Market Power and Efficiency

Relationship between Efficiency and MarketStructure

Christian Michel

Universitat Pompeu Fabra

Fall 2013

Christian Michel (UPF) Efficiency and Market Structure Fall 2013 1 / 29

Key objectives of this lecture

Get basic understanding of the core concepts in competitionpolicy

I Define market powerI Understand the basic Cournot frameworkI Especially focus on horizontal mergers

F Prices and quantities in equilbriumF Welfare and Consumer SurplusF Synergies


Definition Market Power

Definition“Market power is the ability of a firm to profitably raise the market priceof a good or service over marginal cost.” (First line on Wikipedia)

No clear-cut definitionLerner index: L = p−mc

p , p price, mc marginal costI yields percentage markupI often difficult to measure empirically (but extremely important)

Market power not necessarily related to industry concentrationI Will talk more about this later in this course


Graph: Efficiency and Market Power – Williamsontrade-off


Graph: Efficiency and Market Power 2


Cournot Setting

n firms produce homogeneous goodsNotation:

I SupplyF qi firm i ’s quantity producedF Total output Q =

∑ni qi

I DemandF Industry price pF Demand function P(Q)

I TechnologyF Firm i ’s cost function Ci(qi)F Firm i ’s marginal costs ci = ∂Ci (qi )

∂qi


Strategic behavior

Firm i ’s profit function: πi = p(Q)qi − Ci(qi)

Actions: firms choose production levels simultaneouslyI Firms know each others’ production technologies

Equilibrium concept{p∗,q∗1,q∗2, ..,q∗n} is a pure Cournot-Nash equilibrium outcome if foreach firm i ∈ {1, ..,n} the output q∗i is a best response to the outputchosen by the other firms.


Big Picture – Setting Overview

1 Quantity setting gameI Quantity is strategic variable for each firmI Later: also focus on price setting games

2 Homogeneous productsI Implies that consumers do not prefer a specific firm’s productI But production efficiency (technology) can very across firmsI Later: focus on differentiated products

3 Horizontal industryI No manufacturer-retailer relationshipI Later: look at vertical relations issues

4 Static game, no entryI Only one-shot considerationsI Later: focus on dynamic games to study collusive behaviorI Later: consider entry possibilities


Further Assumptions

Farrel and Shapiro (AER 1990) seminal paper

Assumption 1

p′(Q) + qip′′(Q) < 0

Assumption 2∂ci(qi)

∂qi> p′(Q)

Puts restrictions on demand and technologyCombination of Assumptions ensures that SOC π′′i (qi) < 0:ensures interior solution


Characterize best response function

∂πi

∂qi= 0

p′(Q)qi + p(Q)− ci = 0p′(Q)qi + p(Q) = ci

marginal revenue = marginal costp(Q)− ci = −p′(Q)qi

marginal effect = inframarginal effect

Remarks1 No firm wishes to deviate unilaterally from its chosen quantity2 Firm i’s optimal quantity depends only upon its rivals’ aggregate

output Q−i

3 More efficient firms have a higher mark-up


Find equilibrium – 2 firm examplen = 2 and p(Q) = 1− q1 − q2,Constant marginal costs ci :

∂ci∂qi

= 0∀qi

Recall

p(Q)− ci = −p′(Q)qi

⇒ p(Q)− ci = qi

For n = 2:

(1− q1 − q2)− c1 = q1

(1− q1 − q2)− c2 = q2

q1(q2) =12(1− c1)−

12

q2

q2(q1) =12(1− c2)−

12

q1


Find equilibrium – 2 firm example cont.RemarkReaction curves are downward sloping

Set reaction curves into each other to find Nash equilibrium:

q1 =12(1− c1)−

12

q2(q1)

q1 =12(1− c2)−

12(1− c2 − q1)

q∗1 =13(1− 2c1 + c2)

q∗2 =13(1− 2c2 + c1)

Relationship between equilibrium prices and marginal costs∂q∗i∂ci

< 0 (own quantity decreasing in own marginal costs)∂q∗i∂cj

> 0 (own quantity increasing in rival’s marginal costs)


Find equilibrium – general solution

Firm i ’s reaction function π′i (qi) = 0:

p′(Q)qi + p(Q)− ci(qi) = 0

Define yi ≡∑

j 6=i qj .Take total differential:(

2p′(Q) + qip′′(Q)− ∂ci(qi)

∂qi

)dqi+(

∂p(Q)

∂Q∂Q∂yi

+ qip′′(Q)

)dyi = 0


Horizontal Merger

dqi

dyi=

(2p′(Q) + qip′′(Q)− ∂ci (qi )∂qi

)

(∂p(Q)∂Q

∂Q∂yi

+ qip′′(Q))≡ Ri < 0

−1 < Ri < 0: If rivals reduce quantity, firm i as a best responseincrease output by less than the rivals’ output reductionThus if yi falls exogeneously, qi goes up and Q falls as a response


Effect of merger without cost savings

Assume that two firms i and j in the industry mergeI Before merger constant marginal cost ci and cj , ci ≤ cj

I After the merger, joint firm has marginal cost ci

I Pre-merger quantities Q,q i ,q j

Total post-merger output for merging (insider) firm: QI , rivals(outsider) QO

Analyze effect on quantities, prices, and welfare


Merger without cost savings cont.Analysis

FOC pre-merger:


After merger (qi ,qj ) now in one firm

p(Q)− ci < −p′(Q)(qi + qj)

⇒ QI < qi + qj

Thus, if post-merger firm is not more efficient than most efficientpre-merger firm, then supplied quantities always dropEffect on outsiders quantities post merger QO:

p(QO + QI)− co > −p′(QO + QI)(Qo)

⇒ Insiders quantity drop gives incentive to increase outside firms’quantities


Merger without cost savings cont.

Effects on quantities and prices1 Insiders quantities go down: QI −QI < 02 Outsiders quantities go up: QO −QO > 03 Overall quantity goes down: Q −Q < 0.

I Prices go up: p(Q)− p(Q) > 0

Effects on industry profits1 Outsiders’ profits go up2 Profits of insiders may decrease depending on size of merging

firmsI Salant, Switzer, and Reynolds (QJE 1983): If mc constant across

firms, then prices always decrease if less than 80% in marketmerge


Merger without cost savings cont.

Rationalization without synergiesIn the basic Cournot setting, any merger that does not decreasemarginal costs of the most efficient merging firm leads to lowerindustry quantities and a decrease in consumer welfare.

Competition Policy in Cournot SettingWithout efficiency considerations, any a competition authority shouldnever allow a merger in the baseline Cournot setting.

EntryAbsent fixed costs, any firm entry that increases industry output Q isbeneficial to consumers.


Merger related synergies needed to avoid priceincrease

Recall first-order condition of firm i :


After merger, to need non-decreasing total industry quantity afterthe merger:Merged firm need MR > MC at Q, i.e. marginal effect >infra-marginal effect

p(Q)− cI(QI) = −p′(QI)QI

Now try to express infra-marginal effect −p′(QI)QI in terms ofmark-ups


Merger related synergies cont.

PropositionThe merger between the firms in set M reduces price (increasesconsumer surplus) if and only if the post-merger marginal cost satifies:

p(Q)− cI(∑i∈I

qi) >∑i∈I

[p(Q)− ci(qi)],

where the l.h.s is the post-merger profit margin of the merged firm,evaluated at the pre-merger price, and the r.h.s. is the sum of themerger partners’ pre-merger profit margins



Proof.Add pre-merger FOCs:∑

i∈I

[p(Q)− ci(qi)] + p′(Q)∑i∈I

qi = 0.

Due to the assumptions on p(Q), merger reduces prices ifmerged-firms post-merger output QI bigger than pre-merger output QI .Setting the lhs from the Proposition in the lhs above yields

[p(Q)− cI(∑i∈I

qi)] + p′(Q)∑i∈I

qi > 0.



Define industry demand elasticity

ε ≡ ∂Q∂p

pQ

=−p(Q)

Qp′(Q)

Sum up first-order conditions:

[p(Q)− cI(∑i∈I

qi)] > p −∑i∈I

(p + p′(Q)qi).



cI < p + p′(∑i∈I

qi)

cI < p +−p/Qp′

εp′(∑i∈I

qi)

cI < p − pε

∑i∈I qi

Q

cI < p(1−∑

i∈I si

ε)

All right-hand-side components often estimable or observable


External effects of merger

Now consider the external effect E of the mergers on theoutsiders: Consumers and other firms

I Output of outsider firms:∑

i /∈I qiI∫∞

p(Q)D(z)dz: Consumer surplus at price p(Q)

Define market share of firm i : si = qiQ

I Market shares very often observable

Define dqidQ as the change in non-merging firm i ’s output when

industry output changes marginally

E ≡∫ ∞

p(Q)D(z)dz +

∑i /∈I

[(p(Q)qi − ci(qi))]


External effects cont.

PropositionThe output-reducing merger dqi < 0 has a nonnegative external effect,dE ≥ 0, if and only if

sI ≤∑i /∈I

si(dqi

dQ).


External effects cont.

Proof.Taking total differential of E

dE = −Qp′(Q)dQ +∑

i /∈I qip′(Q)dQ +

∑i /∈I [(p(Q)− ci(qi))]dqi

= −qp′(Q)dQ +∑

i /∈I qip′(Q)dqi

= −p′(Q)dQ[q +∑

i /∈I qi(dqidQ )

= −p′(Q)dQ[sI +∑

i /∈I si ](dqidQ )


Summary 1

Cournot-Model implies relatively restrictive conditions for mergerto be beneficial to consumers

I Synergies in merging firms marginal costs needed for merger not tohurt consumer surplus

F But synergies very difficult to observe

I Markups depend on own technology Ci , demand elasticity ∂p(Q)∂Q ,

number of firms n, and rivals’ technology C−i

I Merger can lead to positive external effects even without synergies


Summary 2

Several restrictive assumptionsI No entry considerations

I homogeneous goods in static game

I Current reserach also focuses on dynamic Competition Policy inCournot setting

F Nocke and Whinston (JPE 2011): If competition authority only looks“myopically” at the current merger, this will also lead to the consumersurplus maqimizing dynamic sequence of mergers


Next steps

So far only homogeneous goods:I Products act as perfect substitutes for consumers

I So far simple demand function p(Q)

Now allow for more heterogeneity of p(Q)I Horizontal product differentiation: consumers have different tastes

for product attributes

I Vertical product differentiation: consumers prefer high qualityproducts to low quality products


Documents

Market Power and Efficiency