The Price Theory of Two-Sided Markets

Positive AnalysisNormative Analysis

Conclusion

The Price Theory of Two-Sided Markets

E. Glen Weyl

Department of EconomicsPrinceton University

Fundação Getulio VargasAugust 3, 2007

Weyl (2007) Price Theory of Two-Sided Markets


Conclusion

Definition of a two-sided market

1 Two groups of consumers2 Value from connecting (proportional to partners)3 Price balance matters (Coase/price neutrality fails)



Conclusion

Price theory of two-sided markets

Goal: How are two-sided markets the same and different?How do effects of policies differ?Rochet and Tirole canonical model: multiplicative demandDA(pA)DB(pB)

Problem: Topsy-turvy stop full analysisStrategy: Divide and conquerPositive analysis: vulnerabilityNormative analysis: average surplus



Conclusion

PreliminariesPrice levelPrice balance

The “vulnerability" of demand

Standard monopolist problem (p,D(·), c)Familiar FOC:

m ≡ p − c = pε(p) ≡ γ(p)

To get sufficiency: γ′ < 0 ⇐⇒ log-concave demand,assume thisMargin =“exploitation", γ is consumer’s “vulnerability" ofdemand



Conclusion


Why does competition lower price?

When two symmetric firms D1(p1, p2) = D2(p2, p1), two notionsof elasticity/vulnerability :

Total vulnerability γ = pε vs. own-price vulnerability γo = p

εo

m = γo for Bertrand eq, analogous to monopolyγo < γ as εo > ε

See graphStandard intuition through vulnerability: under competitionraising price drives away more consumers

So optimal to set lower price

The argument parallel in two-sided markets



Conclusion


Starting point of my analysis

Compare monopoly to duopoly ownership of two platforms

Start with Rochet-Tirole (2003) foc’s:

Monopoly:m ≡ pA + pB − c = γA(

pA)= γB(

pB)Duopoly:

m ≡ pA + pB − c = γAo(pA, pB)

= γBo(pB, pA)

Analogous to standard market, but “balance" vulnerabilities(total or own-price) between “buyers" and “sellers"Crucial that γ i decline; log-concavityAnd substitutability γ i

o(pi , pj) < γ i(pi),∀pi , pj , i(multi-homing or own-price elasticity)γ i

o less constrained than γ



Conclusion


Proposition 1

Price level p ≡ pA + pB

Price level under monopoly ownership p?M

Price level at duopoly equilibrium p?C

p?M > p?

C

Many Bertrand eq., holds for all.



Conclusion


Proof strategy

General approach: Separate competition pushing downprices from topsy-turvy (price balance)For this, construct vulnerability level

γ(p) ≡ γA(

pA?(p)

); pA?

(p) solves γA(pA) = γB(p − pA)

given pSame for competition: γo(p)

Then invoke standard market strategy above



Conclusion


Balance of competition and individual prices

Not just interested in price level, but also in individualpricesDifficult to say much generally, but to illustrative extremecases



Conclusion


Proposition 2

If competition completely unbalanced :γA

o (pA, pB) = γA(pA), γBo (pB, pA) < γB(pB),∀pA, pB

pBM > pB

C but pAM < pA

C

Price level falls =⇒ equilibrium vulnerability fallsγA stable and declining =⇒ pA rises



Conclusion


Proposition 3

Opposite extreme; if competition perfectly balanced:γA

o (pA, pB) = αγA(pA), γBo (pB, pA) = αγB(pB)∀pA, pB, α ∈ (0, 1)

pBM > pB

C pAM > pA

C



Conclusion


Analysis of balanced competition

Note that pA?(p) solving γA(pA) = γB(p − pA) also solves

γAo (pA, p − pA) = γB

o (p − pA, pA)

Thus, given price level falls, only need that0 < pA?′

(p) < 1,∀p, implicitly differentiate:

0 < pA?′(p) = γB′

γA′+γB′ < 1



Conclusion


Price controls

Unilateral price control is pA ≤ pAmax , pB unregulated

Proposition 4: Same as completely unbalancedcompetition; pressure on one side, none on the other

Price level control is p ≤ pmax

Proposition 5: Same as perfectly balanced competition;unchanged dynamics of price balance, no topsy-turvy



Conclusion


Subsidies

All subsidies equivalent: reducing cost from c to c − σsame as decreasing effective price from pA to pA − σ

Balance unchanged

Subsidies reduce (effective) price level, simpler formulausing vulnerability, applies (simplifies) in standard markets:

dpdσ

= − 11− γ′



Conclusion

Price balanceOptimal price level and subsidiesApplications

A framework for welfare analysis

Framework from Rochet-Tirole (2003)Multiplicative demand/externality form: DA(pA)DB(pB)under monopolyProfit: (p − c)DA(pA)DB(pB)

Surplus side i :V i(pi) =

∫∞pi Di(p)dp

Log-concavity of surplusAverage surplus:V

i(pi) = V i (pi )

Di (pi )



Conclusion


Welfare criteria

1 Social surplus (consider profits):

πsoc = DAV B + DBV A + (p − c)DADB

2 (Tax-augmented) Consumer surplus (with subsidy σ):

πtax = DAV B + DBV A − σDADB



Conclusion


Linear vulnerability class

Demand has linear vulnerability iff:

D(p) =

{(a−p)α

b p ≤ a0 p > a

Log-concavity and positivity imply b, α > 0Only interesting if p ≤ a, then:

γ(p) = − D(p)D′(p) = a−p

α

Average surplus:

V (p) = V (p)D(p) = a−p

1+α

α measures relative curvature; α > 1 convex; α < 1concave



Conclusion


Price balance

Again, separate balance from levelLike Rochet-Tirole, first consider balance given levelThey ask, does monopolist choose optimal balance?Yes in bi-linear case, not clear how general



Conclusion


Price balance equations

Everything given p > c, easily extended to p ≤ c:

1 Monopolist profit=volume maximizing (RT2003):

γA(pA) = γB(p − pA)

2 Consumer surplus maximizing (RT2003):

VA(pA)γA(pA) = V

B(p − pA)γB(p − pA)

3 Social surplus maximizing(

λ ≡ 11+p−c

):

[1− λ + λV

A(pA)

]γA(pA) = γB(p − pA)

[1− λ + λV

B(p − pA)

]



Conclusion


Corollary 1

Do these often agree?Consider linear vulnerability class:

γ =1 + α

αV

Only agreement when αA = αB

Measure 0 under Lebesgue measure over (αA, αB)

Rochet-Tirole coincidence extremely specialDisagreement proportional to difference in relativecurvature on two sides



Conclusion


Transfers

Monopolist chooses wrong balanceHow do we identify improvements to welfare?

Suppose we start at monopoly prices:

1 If Vi> V

j, transfer from i to j good for social/consumer

welfare (opposite bad)2 If V

i> γ i = γ j , transfer from i to j benefits average i ,

reverse hurts3 Result: some transfers (price balance controls?) benefit

both sides’ average consumers



Conclusion


Optimal price level

Assume both price balance: both prices declining in pricelevel

Price level regulationSubsidiesBalanced competition

1 p? < c2 Value of reducing price level > 0 whenever p ≥ c



Conclusion


Proof that optimal price level is below cost

Let pi(p) to be price on side i with price level pDifferentiating social surplus with respect to price levelyields:

DA′pA′

V B + DB′pB′

V A + (p − c)[DA′

pA′DB + DB′

pB′DA

]Di ′ < 0, pi ′ > 0 and p − c ≥ 0 for p ≥ c so last term(associated with traditional monopoly distortions) isnon-positive. So expression ≤:

DA′pA′

V B + DB′pB′

V A

These are the externalities...clearly this is strictly negative



Conclusion


Propositions 9 and Corollaries 2

To get formula for socially optimal price level, we need totake a stand on balanceNatural choice: socially optimal price balance

Natural Ramsey pricing form:

p?? = c − Vi(

pi??(p??)

)In linear vulnerability case this is:

p?? = ai + aj −ai+aj−c

1−ν

ν ≡ 12+αi+αj

The more concave demand, the great should be c − p



Conclusion


Proposition 10 and Corollary 3 and 4

How should we correct if monopoly governs price balance?“Socially optimal subsidies"

General formula complex, but in linear vulnerability:

p? = ai + aj −ai+aj−c

1−η

η ≡ αiαj(αi+αj )2

[1

1+αi+ 1

1+αj

]

p? > p?? if αi 6= αj

Ramsey pricing + adjustmentGive less subsidies because monopolist does not optimallyallocate them



Conclusion


Proposition 11 and Corollary 5

In standard market, subsidies are big transfer to firm; badfor tax-augmented consumer welfareIs this still true in two-sided markets?General conditional complexBut in linear vulnerability, subsidy increasestax-augmented consumer surplus if both demands convex



Conclusion


Welfare effects of “balanced” competition/regulation

Competition has two effects: price level and balanceWhen competition is perfectly (sufficiently) balanced orwhen price level control imposed, both prices fallThus only level effectSo by Proposition 8, these are welfare-enhancing



Conclusion


Unbalanced competition

What about unbalanced competition and regulation?Level effect always goodBalance effect may be positive or negative (in a strongsense) by Lemma 1Balance may dominate level effectSufficiently small, sufficiently unbalanced fall in price levelmay harm both sides (on average)!Sufficiently small, sufficiently unbalanced fall in price levelmay benefit both sides more than any balanced reductionin price levelAnything goes?



Conclusion

Vertical relationshipsPolicy implications

A related project

Some two-sided markets have intermediary betweenplatform and consumers on one side: debit card clearingnetwork (Star, Interlink) and issuing banksIs it better that these be integrated (Interlink by Visa) orseparate (Star)?



Conclusion


Results on vertical integration

Proofs available in longer version of paper (separate papersoon)Price level, buyers price always lower under integrationSeller’s price depends on curvature of buyer’s vulnerabilityQuite robust (competition, strategic set-up)Two-sided double marginalization problemBonus: new characterization of standard doublemarginalization problem using vulnerability



Conclusion


Is policy important in two-sided markets?

Monopoly may not distort too much in two-sided markets(Rochet and Tirole 2003?, Wright 2003, 2004 )Policy too unpredictable to intervene (Wright 2006)No difference between importance of policy in two-sidedversus standard markets (Evans 2003)My results: even more important than in standard marketsFirst-order harm from market power + second orderTwo dimensions of distortion (relative to social optimum)



Conclusion


Insights for antitrust

1 Cannot infer “anti-competitive behavior" or collusion fromindividual prices; instead use price level

2 Price level better surrogate for welfare than individualprices...but not sufficient

3 Competition may cause harm, so if authority know this isthe situation, forbearance may be advisable

4 But ex-ante probably balance effects neutral, socompetition policy important

5 Vertical integration probably good



Conclusion


Insights for regulation (and subsidies)

1 Unilateral price controls (net neutrality, interchange feeregulation) raises prices to other side of the market

2 Price level controls an interesting alternative (at least weknow direction)

3 Price balance controls can help in theory4 But strategic issues emerge in identifying which way to

move5 Subsidies very attractive, relative to standard market


The Price Theory of Two-Sided Markets

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