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Product Differentiation Product differentiation Industrial Organization Bernard Caillaud Master APE - Paris School of Economics September 22, 2016 Bernard Caillaud Product differentiation Motivation The Bertrand paradox relies on the fact buyers choose the cheap- est firm, even for very small price differences. In practice, some buyers may continue to buy from the most expensive firms because they have an intrinsic preference for the product sold by that firm: Notion of differentiation. Indeed, assuming an homogeneous product is not realistic: rarely exist two identical goods in this sense For objective reasons: products differ in their physical char- acteristics, in their design, ... For subjective reasons: even when physical differences are hard to see for consumers, branding may well make two prod- ucts appear differently in the consumers' eyes Bernard Caillaud Product differentiation Motivation Differentiation among products is above all a property of con- sumers' preferences: Taste for diversity Heterogeneity of consumers' taste But it has major consequences in terms of imperfectly competi- tive behavior: so, the analysis of differentiation allows for a richer discussion and comparison of price competition models vs quan- tity competition models. Also related to the practical question (for competition authori- ties) of market definition: set of goods highly substitutable among themselves and poorly substitutable with goods outside this set Bernard Caillaud Product differentiation Motivation Firms have in general an incentive to affect the degree of differ- entiation of their products compared to rivals'. Hence, differen- tiation is related to other aspects of firms’ strategies. Choice of products: firms choose how to differentiate from rivals, this impacts the type of products that they choose to offer and the diversity of products that consumers face. Entry: is there enough room for differentiation so that a firm could enter profitably Advertising: advertising is a powerful marketing strategy to cre- ate differentiation in the consumers' perception about products Bernard Caillaud Product differentiation Today's session Product differentiation: Horizontal differentiation Vertical differentiation and natural oligopolies Differentiated products oligopoly: general results Nature of competition: prices vs quantities Market definition Empirical strategy to analyze diffferentiation Monopolistic competition and the Chamberlin model Advertising: Imperfect competition with "reach" advertising Dispersion of consumers and demand rotation Advertising: the content matters Bernard Caillaud Product differentiation Views on product differentiation Differentiation can be incorporated in representative consumer's preferences that rely on consumption of the various products Preferences usually on existing products Problematic when considering entry by a new product Or as a consequence of consumers' heterogeneity Heterogeneity in valuations of consumers with respect to the set of characteristics of products: characteristics approach (Lancaster, 1971) Often discrete approach: consumers buy 1/0 units, focus on one characteristic, others treated as random variables Bernard Caillaud Product differentiation Views on product differentiation Representative consumer approach used to compare price vs quan- tity competition Discrete choice models widely used: easily tractable for theoret- ical analysis, nice interpretation, used in empirical work. Horizontal vs vertical differentiation models: Horizontal: a product always preferred by some consumers Vertical: consumers agree which one they prefer (quality) But for which prices ? What if very different costs of pro- duction: production side also matters (think about quality) Vertical differentiation: when all consumers prefer one prod- uct to the other when both priced at marginal cost; other- wise, some horizontal differentiation Bernard Caillaud Product differentiation Horizontal Differentiation: Hotelling model Each version of the good attached to an "address" in space of pos- sible configurations. Each consumer's utility depends on quantity and "distance" between ideal version and purchased version Initially, a spatial competition (discrete choice model); where to buy? Disutility interpreted as transportation costs. Hotelling's linear city: Buyers uniformly distributed on [0; 1]. They have unit de- mand, with gross utility v (assumed large) for the product Firms 1 and 2, located at extremities, produce same good at unit cost c. Consumers incur quadratic transportation cost: buyer at x, 2 2 maxfv − p1 − tx ; v − p2 − t(1 − x) g Bernard Caillaud Product differentiation Hotelling model Marginal or indifferent buyerx ~: 2 2 v − p1 − tx~ = v − p2 − t(1 − x~) : Demands faced by the firms: 1 p − p D (p ; p ) =x ~ = − 1 2 ; 1 1 2 2 2t 1 p − p D (p ; p ) = 1 − x~ = − 2 1 : 2 1 2 2 2t Profit functions: πi(pi; pj) = (pi − c)Di(pi; pj): Bernard Caillaud Product differentiation Hotelling model FOC conditions yields increasing best replies: p + t + c P (p ) = j i j 2 Price equilibrium is unique and symmetric: p∗ = c + t and equi- librium profits are equal to t=2. When t increases, products are increasingly differentiated (for consumers). Firms compete less fiercely for the same clients, their neighboring consumers become somehow captive and mar- ket power increases But the model reduces to standard Bertrand when: t = 0, i.e. no differentiation If firms were located at same address (minimal differentia- tion), instead of at extremities (maximal differentiation) Bernard Caillaud Product differentiation Hotelling with endogenous locations Assume firm 1 located at a, and firm 2 at 1 − b with 0 ≤ a ≤ 1 − b ≤ 1. Now, consumer at x: 2 2 maxfv − p1 − t(x − a) ; v − p2 − t(x + b − 1) g Demands are given by: 1 − a − b p − p D (p ; p ; a; b) = a+ − 1 2 = 1−D (p ; p ; a; b) 1 1 2 2 2t(1 − a − b) 2 1 2 Characterization of equilibrium prices for given locations: a − b p∗(a; b) = c + t(1 − a − b) 1 + 1 3 b − a p∗(a; b) = c + t(1 − a − b) 1 + 2 3 Bernard Caillaud Product differentiation Hotelling with endogenous locations Consider a two-stage game to endogenize the choice of location, i.e. the choice of firms about how to differentiate from rivals. Firms choose the characteristic of their products/locations; Firms choose their prices. At stage 1, problem of firm 1: ∗ ∗ max Π1(a; b) ≡ π1 (p (a; b); p (a; b); a; b) a 1 2 ∗ ∗ ∗ = (p1(a; b) − c) D1 (p1(a; b); p2(a; b); a; b) Bernard Caillaud Product differentiation Hotelling with endogenous locations At interior equilibrium (in locations) for firm 1: dΠ @π @π @p∗ @π @p∗ 1 (a; b) = 1 + 1 1 + 1 2 = 0: da @a @p1 @a @p2 @a |{z} |{z} | {z } Direct effect =0 (Enveloppe Thm) Strategic effect Direct effect: @π @D 1 = (p∗ − c) 1 > 0 @a 1 @a Given p2, firm 1 wants to get closer (lower differentiation) to the center to increase its own demand if a < 1=2. Strategic effect: @π @p∗ 1 2 < 0 @p2 @a Moving away from the center (higher differentiation) allows to soften the competition in prices: firm 2 is less aggressive Bernard Caillaud Product differentiation Hotelling with endogenous locations The maximum differentiation principle dΠ1 In the Hotelling model described above: da < 0, so that firms want to differentiate as much as possible! The strategic effect dominates the demand effect. Critical: uniform distribution, v large (fully covered market) With linear transportation costs, non existence of p.s. price equilibrium is many subgames... If prices are fixed, equal to p, say because of regulation, a minimum differentiation principle prevails (Hotelling's orig- inal point !), as only demand effect exists Socially optimal differentiation minimizes total transporta- 0 1 0 tion costs, hence x1 = 4 = 1 − x2. Bernard Caillaud Product differentiation Horizontal differentiation and entry Force towards excessive differentiation compared to what's so- cially optimal. But when firms differentiate, they create an op- portunity for entry in between ! Is there excessive entry, i.e. too many products in equilibrium ? Hotelling's linear city not well fitted to analyze this question because of boundary effects. Salop (1979) proposes a version without boundaries to address the question of excessive entry A circular space: unit-length circle Consumers are uniformly distributed N firms are symmetrically located Bernard Caillaud Product differentiation Horizontal differentiation and entry Look for a symmetric price equilibrium p By deviating at pi slightly below p, firm i gets market share 2 1 2 2S given by: pi + tS = p + t( N − S) and profits: N t (p − c)( + p − p ) t i N 2 i t NC for p to be a symmetric equilibrium: p = c + N 2 with t equilibrium profits N 3 Free entry with setup cost f leads to an equilibrium number of 1 t 1=3 2 3 firms N∗ = ( f ) and p = c + (tf ) Bernard Caillaud Product differentiation Horizontal differentiation and entry Price above marginal cost, yet no profits: market power is about pricing above marginal cost, NOT above average cost ! As f decreases, more firms with smaller price; in the limit market becomes approximately competitive and consumers purchase a product close to their preferred one As t increases, more firms with higher price (increase possi- bility of differentiation) There is too much entry compared to social optimum Price doesn't matter, all consumers are served one unit Social cost = duplication of entry costs + total transporta- tion costs paid by consumers 0 t 1=3 ∗ Socially optimal diversity: N = ( 6f ) < N Business - stealing effect Bernard Caillaud Product differentiation Model of vertical differentiation A model of competition with different qualities. Two firms, 1; 2, with qualities
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