasticity of demand eij = (dQi/dPj)/(Qi/Pj), where Qi and Pi denote the quantity and price of products i and j

• Cross price elasticity = How demand for good i reacts to price increase of good j?

• Sounds like nice idea to delineate markets: goods belong to same relevant market if they are good-enough substitutes


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• Rule used in some competition cases:– Goods i and j are on same market if cross-price elasticity is

large enough and otherwise are on different markets• Cross price elasticity is not a good measure for market

delineation– Market delineation is not question of how much demand will

flow from i to j as Pi increases• Cross-price elasticity is usually not symmetric, eij eji

– eij: ”i and j on same mkt” and eij: ”i and j on different mkt” is possible

• Even if a cross price elasticity is small, market need not be narrow, as there may be many other goods that restrict the market power of hypothetical monopolist– If there are many substitutes, price increase will divert

demand to many goods cross price elasticity must be small– This indicates competition, not sepatate markets


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• Price and cross price elasticities are connected:– Own-price elasticity = 1 + weighted average of all cross-price

elasticities• Weight: share of income in relation to share of income of

the good in question

”Cellophane Fallacy”• US Supreme Court: high cross price elasticy between cellophane

and paper wrapping relevant market wider than cellophane Du Pont not dominant– Also SSNIP test ignores fact that firm may already have

market power• Firm with market power wants to increase price to level where

competition constrains start to bite– Demand usually turns more elastic as price increases


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• Then goods actually outside of relevant market seem to be substitutes

• High cross price elasticy indication of use of market power, not an indication of wide market

• Cellophane fallacy means that different approach is required in abuse of dominance cases


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3. Market Power

• Market power = ability to profitably charge P > MC• Some sources of market power

– Only few firms active in the market– Products are differentiated, and some customers prefer one

firm’s product to other• Firm that attempts to ”steal” customers from its competitor

must reduce price a lot• Then firms have less incentives to lower their prices

– Capacity constraints• Firm have less incentive to win more customers, giving

other firms incventives to charge higher prices– Customers are not informed of all firms’ prices

• Incentive to lower price is reduced– Switching costs

• Each firm monopolizes its customer base– Cartel or collusion (later in Oligopoly section)


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3. Market Power

• Market power is source of inefficiency– Allocative inefficiency

• Harberger triangle• Rent seeking

– X-inefficiency• Less need to control costs or to concentrate on key

capabilities• Less need to provide value to customers

– Dynamic inefficiency• Less incentive to innovate

• Market power allows restrictions on competition– Entry deterrence– Predation– Price squeeze– Cartel or collusion


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3. Market Power

Monopoly’s profit maximization• Assuming constant MC, monopoly’s profits are

= [P(Q) - C] Q - F• To maximize profits, set d/dQ = 0:

d/dQ = P(Q) + Q dP/dQ - C = 0 (MR - MC = 0) P*(Q) - C = -Q dP/dQ

• Divide both sides by P*– (P* - C)/P* = -(Q/P*)(dP/dQ)

• Rewrite this as L = 1/e– L = Lerner Index– e = elasticity of market demand

• Under perfect competition or perfectly elastic demand:P = C, hence L = 0

• L is usefull measure of market power: 0 ≤ L ≤ 1/e• If we can estimate P, e and C, we can estimate market power L


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3.1 Measuring Market Power

• To measure market power, we need to estimate demand consistently

• Basic idea: how well other goods substitute for goods produced by firm i and constrain its market power?

• Answer: elasticity of residual demand– Residual demand does not tell who or what constrains market

power• Straightforward approach is to specify system of demand

equations q = D(p;r), where q is vector of quantities demanded, p is a vector of prices, and r is a vector of exogenous variables that shift demand– Need to define D(.) in a way that is both flexible and

consistent with economic theory• Problem 1: Number of parameters estimated increases with

square number of products– 10 firms, each with 20 brands 40 000 elasticities


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• Problem 2: Simultaneity– Equilibrium price and quantity determined jointly by demand

and supply schedule– Price increase by i is followed by rivals need to take into

account how rivals react residual, not market demand• Problem 3: Simple approach ignores consumer heterogeneity• Solutions to problems include

– 1) assume problems away– 2) assume symmetric representative consumer– 3) assume multi-stage budgeting– 4) use discrete choice/address models

1. Avoid problem• Focus on aggregate demand

– All eastbound rail traffic, not differentiated across cities• Focus on narrowly defined product

– Self service 87 octane


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• Focus only on sub-markets– Particular segment in beer industry

• This is enough in some cases2. Symmetric representative consumer• Use Constant Elasticity of Substitution (CES) utility function

– Dimensionality problem is solved by imposing symmetry between products

– Estimation involves a single parameter, regardless of number of products, and can be achieved using simple econometrics

• Cross-price elasticities are restricted to be equal, regardless of how “close” the products are– Are MB and Opel equally good substitues to BMW?– This restriction can have important implications and in many

cases would lead to the “wrong” conclusions• For some industries or cases this model of differentiation is

adequate, for most markets this is not


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3. Separability and multi-stage budgeting• Divide products into smaller groups and allow for flexible demand

within each group• Multi-stage budgeting

– Consumer allocates expenditure in stages• at highest stage expenditure is allocated to broad groups

(food, housing, clothing, transportation…)• at lower stages group expenditure is allocated to sub-groups

(cereal, bread, cheese, ..)• until expenditures are allocated to individual products

– At each stage, allocation decision is function of only that group’s total expenditure and prices of commodities in that group (or price indexes for the sub-groupings)

– Then we have cross elasticities between Opel sedan and VW sedan, between Opel van and VW van, and between sedan and van categories, but not between Opel sedan and VW van

– Reduces number of parameters to be estimated


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• Three stage system– Top level: overall demand for the product (cars or ready-to-eat

cereal)– Middle level: demand for different segments (sedan, suv, stw,

minivan; or family, kids, adults cereal)– Bottom level: brand demand corresponding to competition

between different brands within each segment4. Discrete Choice Models• Model products as bundles of characteristics

– sweetness, fiber content, …– alcohol content, bitterness, ...– horsepower, length, ...

• Preferences are defined over characteristics space• Each consumers chooses the product with best characteristics for

her– use bus if U(bus) > U(car), U(train), U(walk), ...


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• Discrete choice models yield Logit demands (under some assumptions)– prob that n chooses i has logistic distribution

• Dimension of characteristics relevant dimension for empirical work

• Heterogeneity is modeled and estimated explicitly• Can be estimated using individual or aggregate market data

Comparison• Symmetric average consumer models least adequate for

modeling demand for differentiated products– Problem: all goods are assumed to be equally close, equally

good substitutes• Logit models widely used because they are simple• Multi-level model requires a priori segmentation of market into

relatively small groups, which might be hard to define


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• Typically, multi-stage budgeting models assume all consumers consume all products– For broad categories like food and shelter reasonable– For differentiated products, it is unlikely that all consumers

consume all varieties• Multi-stage budgeting model is closer to classical estimation

methods and neo-classical theory, and more intuitive to understand

• Discrete choice models require characteristics of products, are more technical to use, and rely on distributional assumptions and functional forms


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3.2 Application

• Nevo (2001) uses discrete choice models succesfully– Panel of quantities and prices for 25 brands of cereal in 65 U.S.

cities over 20 quarters, using scanner data– Estimate own price and cross-price demand elasticities– Compute price-cost margins implied by three industry

structures:• each brand on its own• actual structure of few multi-product firms• monopoly or collusion

– Markups implied by current industry structure and imperfect competition match observed price-cost margins

– High margins due to consumers' willingness to pay for favorite brand, and to pricing decisions that take into account substitution between own brands

– Market power entirely due to the firms' ability to maintain portfolio of differentiated products and influence perceived product quality through advertising


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4 Oligopoly

• Topics– Basic models of oligopolistic competition– How can firms change rules of game to their advantage?– How can firms avoid intensive rivalry?– When cartel or implicit collusion is stable?

• Read or review– Chapter on Oligopoly in any modern Micro or Industrial

Organization textbook, and/or– Europe Economics report available at

http://europa.eu.int/comm/enterprise/library/lib-competition/libr-competition.html

• I will use game theoretic reasoning and Nash equilibrium, so you should soon get comfortable with these ideas– Note: topics following oligopoly (Collusion and Mergers) will

be based on oligopoly theory


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4.1 Cournot or Quantity Competition

• Assumptions– Market demand: price function of total quantity produced,

p = p(q), eg. p = a – bq– Assume 2 firms on relevant market denoted by i and j

– Firms produce quantities qi and qj

– Firms have constant marginal costs ci

– No threat of entry• Profits for firm i = Total Revenue - Total Costs

i = pi(qi,qj) qi - c(qi,qj) = p[(qi+qj)-ci]qi

– Note: i's profit depends on what rival j does, unlike in monopoly or perfect competition

– Firm faces a problem of strategic interaction or plays a game• How much will i want to produce?

– Depends on how much i expects j to produce, qje

• How much will j want to produce?

– Depends on how much j expects i to produce, qie


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• Note, for each qje, there is an optimal output

qi*(qje) = argmax i(qi,qj

e)

• qi*(qje) is called i’s reaction function

– Compare with monopoly profit max

Problem• i needs to put himself on j’s position and try to predict how j will

behave• j needs to put himself on i’s position and try to predict how i will

behave• i needs to to put himself on j’s position and try to predict how j

will think how i will behave• j needs to ... predict how i will think how j will behave• etc. ad inf.


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Solution

• Suppose both i and j know p(q), ci and cj, and also expect that rival will produce profit-maximizing quantityqi*(q-i

e) = argmax j(qi,q-ie)

• Then i should choose qi* = argmax i(qi,qj*) and jqj* = argmax j(qj,qi*)

– Each firm chooses its strategy taking rivals equilibrium strategy as given

– Firm i needs to predict j’s equilibrium production• Simultaneously but individually

max i = p(qi+qj)qi - cqi max j = p(qi+qj)qi - cqj

• At a maximum, small change in output should not increase profits; differentiating each max problem yieldsdi/dqi = qi(dp/dqi) + p(qi+qj) - ci = 0 dj/dqj = qj(dp/dqj) + p(qi+qj) - cj = 0


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These are familiar 1st order conditions MR - MC = 0 Compare with monopoly profit max

Plug in p(qi+qj) = a - b(qi+qj) and solve for qi*(qje) and qj*(qi

e), you get reaction fns:

(1)qi*(qj) = (a - ci)/2b - qj/2

(2)qj*(qi) = (a - cj)/2b - qi/2

Solve simultaneously [eg, insert qj*(qi) from (2) into (1) to replace qj] to get Cournot-Nash equilibrium quantities

(3)qi* = (a + cj - 2ci)/3b

(4)qj* = (a + ci - 2cj)/3b

Note: Each firms is on her reaction function In equilibrium, no firm has incentive to alter her strategy

choice unilaterally


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• Insert then qi* and qj* to demand function to get equilibrium price p*, and then plug these to profit function to get equilibrium profits

Reaction functions (1) and (2) are downward-sloping:dqi*(qi)/dqj = -1/2 < 0

– This also applies to more general Cournot games – If j increases her production (eg, due to reduction in marginal

cost cj), i will want to reduce his output

– Lower action by one firm induces higher reaction from rivals– Note, these are equilibrium reactions

• Strategies qi are here strategic substitutes

• Downward-sloping reaction functions strategic substitutes


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Properties of Cournot-Nash Equil• Go back to reaction functions (1) and (2), and rewrite as(5)p(q) - ci = -qi dp/dqi |:p

(6)Li = si/e, where

si = qi/q is i’s market share, q = iqi,Li = (p - ci)/p is firm i’s mark-up or Lerner Indexe = -p(q)/qp’(q) is elasticity of market demand

(6) is basic Cournot pricing formula• Compare to monopoly’s profit max condition

• In Cournot-Nash equilibrium, market share determined by– firm’s relative cost efficiency

• Each firm has limited mkt power:

– i’s marginal revenue MRi is p + qip’, so

– p - MRi = qip’(q) > 0 MR > MC


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• Smaller market shares s (or more rivals) smaller mark-up, more vigorous competion reduces mark-up

• Greater demand elasticity larger mark-up, less competitive equilibrium

• Mark-up is proportional to firm market share• Market shares are directly related to firms cost-efficiency ci

– Market shares determined by cost-efficiency• Less efficient firms are able to survive

– sj > 0 even if cj >> min c• Average industry-wide mark-up i si (p - ci)/p = MU • In Cournot-Nash equil, MU = i si

2/e = HHI/e, where HHI is the Herfindahl-Hirschman Index– Market performance negatively related to HHI

• These properties give some basis for competition policy opposing mergers on oligopolistic markets– What if competition is not Cournot-type?


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4.2 Bertrand or Price Competition

• In reality, firms choose and compete with prices, not quantities• Often prices are easier to adjust than quantities• Who chooses prices in Cournot game?

– Cournot unrealistic model?

• Naive thought: firms select prices as in (6) above: pi* st.

(pi* - ci)/pi* = si/e?

• Bertrand paradox: No• Model: identical product, mkt demand q = q(p), eg. q = a – bp• Demand for firm i:

pi > pj i cannot sell at all, qi = 0pi = pj i and j split demand, qi = q(p)/2pi < pj i sells total mkt demand, qi = q(p)

– Note: small change in rival’s price causes huge change in firm’s demand


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• Suppose cj = ci = c

• If i charges pi > c, j can increase her profits by undercutting i slightly

• If i charges pi < c, i is making losses but j can guarantee j = 0 by staying out of mkt

Only equil price can be pi = pj = c

– Duopoly enough for perfect competition!• Result depends crucially on

– firms able and willing to serve all customers at announced price

– identical products– customers have complete information eg on prices firms

have no bargaining power wrt customers


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Product Differentation and Price Competition• Simple example only• Products are imperfect substitutes, demands are symmetric

qi = a - fpi + gpj

• Assume constant marginal costs ci

• Product differentation is assumed fact, not designed by firms– g/f measures degree of product differentation (how?)

• Profit for i herei = (pi - ci)(a - fpi + gpj)

• Bertrand-Nash equilibrium found similarly as above:

– Firm i maximizes profits wrt to strategy variable pi

– Solve for reaction functions– Find where reaction functions intersect– Then solve for equilibrium prices, quantities, and profits


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• Reaction functions slope up– The higher the price i charges, the higher the price rival j

wants to charge• Prices are strategic complements

– Higher strategy draws a higher reaction from rivals• Upward-sloping reaction functions strategic complementsCapacity Constraints and Price Competition• Firms first choose capacities q and then select prices p?• We have a 2-stage game (more on this later)

– In equilibrium, higher price than without capacity constraints• Intuition

– Limited capacity business stealing not attractive option want to price less aggressively rivals price less aggressively higher profits


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4.2 Sum Up

• Cournot outcome possible with price competition– Interpret: Cournot = capacity competition followed by price

competition• Under some assumptions

• Cournot– Markets where production desicions in advance, price is

flexible, and storage costs arehigh– Consistent with empirical evidence

• Bertrand– More realistic assumptions, less realistic outcome?– Generalized price competition models more consistent


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4.3 Dynamic Competition

• Simplest way to model dynamic rivalry is to introduce two stages– Model j’s reactions to strategic moves by firm i– Firms try change game they are playing

• Idea: Choose a strategy now that affects game you play tomorrow so that your expected profits increase

• Capacity-Price -model above an example: Smaller capacity now reduce ability to compete aggressively in future draw less aggressive reactions from rivals higher profit

Stackelberg Oligopoly• Stackelberg-Cournot game: Firm i chooses its output first, and j

after i’s choice• Precommitment by i is relevant, not physical timing of moves• Solve by backward induction:

– First look at last possible moves of the game– Then work backward to beginning of game, as in dynamic

programming


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Last move• Firm i chooses his capacity first

• When j chooses her capacity, she knows i’s capacity qiS

• j's optimal capacity determined by her reaction function (2)qj*(qi) = a/2b - qi/2

Penultimate move• To design good strategy, i must put himself on j’s shoes and try

to think how he would behave were he the last to move

• i chooses qiS to maximize profits, taking as given i’s reaction

function, not equilibrium output as in Cournot game• i chooses best point from rival’s reaction function

• Plug (2) into i’s profit function (a - b(qi+qj))qi and solve for qiS

• Plug qiS back to (2) and solve for qj*, and then solve for prices

and profits


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• In Stackelberg game, i’s profits higher and j’s lower than in Cournot game

• First-mover advantage• Intuition: Commit to flood the market induce rival to lower

output increases your profit– Equilibrium above “subgame perfect Nash equilibrium”– Also other Nash equil possible:

• i announces to produce qi s.t. p(qi) < cj if j enters

• This is not be credible: i will not want to undertake threat should j enter (more on this later)

• Crucial reasons: 1) commitment, 2) strategies substitutes– In Stackelberg-Bertrand duopoly, there is second mover

advantage– Once rival has committed to a price, firm has strong

incentives to undercut


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4.4 Modeling Dynamic Competition

• 2 time periods, denoted by 1 and 2• Firm i can take strategic action k on period 1

– k: Advertising, R&D, product design, …– Strategic action measured by its cost– Strategy k is sunk on 2nd period, i cannot revoke it– k is investment, precommitment

• On period 2, i and j compete– To concentrate on strategic effects, assume k does not affect

j’s demand or costs directly

• i’s 2nd period profits are i(qi,qj,k)

• i’s 1st period profits are i (qi,qj,k) - k

• k shifts i’s 2nd period profit fn– Strategic move k alters i’s own incentives to choose later 2nd

period tactics


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• To find equilibrium, solve for by backward induction starting from 2nd period game

2nd period• For any given k, equilibrium again given by

di/dqi = 0di/dqj = 0

• 2nd period reaction functions qi(qj,k) and qj(qi,k), and optimal tactics qi*(k) are now functions of k

• Equilibrium profits are i(qi*(k),qj*(k),k)

1st period• How to choose k?• Profits are i(qi*(k),qj*(k),k) - k• To find max profit, differentiate i wrt k to get MR – MC = 0; this

gives01 =++ dk

ddkdq

dqd

dkdq

dqd ij

jii

ii


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• First term is zero because i will choose second stage tactic qi stdi/dqi = 0; we have:

• LHS 2nd term: direct effect• LHS 1st term: strategic effect• RHS: Direct cost of commitment• How can k alter j’s 2nd period tactics since k does not directly

affect j’s profits?• Strategic move k alters i’s own incentives to choose alters j’s

incentives to react changes i’s profits• Sign of strategic effect is equal to sign of

1=dkd

dkdq

dq)k,q,q(d i

*j

j

*j

*ii

j

i

ji

i

i

i

dqd

qdqd

dkdqd 22


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Three effects• How commitment k changes i’s own optimal tactics• How j reacts to changes in i’s incentives• How i’s profits are affected by changes in j’s tactics

Strategic effect > 0 overinvest in kStrategic effect < 0 underinvest in k

• Example: Cost reduction in Cournot and Bertrand games– How reaction functions shift as marginal costs of j are

decreased?• Example: Increased marketing in Cournot and Bertrand games

– How reaction functions shift as j increases her marketing expenses?


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Taxonomy for Strategies• Strategic substitutes vs complements

– Cournot game = strategic substitutes– Bertrand game = strategic complements

• Commitment makes firm tough vs soft• Investment k makes i tough

– i will produce more or price below– k shifts i’s rf right and up in Cournot game– k shifts i’s rf right and down in Bertrand game

• Investment k makes i soft– i will produce less or price above – k shifts i’s rf left and down in Cournot– k shifts i’s rf left and up in Bertrand


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Stage 2 variables are

Commitment makes firm

Tough Soft

StrategicComplements

(eg, prices)

Puppy Dog PloyStrategic effect < 0Commitment cause rivals behave more

aggressively

Fat Cat EffectStrategic effect > 0Commitment cause rivals behave less

aggressively

StrategicSubstitutes

(eg, capacities)

Top-Dog StrategyStrategic effect > 0Commitment cause rivals behave less

aggressively

Lean and Hungry LookStrategic effect < 0Commitment cause rival behave more

aggressively


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Strategic Incentives to Commit in Cournot• Commitment makes firm tough

– Reaction function shifts outward– Firm will produce more for all given rivals’ output– Example: Marginal cost reducing innovation– Strategic effect might outweigh direct effect Invest even if

NPV < 0!– Beneficial strategic side-effect– Top-Dog: Big or strong to become aggressive

• Commitment makes firm soft– Firm will produce less for all given rivals’ output– Reaction function shifts inward– Example: Marginal cost increasing entry into other mkt– Negative strategic side-effect– Lean and Hungry Look: Refrain from expanding to avoid

weakness


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Strategic Incentives to Commit in Bertrand• Commitment makes firm tough

– Firm will underprice– Reaction function shifts inward– Example: MC-reducing innovation– Negative side-effect– Puppy-Dog Ploy: stay small or weak to avoid agressive

competition Do not lower costs!• Commitment makes firm soft

– Firm will overprice– Reaction function shifts outward– Beneficial side-effect– Example: Target small niche, Product differentation– Fat-Cat Effect: Become soft to attract only weak competition

Sumo-strategy


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• Need to look more than just direct effects of irreversible decisions• Nature of future competition affects incentives to make

investments or commitments now• Need to look at how equilibrium changes, not just first effetcsExamples of 1st Stage Commitments• Build excess capacity deter entry• Enter and underinvest avoid attracting tough competition• R&D: reduce costs price aggressively / gain mkt share• Build large customer base, costly to switch less competition in

future• Underinvest in marketing less loyal customers become

aggressive in 2nd stage• Overinvest in marketing loyal customers become soft in 2nd

stage


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5 Cartels and Collusion

• Competition leads to less than jointly maximal profit firms have incentives to avoid competition

• These incentives are basis for competition policy• Explicit cartels, implicit tacit collusion• How would these show up in reaction fn picture?

How Can We Detect Cartels and Collusion?• Hard without ”smoking gun”

• Lerner Index L = (p - ci)/p = si/e?

– If p, si and e known, make inference on p - ci

– Often not practical: p, ci and e not known accurately enough

– But with good enough data this can be done• Identical prices?

– Not evidence for cartel– Perfect competition identical prices


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5.1 Explicit Cartel

• Intuition:– ”Few” competitors easy to form cartel/collude– ”Many” competitors hard to form cartel/collude

• Selten (1973): 4 is few, 6 is many– Intuition: with 6 firms, staying outside cartel gives more than

joining cartel with 5 other firms• Result from 2-stage model:

– 1. Decide to join/stay out– 2. Choose output– If n > 5, best strategy in stage 1 is to stay out– If n < 5, best strategy in stage 1 is join cartel


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5.2 Implicit Collusion

• Implicit agreement or understanding not to compete– Eg. firms ”agree” on monopoly price and output

• But this is unstable– Cheating and undercutting gives even higher profits than

collusion, if rivals adher to agreement• Need mechanism to remove incentives for cheating• "Stick-and-Carrot" Theory:

– Cheating draws punishment and low profits in future– Collusion draws rewards (high profits)– Deters from cheating on promise to fix prices

• Future reward Collude now– Requires that future matter

• How to punish? Price war an example– Punishment will also hurt the punisher– Need incentives to punish


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Collusion in Bertrand Competition• Model: firms interact repeatedly• Assume c = 0, mkt demand q = a - bp

• Per period profits now it = pit qit(pit, pjt)

• Bertrand equilibrium price for one-shot game = 0

• On each period t each firm chooses price pit knowing all previous prices pit-s, s = 1,2,3,…

• No end-game problem: repeat per-period game infinitely many times– Or: Prob(next period is last) < 1

• Future matters but less than today: firms discount future profits with discount factor 0 < < 1


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• Owners of firms value monetary stream m such that mt+1 = mt,

• where r is discount (or interest) rate, P probability that game ends after this period and k firm's marginal cost of capital

• Firm goal: maximize present value of per-period profit streamVi = t ti

t

• Strategy?– Plan ahead how to play entire game– What per-period moves to choose after any history– Think: players desing strategy before game starts and then

leave computers to execute strategy

k

P

r

1

1

1

1


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• Examples of simple strategies:– One-shot Bertand price always– Tit-for-Tat: do today what rival did yesterday

– pi1= pM; pit= pM if pjt-1= pM, else pit= 0

• Equilibrium: No incentive to change strategy• Is "always one-shot Bertrand equil behavior” still an equil strategy?

– Yes: if i always chooses pit = 0, best j can do is to choose pjt = 0 it = 0

• Both always charge monopoly price and earn it = iM/2 > 0

equilibrium?

– If j always charges pjt= pM, what should i do?

– Look at reaction function: i should choose pit= pM- – If i deviates from pM, it earns higher profits every period i

D = pM- > pM/2 (D: deviate or defect), henceVi

D = t t it(piD,pj

M) > ViM = t t it(pi

M,pjM)


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Strategy ”always monopoly price” is not in equilibrium• ”Grim Strategy” (GS):

– Choose pi1= pM

– Choose pit= pM if pjt-1= pM

– Else always choose pit= 0

• Suppose j knows i plays GS; what is best for j?– GS is best reply (among others)

GS is a best reply against itself Both firms using GS is an equilibrium• Punishment needs to be credible, otherwise it is only empty threat

– There must be incentives to start punishment– Punishment must be part of equilibrium path from that moment

onward, so that no firm will want to deviate from punishment• One-shot Nash equil behavior always credible punishment


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• GS punishes defection forever• Punishment "too hard", lesser punishment suffices• Optimal punishment: shortest number of periods T such that extra

profits gained by defection are vanished– Stay on intended equil path: earn M/2 each period– Temptation: gain M - M/2 - = M/2 - during defection– Punishment: earn zero profits long enough so that profits

(defect + punishment) < profits (collusion)• Minimum length of sufficient punishment depends on discount

factor • Often optimal punishment is minimax strategy of per period game,

ie tougher than one-shot equil behavior• GS easy to use• Point here collusive outcome, not details how one supports

outcome


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• ”Folk Therorem": Any outcome that leaves each player more than one-shot minmax outcome is sustainable as an equilibrium outcome in infinitely repeated game– There are many equilibrium strategies– ”Anything” is in equil– No predictive power without more assumptions

• Generally collusion is sustainable if temptation to defect is low enough and punisment following the deviation strong enough

• Firm wants to keep colluding if present value of devi-ating is smaller than present value of adhering to collusive agreement

• PV of collusion hereVi

C = ttit(piC,pj

C) = piC/(1-)

as t dt = 1/(1-d) if |d| < 1


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• PV of deviation = profits reaped during deviation + present value of profits earned during punishment:Vi

D = D + ttit(piP,pj

P) = D + piP/(1-)

– Note: here punishment assumed to be infinitely long• Collusion is sustainable if

• Incentive to deviate depends on discount factor• If discount factor is too low to support collusion, either toughen up

punishment or try to lower degree of collusion– Longer or harder price war– Reduce collusive prices from monopoly price

• Note: punisments are never observed– None used since threat is enough

Pi

Di

Ci

Di

PiD

i

Ci

11


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Collusion with Imperfect Information• What if firms cannot observe rivals' exact prices nor outputs?

– Don't know if rival defected know when to start price war• No threat of price war collusion not sustainable?• Use other info: Sales were less than expected

– Think Bertrand oligopoly with identical goods and with stochastic demand

– Firm has 0 demand today: somebody deviated and stole customers or shift in demand?

– Start price war when price or demand drops "enough"– Start price war even if you know nobody deviated, as nobody

has incentives to deviate– Intuition: no punishment no firm has incentives to collude

per period equilibrium only possibility– Better off with some price war instead of permanent rivalry


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Factors that Help Collusion• General idea: stronger, earlier and more certain punishment

increases possibilities to collusion”Topsy-Turvy” principle: the more firms have opportunities for aggressive competition, the less competition there is

• Public prices and other market transparency– Easy to observe deviation

• Size of cartel– N equally sized firms– Each firm receives 1/Nth share of total monopoly profits– Collusion sustainable if one shot defection followed by

punishment leaves less profits that staying on collusive path:

1)(1

)(MM

MM pQpN

pQp 1

1N


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• Product differentation works two ways– More products are differentiated, the larger price decrease

needed to• steal mkt share• punish deviator

– More products are differentiated, less incentive to cheat and try to steal mkt share

– More products are differentiated, less price war by rivals affects profits

– Introduces non-price competition: more variables to monitor and more ways to cheat

• Cost conditions and capacity utilization– Capacity constraint or steeply rising MC reduce profit margin for

extra output• Reduce incentive to cheat• Reduces possibilities and incentives to punish


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• Free capacity– Increases temptation to cheat– Allows harsher punishment increases possibilities and

incentives to punish• Elasticity of firm demand

– Inelastic firm demand more mkt share means significant reduction in price less incentive to cheat

– More elastic demand is, the harder it is to sustain collusion• Multimarket contact

– Firms produce several competing goods or operate on several geographic mkts

– More opportunities to cheat– Price war on all mkts allows more severe punishments


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• Firm symmetry– Firms have different shares of a specific asset (capital) which

affects marginal costs– Joint profit maximization: output is shifted away from small

(inefficient) firms towards large (efficient) firms– Smallest firm has highest potential to steal business of its rivals

and, has highest incentives to disrupt collusive agreement– Incentives to deviate are reversed when equilibrium calls for

punishments– Largest firm loses most at punishment phase, it will have

highest incentives to deviate from punishment• Capacity constraints

– Incentives to stay in collusive equilibrium are very different for large and small firms

– Small firm will have some incentive to cheat in short run, as it can only increase its sales marginally up to capacity level


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– Large firm has a lot more capacity available and can gain more customers with same price deviation from collusive norm

• Large firms tend to have a greater incentive to deviate from collusive price

– Asymmetry in capacities will also have an important effect on effective punishments

• Worst punishment firm can impose on its competitors is to produce up to full capacity

• Small firm that is already producing at almost full capacity has low possibilities to punish rivals that do not follow collusive norm

• Large firm competing with small firm will have large incentives to deviate from any collusive norm without this being disciplined threat of low prices in future

– Increases in asymmetries in capacities make collusion more difficult


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Collusion and Antitrust• Read Motta Ch 4, Europe Economics report, UPM/Haindl decision p.

18-, and browse my ”forest” paper – Joint dominance, coordinated effects are legal jargon ~

collusion in economics jargon• How to identify collusion or separate collusion from competition?• Authorities/customers argue that collusive equilibrium is played • Suspected firms want to argue that behavior is as if noncooperative

Cournot or Bertrand equil is being played• Possible to detect collusion from behavior alone?

– Firms have more mkt power than one shot equil?– Estimate cost, demands and reaction fns and compare actual

behavior to non-cooperative and collusive equil– Doable, but technical (eg. Nevo, Slade), see my ”forest” paper


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• Core of policy problem: Collusion arises as equilibrium behavior– Hard to prohibit or deal with ex post

• Solution: try to prevent collusion, ban business practices and mergers that help facilitate collusion

• Analyses of asymmetry in assets and capacity constraints suggest merger guidelines that differ from traditional wisdom

• For a given number of firms, Herfindahl and other concentration tests tend to predict that a more symmetric industry is more likely to be more competitive

• Asymmetry may be pro-competitive– Asymmetry in industry may even more than compensate for

reduction in number of firms in merger involving large firm– Increased asymmetry hurts collusion and may benefit

competition

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