Differentiated Durable Goods Monopoly and Competition Nava and - PowerPoint PPT Presentation

Differentiated Durable Goods Monopoly and Competition Nava and Schiraldi London School of Economics March 2018 Nava (LSE) Differentiated Durable Goods Mar 18 1 / 74

Focus: Differentiated Durable Goods We study the incentives to differentiate products when goods are sold over time and without commitment. The results on the monopoly : characterize limiting outcomes in terms of a simple static problem ; deliver a robust Coase conjecture for all multi-product settings; develop insights on product design . The results on the competition show why: competition can unambiguously increase market power ; such instances arise when competitors choose products. Nava (LSE) Differentiated Durable Goods Mar 18 2 / 74

Coase Conjecture 1972 Coase’s seminal conjecture first raised the time consistency problem: Upon selling to high value buyers, a monopolist cannot stop selling. If so, prices keep falling and forward looking buyers expect this. But if so, buyers are unwilling to pay a high price in the first place. As the time between offers vanishes, the opening price converges to its lowest valuation and the competitive quantity is sold in a twinkle of an eye . Formal proofs in Stokey 1981; Fudenberg, Levine, Tirole 1985; Gul, Sonnenschein, Wilson 1986; Asubel, Deneckere 1989 established that: Varieties Gap MC MC Time Efficient Competitive Unique 1 No Yes Infinite Yes MPE Folk 1 Yes Yes Finite Yes Yes PBE Nava (LSE) Differentiated Durable Goods Mar 18 3 / 74

Monopoly: Related Literature The more recent literature on durable goods monopoly has analysed: The robustness of Coase’s insight to changes in the assumptions. 1 Bond-Samuelson 1984; Kahn 1986; Ausubel-Deneckere 1989; Bagnoli-Salant-Swierzbinski 1989; Sobel 1991; Fehr-Kuhn 1995; Biehl 2001; Takeyama 2002; Hahn 2006; Inderst 2008; McAfee-Wiseman 2008; Deb 2011; Montez 2013; Ortner 2014; Board-Pycia 2014. Tactics that could be used to avoid the commitment problem. 2 Bulow 1982; Butz 1990; Levinthaland-Purohit 1989; Waldman 1993; Choi 1994; Waldman 1996; Fudenberg-Tirole 1998; Lee-Lee 1998. Many of these studies are cast as violations of the Coasian conclusion. Nava (LSE) Differentiated Durable Goods Mar 18 4 / 74

Monopoly: Contributions In the monopoly case we establish that: Static and dynamic market-clearing prices coincide. 1 Optimal market-clearing profits bound PBE profits from below. 2 Mixing may be required on-path to conceal discounts . 3 Limiting MPE profits converge to optimal market-clearing profits . 4 Robustness of these conclusions to alternative specifications. 5 Product design implications. 6 Equilibrium pricing is neither minimal, nor competitive, nor efficient . But, the Coasian logic survives in that optimal market-clearing and agreement govern pricing . Nava (LSE) Differentiated Durable Goods Mar 18 5 / 74

Competition: Related Literature The seminal contribution on competition by Gul 1987 : considers markets in which firms produce the same product ; proves a Folk theorem as an incumbent may benefit from entry. These anti-competitive insights however: rely on high discount factors to sustain collusion; apply only when products are not differentiated; do not extend to stationary equilibria . Nava (LSE) Differentiated Durable Goods Mar 18 6 / 74

Competition: Contributions Competition increases market power if the present value of profits of every seller is higher than in their respective monopoly setting. With differentiated products , competition can increase market power: in all PBE even in stationary equilibria ; regardless of the value the discount factor . In the competition case we: find conditions for competition to increase market power in all PBE; 1 endogenize the choice of products in a location choice model; 2 show that this naturally leads to increased in market power. 3 Nava (LSE) Differentiated Durable Goods Mar 18 7 / 74

Model Nava (LSE) Differentiated Durable Goods Mar 18 8 / 74

Model: The Monopolist The time is countably infinite, t ∈ { 0 , 1 , ... } . A single firm operates in the market in every period. Two varieties , a and b , of a durable good can be produced and sold. At each time period the monopolist sets prices for the two varieties p = ( p a , p b ) . The marginal cost of producing units of each variety is zero . The monopolist discounts the future with a discount factor δ . Its payoff amounts to the present discounted value of future profits. Nava (LSE) Differentiated Durable Goods Mar 18 9 / 74

Model: Buyers All buyers have unit-demand for the durable good. Buyers exit the market upon purchasing any one variety. There is a unit measure of buyers. Buyers are characterised by their values for the two products v = ( v a , v b ) . Value profiles are private information of buyers. Buyers discount the future by the common factor δ . The payoff of consuming variety i at price p i at date t amounts to δ t − 1 ( v i − p i ) . Nava (LSE) Differentiated Durable Goods Mar 18 10 / 74

Model: Buyers’ Values A measure F on the unit square [ 0 , 1 ] 2 describes the distribution of values. Let F be the associated cumulative and V be the support. Let F i be the marginal cumulative of variety i and V i be its support. Definitions (Regularity Assumption) The market is said to be regular if: V is convex; F is absolutely continuous on R 2 ; its density f satisfies f ( v ) ∈ ( f , f ) for any v ∈ V . The monopolist knows F , but not the value of a given buyer. Nava (LSE) Differentiated Durable Goods Mar 18 11 / 74

Model: Information and Solution Concepts Players observe for every previous period: the prices posted by the monopolist; (possibly) the total measure of buyers for each variety. At any history, a strategy: for the monopolist specifies a profile of prices. for an active buyer specifies which variety to purchase, if any. Let A t be the set of active buyers at a given history h t . Those buyers who have yet to purchase a variety at date t . Our results characterize the measurable PBE of this game. MPE are PBE in which buyers’ strategy depends only on current prices . Nava (LSE) Differentiated Durable Goods Mar 18 12 / 74

Optimal Market Clearing Nava (LSE) Differentiated Durable Goods Mar 18 13 / 74

Static Demand Functions Momentarily consider the static version of the model. Given prices, the static demand for product i amount to d i ( p ) = F ( v i − p i > max { v j − p j , 0 } ) . Nava (LSE) Differentiated Durable Goods Mar 18 14 / 74

Static Market Clearing Prices A market clearing price is a price profile that clears the market. Let M be the set of market clearing prices � � p ∈ R 2 | max i { v i − p i } ≥ 0 for any v ∈ V M = . Independence Concordance Discordance Nava (LSE) Differentiated Durable Goods Mar 18 15 / 74

Static Optimal Market Clearing An optimal market clearing price ¯ p solves the following static problem max p ∈ M [ d a ( p ) p a + d b ( p ) p b ] . The value ¯ π of this program is the optimal market clearing profit . Nava (LSE) Differentiated Durable Goods Mar 18 16 / 74

Static Market Clearing: Minimal Values Let w i denote the minimal value of variety i in the support V . Let w g denote the minimal value of the durable good w g = min v ∈ V max { v a , v b } . Clearly it must be that w g ≥ max { w a , w b } . w g = 0 w g = 0 w g > 0 Nava (LSE) Differentiated Durable Goods Mar 18 17 / 74

Static Market Clearing: Special Cases Varieties are identical if v a = v b for all v ∈ V . Varieties are ranked if they are not identical and v i ≥ v j for all v ∈ V . Varieties are unranked if for any i there is v ∈ V such that v i > v j . Identical Ranked Unranked Nava (LSE) Differentiated Durable Goods Mar 18 18 / 74

Static Optimal Market Clearing: Minimal Pricing Lemma Optimal market-clearing profits: (1) weakly exceed w g ; (2) strictly exceed max i w i if varieties are unranked; (3) equal min i w i if and only if varieties are identical; (4) equal 0 if and only if varieties are identical and ( 0 , 0 ) ∈ V . Nava (LSE) Differentiated Durable Goods Mar 18 19 / 74

Static Optimal Market Clearing: Minimal Pricing Lemma Optimal market-clearing profits strictly exceed w g : (5) if varieties are ranked and w a = w b ; (6) if varieties are independently distributed and w a = w b . Nava (LSE) Differentiated Durable Goods Mar 18 20 / 74

Some Intuition: OMC Lemma Let w a ≥ w b , OMC profits: amount to w a at the MC price p = ( w a , 1 ) ; can thus amount to w b only if w a = w b = w ; amount to w at the MC price ( p i , p j ) = ( w + e , w ) only if d i ( w + e , w ) = F ( v i − v j > e ) = 0. Nava (LSE) Differentiated Durable Goods Mar 18 21 / 74

Static Optimal Market Clearing: Efficiency A price is efficient if every buyer purchases its preferred variety. Fact Optimal market-clearing prices are inefficient: (1) if varieties are ranked and w a = w b ; (2) if varieties are independently distributed and w a = w b . Nava (LSE) Differentiated Durable Goods Mar 18 22 / 74

Static Optimal Market Clearing: Comments In contrast to the 1-variety case, market-clearing no longer implies that: profits amount to the minimal value of a variety or of the good; pricing is efficient or at the minimal value of varieties or of the good; profits equal 0 when there are no gaps and ( 0 , 0 ) ∈ V . Nava (LSE) Differentiated Durable Goods Mar 18 23 / 74

Coase Conjecture Nava (LSE) Differentiated Durable Goods Mar 18 24 / 74