Price Theory of Two-Sided Markets

Transcription

1 The E. Glen Weyl Department of Economics Princeton University Fundação Getulio Vargas August 3, 2007

2 Definition of a two-sided market 1 Two groups of consumers 2 Value from connecting (proportional to partners) 3 matters (Coase/price neutrality fails)

3 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 demand D A (p A )D B (p B ) Problem: Topsy-turvy stop full analysis Strategy: Divide and conquer Positive analysis: vulnerability Normative analysis: average surplus

4 The vulnerability" of demand Preliminaries Price level Standard monopolist problem (p,d( ), c) Familiar FOC: m p c = p ɛ(p) γ(p) To get sufficiency: γ < 0 log-concave demand, assume this Margin = exploitation", γ is consumer s vulnerability" of demand

5 Preliminaries Price level Why does competition lower price? When two symmetric firms D 1 (p 1, p 2 ) = D 2 (p 2, p 1 ), two notions of elasticity/vulnerability : Total vulnerability γ = p ɛ vs. own-price vulnerability γ o = p ɛ o m = γ o for Bertrand eq, analogous to monopoly γ o < γ as ɛ o > ɛ See graph Standard intuition through vulnerability: under competition raising price drives away more consumers So optimal to set lower price The argument parallel in two-sided markets

6 Starting point of my analysis Preliminaries Price level Compare monopoly to duopoly ownership of two platforms Start with Rochet-Tirole (2003) foc s: Monopoly: m p A + p B c = γ A( p A) = γ B( p B) Duopoly: m p A + p B c = γo A ( p A, p B) = γo B ( p B, p A) Analogous to standard market, but balance" vulnerabilities (total or own-price) between buyers" and sellers" Crucial that γ i decline; log-concavity And substitutability γ i o(p i, p j ) < γ i (p i ), p i, p j, i (multi-homing or own-price elasticity) γ i o less constrained than γ

7 Proposition 1 Positive Analysis Preliminaries Price level Price level p p A + p B Price level under monopoly ownership p M Price level at duopoly equilibrium p C p M > p C Many Bertrand eq., holds for all.

8 Proof strategy Positive Analysis Preliminaries Price level General approach: Separate competition pushing down prices from topsy-turvy (price balance) For this, construct vulnerability level ) γ(p) γ (p A A (p) ; p A (p) solves γ A (p A ) = γ B (p p A ) given p Same for competition: γ o (p) Then invoke standard market strategy above

9 Preliminaries Price level Balance of competition and individual prices Not just interested in price level, but also in individual prices Difficult to say much generally, but to illustrative extreme cases

10 Proposition 2 Positive Analysis Preliminaries Price level If competition completely unbalanced : γ A o (p A, p B ) = γ A (p A ), γ B o (p B, p A ) < γ B (p B ), p A, p B p B M > pb C but pa M < pa C Price level falls = equilibrium vulnerability falls γ A stable and declining = p A rises

11 Proposition 3 Positive Analysis Preliminaries Price level Opposite extreme; if competition perfectly balanced: γ A o (p A, p B ) = αγ A (p A ), γ B o (p B, p A ) = αγ B (p B ) p A, p B, α (0, 1) p B M > pb C p A M > pa C

12 Preliminaries Price level Analysis of balanced competition Note that p A (p) solving γ A (p A ) = γ B (p p A ) also solves γ A o (p A, p p A ) = γ B o (p p A, p A ) Thus, given price level falls, only need that 0 < p A (p) < 1, p, implicitly differentiate: 0 < p A (p) = γb γ A +γ B < 1

13 Price controls Positive Analysis Preliminaries Price level Unilateral price control is p A p A max, p B unregulated Proposition 4: Same as completely unbalanced competition; pressure on one side, none on the other Price level control is p p max Proposition 5: Same as perfectly balanced competition; unchanged dynamics of price balance, no topsy-turvy

14 Subsidies Positive Analysis Preliminaries Price level All subsidies equivalent: reducing cost from c to c σ same as decreasing effective price from p A to p A σ Balance unchanged Subsidies reduce (effective) price level, simpler formula using vulnerability, applies (simplifies) in standard markets: dp dσ = 1 1 γ

15 A framework for welfare analysis Optimal price level and subsidies Applications Framework from Rochet-Tirole (2003) Multiplicative demand/externality form: D A (p A )D B (p B ) under monopoly Profit: (p c)d A (p A )D B (p B ) Surplus side i: V i (p i ) = p D i (p)dp i Log-concavity of surplus Average surplus: V i (p i ) = V i (p i ) D i (p i )

16 Welfare criteria Positive Analysis Optimal price level and subsidies Applications 1 Social surplus (consider profits): π soc = D A V B + D B V A + (p c)d A D B 2 (Tax-augmented) Consumer surplus (with subsidy σ): π tax = D A V B + D B V A σd A D B

17 Linear vulnerability class Optimal price level and subsidies Applications Demand has linear vulnerability iff: D(p) = { (a p) α b p a 0 p > a Log-concavity and positivity imply b, α > 0 Only interesting if p a, then: Average surplus: γ(p) = D(p) D (p) = a p α V (p) = V (p) D(p) = a p 1+α α measures relative curvature; α > 1 convex; α < 1 concave

18 Positive Analysis Optimal price level and subsidies Applications Again, separate balance from level Like Rochet-Tirole, first consider balance given level They ask, does monopolist choose optimal balance? Yes in bi-linear case, not clear how general

19 equations Optimal price level and subsidies Applications Everything given p > c, easily extended to p c: 1 Monopolist profit=volume maximizing (RT2003): γ A (p A ) = γ B (p p A ) 2 Consumer surplus maximizing (RT2003): V A (p A )γ A (p A ) = V B (p p A )γ B (p p A ) ( ) 3 Social surplus maximizing λ 1 1+p c : [ ] [ ] 1 λ + λv A (p A ) γ A (p A ) = γ B (p p A ) 1 λ + λv B (p p A )

20 Corollary 1 Positive Analysis Optimal price level and subsidies Applications Do these often agree? Consider linear vulnerability class: γ = 1 + α α V Only agreement when α A = α B Measure 0 under Lebesgue measure over (α A, α B ) Rochet-Tirole coincidence extremely special Disagreement proportional to difference in relative curvature on two sides

21 Transfers Positive Analysis Optimal price level and subsidies Applications Monopolist chooses wrong balance How do we identify improvements to welfare? Suppose we start at monopoly prices: 1 If V i > 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 hurts 3 Result: some transfers (price balance controls?) benefit both sides average consumers

22 Optimal price level Positive Analysis Optimal price level and subsidies Applications Assume both price balance: both prices declining in price level 1 p < c Price level regulation Subsidies Balanced competition 2 Value of reducing price level > 0 whenever p c

23 Optimal price level and subsidies Applications Proof that optimal price level is below cost Let p i (p) to be price on side i with price level p Differentiating social surplus with respect to price level yields: D A p A V B + D B p B V A + (p c) [D A p A D B + D B p B D A] D i < 0, p i > 0 and p c 0 for p c so last term (associated with traditional monopoly distortions) is non-positive. So expression : D A p A V B + D B p B V A These are the externalities...clearly this is strictly negative

24 Propositions 9 and Corollaries 2 Optimal price level and subsidies Applications To get formula for socially optimal price level, we need to take a stand on balance Natural choice: socially optimal price balance Natural Ramsey pricing form: p = c V i( ) p i (p ) In linear vulnerability case this is: p = a i + a j a i +a j c 1 ν ν 1 2+α i +α j The more concave demand, the great should be c p

25 Optimal price level and subsidies Applications 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: η p = a i + a j a i +a j c 1 η [ ] α i α j 1 (α i +α j ) 2 1+α i α j p > p if α i α j Ramsey pricing + adjustment Give less subsidies because monopolist does not optimally allocate them

26 Proposition 11 and Corollary 5 Optimal price level and subsidies Applications In standard market, subsidies are big transfer to firm; bad for tax-augmented consumer welfare Is this still true in two-sided markets? General conditional complex But in linear vulnerability, subsidy increases tax-augmented consumer surplus if both demands convex

27 Optimal price level and subsidies Applications Welfare effects of balanced competition/regulation Competition has two effects: price level and balance When competition is perfectly (sufficiently) balanced or when price level control imposed, both prices fall Thus only level effect So by Proposition 8, these are welfare-enhancing

28 Unbalanced competition Optimal price level and subsidies Applications What about unbalanced competition and regulation? Level effect always good Balance effect may be positive or negative (in a strong sense) by Lemma 1 Balance may dominate level effect Sufficiently small, sufficiently unbalanced fall in price level may harm both sides (on average)! Sufficiently small, sufficiently unbalanced fall in price level may benefit both sides more than any balanced reduction in price level Anything goes?

29 A related project Positive Analysis Vertical relationships Policy implications Some two-sided markets have intermediary between platform and consumers on one side: debit card clearing network (Star, Interlink) and issuing banks Is it better that these be integrated (Interlink by Visa) or separate (Star)?

30 Results on vertical integration Vertical relationships Policy implications Proofs available in longer version of paper (separate paper soon) Price level, buyers price always lower under integration Seller s price depends on curvature of buyer s vulnerability Quite robust (competition, strategic set-up) Two-sided double marginalization problem Bonus: new characterization of standard double marginalization problem using vulnerability

31 Vertical relationships Policy implications 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-sided versus standard markets (Evans 2003) My results: even more important than in standard markets First-order harm from market power + second order Two dimensions of distortion (relative to social optimum)

32 Insights for antitrust Positive Analysis Vertical relationships Policy implications 1 Cannot infer anti-competitive behavior" or collusion from individual prices; instead use price level 2 Price level better surrogate for welfare than individual prices...but not sufficient 3 Competition may cause harm, so if authority know this is the situation, forbearance may be advisable 4 But ex-ante probably balance effects neutral, so competition policy important 5 Vertical integration probably good

33 Vertical relationships Policy implications Insights for regulation (and subsidies) 1 Unilateral price controls (net neutrality, interchange fee regulation) raises prices to other side of the market 2 Price level controls an interesting alternative (at least we know direction) 3 controls can help in theory 4 But strategic issues emerge in identifying which way to move 5 Subsidies very attractive, relative to standard market