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Topic 6. Product differentiation (I): patterns of price setting

Topic 6. Product differentiation (I): patterns of price setting. Economía Industrial Aplicada Juan Antonio Máñez Castillejo Departamento de Estructura Económica Universidad de Valencia. Index. Topic 7. Product differentiation: patterns of price setting Introduction

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Topic 6. Product differentiation (I): patterns of price setting

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  1. Topic 6. Product differentiation (I): patterns of price setting Economía Industrial Aplicada Juan Antonio Máñez Castillejo Departamento de Estructura Económica Universidad de Valencia

  2. Index Topic 7. Product differentiation: patterns of price setting • Introduction • Horizontal versus vertical product differentiation • The linear city model 3.1 Linear transport costs 3.2 Quadratic transport costs 4. Applications: Coca-Cola versus Pepsi-Cola 5. Conclussions Departamento de Estructura Económica

  3. 1. Introducción • Aim: To study an oligopoly model relaxing the homogeneous product assumption, to analyse the effect of product differentiation on price competition intensity and product choice. • Main implication of the homogeneous product assumption in an oligopoly model of price competition (à la Bertrand) • Bertrand paradox  Price competition between two firms is a sufficient condition to restores the competitive situation p = c Departamento de Estructura Económica

  4. 2. Horizontal and vertical product differentiation • Horizontal product differentiation: two products are differentiated horizontally if, when they are offered at the same price consumers do not agree on which is the preferred product. Example: pine washing-up liquid and lemon-washing up liquid • Vertical product differentiation: two products are differentiated vertically if, when they are offered at the same price consumers agree on which is the preferred product. • Example: washing-up liquid with and without product moisturizing add-up. Departamento de Estructura Económica

  5. Horizontal Dif. Opel Astra Ford Focus Vertical Dif. Vertical Dif. Opel Corsa Ford Fiesta Horizontal Dif. Example Departamento de Estructura Económica

  6. L 0 3.1 Linear city model with linear transport costs : assumptions • Two firms (firms 1 and 2) are located along the segment • The two firms sell a product that is identical except for the location of the firm. • The two firms have constant and identical marginal cost c  c1=c2=c • Each consumer buys a single unit of the product.  Alternative interpretation of the segment as a product characteristic • Consumers are uniformly distributed with unit density along a segment of L length Departamento de Estructura Económica

  7. F1 F2 L 0 3.1 Linear city model with linear transport costs : two-stage game Stage 1: the two firms choose simultaneously their location (long-run decision) Stage 2: the two firms choose simultaneously their prices (short-run decision) We impose maximum product differentiation and so we focus on the determination of the Nash equilibrium in prices (Stage 2). Departamento de Estructura Económica

  8. 3.1 Linear city model with linear transport costs : consumers’ utility function r: reservation price pj: price of the product of firm j xij.: distance (along the segment) between the location of consumer i and the location of firm j t: transport cost per unit of distance (or alternatively intensity of the preference for a given product) • The utility that a consumer i located in X obtains from the purchase of of the good of firm j is given by: Departamento de Estructura Económica

  9. F1 F2 x L-x X L 0 3.1 Linear city model with linear transport costs : transport costs • Transport cost if the product is bought at firm 1 = tx • Transport cost if the product is bought at firm 2 = t(L-x) • Total cost of the product = price + transport costs • Total cost if the product is bought at firm 1 = p1+ tx • Total cost if the product is bought at firm 2= p2+ t(L-x) • With linear transport costs per unit of distance : Departamento de Estructura Económica

  10. F1 F2 d1=x d2=L-x X 0 L 3.1 Linear city model with linear transport costs : demands determination Departamento de Estructura Económica

  11. 3.1 Linear city model with linear transport costs : demand properties • Price elasticity of demand • Price elasticity of demand and transport costs Departamento de Estructura Económica

  12. p2 p1 d2 d1 F1 F2 x L 0 3.1 Linear city model with linear transport costs : demands determination • Total cost of buying at 1 = Total cost of buying at 2 x0 x1 Departamento de Estructura Económica

  13. 0 L F2 F1 3.1 Linear city model with linear transport costs : firm 1 demand Departamento de Estructura Económica

  14.  Firm 1 reaction function  Firm 2 reaction function 3.1 Linear city model with linear transport costs : Obtaining the Nash equilibrium in prices (I) • Maximization problem of firm 1 • Maximization problem of firm 2 Departamento de Estructura Económica

  15. p2 p1 3.1 Linear city model with linear transport costs : Obtaining the Nash equilibrium in prices (II) • Solving the system of equations given by the two reaction functions we obtain the price equilibrium: (given locations) • Profits for both firms are: p*1(p2) p*2(p1) Lt+c (Lt+c)/2 (Lt+c)/2 Lt+c Departamento de Estructura Económica

  16. 3.1 Linear city model with linear transport costs : Obtaining the Nash equilibrium in prices (I) • Although both products are physically identical, as long as t>0 the price is greater than the marginal cost • Why?: • The larger is t the more differentiated are the products for the consumers  the higher is the costs of buying in a further shop. • The larger is t the lower in the intensity of competition between firms 1 and 2 (for the consumers located between the two firms). • When t=0 the products are not differentiated any more  price is equal to marginal cost as in the Bertrand model with homogeneous. Departamento de Estructura Económica

  17. E1 y E2 E1 p0 p1 E2 E1 p2 E1 y E2 p3 c F1 y F2 0 L 3.1 Linear city model with linear transport costs : Analysis of the location decisions (I) • Two extreme cases: • Maximum product differentiation: if t >0  p>c y >0 • Minimum product differentiation: both firms choose the same location  no differentiation  Bertrand model with homogeneous products Departamento de Estructura Económica

  18. F1 F2 L a L-b 0 where a  0 , b 0 y L-a-b  0  It allows the consideration of captive demands • If a+b=L  minimum differentiation • If a=b=0  maximum differentiation F1,F2 F1 F2 L a 0 L-b a=0 L b=0 3.1 Linear city model with linear transport costs : Analysis of the location decisions (II) • With a gain of generality we can assume: Departamento de Estructura Económica

  19. c c F1 F2 a’ a L-b L 0 3.1 Linear city model with linear transport costs : Analysis of the location decisions (III) • Nash equilibrium in locations is the one in which firm i (i=1,2) takes its optimal decision of location and price given its rival’s locations an price decisions • The original result in the Hottelling model (1929): minimum differentiation. Once prices have been chosen, both firms locate in the centre of the segment  L/2 Departamento de Estructura Económica

  20. c c F1 F2 a L-b 0 L 3.1 Linear city model with linear transport costs : Analysis of the location decisions (IV) • This result of minimum differentiation is subject to two important critiques: (D’ Aspremont et al., 1979) • Critique 1: Demand discontinuity. Suppose that both firms are located very close each other Departamento de Estructura Económica

  21. Price competition with homogeneous products c a’ L 0 3.1 Linear city model with linear transport costs : Analysis of the location decisions (V) • Critique 2: Suppose that both firms are located at L/2 • There is no product differentiation: each firm has an incentive to undercut the price of the rival until p1=p2=c. • D’Aspremont et al. (1979) shows that que a=b=L/2 is not a Nash equilibrium in locations  both firms have an incentive to deviate from L/2 to set a p>c y and in this way they would obtain positive profits Departamento de Estructura Económica

  22. F1 F2 L a L-b 0 • Utility function where a  0 , b 0 y L-a-b 0 • We do not impose maximum product differentiation to obtain the Nash • equilibrium in prices. 3.2 Linear city model with quadratic transport costs :Assumptions • It solves the problem of the inexistence of Nash equilibrium in locations that arises in the model with linear transport cost. • Differences with the linear transport costs model : Departamento de Estructura Económica

  23. c 0 L a L-b x 3.2 Linear city model with quadratic transport costs :Discontinuities in demand • With quadratic transport costs the umbrellas that represent the total cost of purchase are U-shaped. Departamento de Estructura Económica

  24. X 0 L a L-b x1 x2 3.2 Linear city model with quadratic transport costs :Obtaining the demands (I) • The consumer located at X will be indifferent between consuming in firms 1 and 2 whenever: Departamento de Estructura Económica

  25. 3.2 Linear city model with quadratic transport costs :Obtaining the demands (II) • If p1=p2: • Firm 1 sells to all the consumers located at the left of its location and firm 2 sells to all the consumers located at its right. • Both firms share evenly the consumers located between them. • The third term catches the sensibility of the demand to price differentials (differences between the prices of two firms) • Demands for firms 1 y 2 Departamento de Estructura Económica

  26. 3.2 Linear city model with quadratic transport costs :Obtaining the equilibrium in prices and locations (II) • Two-stage game: • Stage 1: Firms choose locations simultaneously. • Stage 2: Firms choose prices simultaneously. • We solve by backwards induction:  each firm anticipates that its location decision affects not only its demand but also price competition intensity • To obtain the Nash equilibrium in prices given locations (a,b). • To obtain the Nash equilibrium in locations given prices. Departamento de Estructura Económica

  27. 3.2 Linear city model with quadratic transport costs :Obtaining the price equilibrium given locations (I) • To obtain the price equilibrium, we solve the maximization problems of firms 1 and 2: • Maximization problem of firm 1: • Maximization problem of firm 2: Departamento de Estructura Económica

  28. Symmetric eq. : a=b  •  apc 3.2 Linear city model with quadratic transport costs :Obtaining the price equilibrium given locations (II) • To obtain the price equilibrium, we solve the system of FOCs: • Properties of the price equilibrium: • Asymmetric eq. : a  b  p1-p2 = 2/3 t(L-a-b)(a-b) • That firm located closer the center of the segment sets a higher price • Si a>b  p1>p2 • Si a<b  p2>p1 Departamento de Estructura Económica

  29. 3.2 Linear city model with quadratic transport costs :Obtaining the equilibrium in locations (I) • In the equilibrium in locations, each firm choose location taking as given the rival’s location: • Firm 1 maximizes 1(a,b) choosing a and taking b as given • Firm 2 maximizes 2(a,b) chooseli b and taking a as given • D’Aspremont et al. (1979) shows that with quadratic transport costs the equilibrium in location involoves maximum differentiation : both firms are located in the ends of the segment • Each one of the firms choose the furthest possible location from its from its rival with the aim of differentiating the product and minimizing the effect of a potential price reduction by the rival on its own demand Departamento de Estructura Económica

  30. 3.2 Linear city model with quadratic transport costs :Obtaining the equilibrium in locations (II) • The reduced form of the profit functions show that the location decision: • Has an effect on firms’ demands • Has an effect on firms’ prices • The algebraic derivation of the Nash equilibrium in location is quite complicated, and so we make use of a graphic analysis • We analyze firm 1 location decision that depends on : • Direct effect • Strategic effect Departamento de Estructura Económica

  31. 0 L a a’ L-b x d1 x’ d1’ 3.2 Linear city model with quadratic transport costs :Obtaining the equilibrium in locations (III): direct effect • Direct effect: for a given pair of prices ( ) and a given the location of firm 2, as firm 1 moves its location towards the location of firm 2 (i.e. towards the center of the segment) its demand increase, and so its profis. • Direct effect  minimum differentiation tendency Departamento de Estructura Económica

  32. 3.2 Linear city model with quadratic transport costs :Obtaining the equilibrium in locations (IV): strategic effect • In our two-stage game, the prices (that are chosen in the second stage) are not given, they depend on the first-stage locations decision  strategic effect. Strategig effect. For a given location for firm 2, as firm 1 moves its location towards the center (i.e. closer to its rival), product differentiation decreases  increase of price competition  price reduction  negative effect on prices  maximum differentiation tendency Departamento de Estructura Económica

  33. p2 p1 p2’ x x’ a L-b L 0 d1 3.2 Linear city model with quadratic transport costs :Obtaining the equilibrium in locations (V): strategic effect Departamento de Estructura Económica

  34. p2 p1 p2’ x’ x a a’ L-b d1 0 L d1’ 3.2 Linear city model with quadratic transport costs :Obtaining the equilibrium in locations (VI): strategic effect Strategic effect: maximum differentiation tendency Departamento de Estructura Económica

  35. 3.2 Linear city model with quadratic transport costs :Obtaining the equilibrium in locations (VI): strategic effect vs. direct effect • Direct effect: minimum differentiation tendency • Strategic effect: maximum differentiation tendency. • D’Aspremont et al. (1979) show analytically that, in general the strategic effect dominates over the direct one  final result: maximum differentiation. • Impact of t on the intensity of price competition (that determines the strategic effect) and on the location decision: • If t is low, each firm try to separate from its rival to avoid the strategic effect. • If t is high, firms locate close (each other) to take advantage of the direct effect. Departamento de Estructura Económica

  36. 4. Application: Coca-Cola vs. Pepsi-Cola • Coca-Cola and Pepsi-Cola, the world leaders on the carbonated colas market, sell horizintally differentiated products. • Simplifying assumption: the relevant competition dimension is price ( advertising) • Laffont, Gasmi y Vuong (1992) analyse price competition between Coca-Cola and Pepsi-Cola. They estimated using econometric methods the following demand and marginal costs functions. Departamento de Estructura Económica

  37. 4. Application: Coca-Cola vs. Pepsi-Cola: demand and costs functions • Demand functions for Coca-Cola (product 1) and Pepsi-Cola (product 2). Q1 = 63.42 - 3.98 p1 + 2.25 p2 Q2 = 49.52 - 5.48 p2 + 1.40 p1 • Marginal costs for Coca-Cola and Pepsi-Cola c1=4.96 c2=3.96 • Which is the optimal price for Coca-Cola and Pepsi-Cola? Departamento de Estructura Económica

  38.  Coca-Cola’s reaction function •  Pepsi-Cola’s reaction function 4. Application: Coca-Cola vs. Pepsi-Cola: optimal prices determination • Step 1: solve the maximization problems of Coca-Cola and Pepsi-Cola. • Coca-Cola’s maximization problem: • Pepsi-cola’s maximization problem: Departamento de Estructura Económica

  39. PPEPSI PCOCA(pPEPSI) P*PEPSI PPEPSIi(pCOCA) pCOCA P*COCA 4. Application: Coca-Cola vs. Pepsi-Cola: optimal prices determination (II) • Step 2: solve the system of reaction functions. p1=12.72 y p2=8.11 • Coca-Cola sets a price higher than the Pepsi-Cola one. Departamento de Estructura Económica

  40. 4. Application: Coca-Cola vs. Pepsi-Cola: optimal prices determination (III) • Why Coca-Cola’s price is higher that Pepsi-Cola’s one? • Cost asymmetries • Demand asymmetries Departamento de Estructura Económica

  41. 4. Application: Coca-Cola vs. Pepsi-Cola: optimal prices determination (IV) • Costs asymmetries: • Coca-Cola marginal cost (4.96) > Pepsis-Cola marginal cost (3.96)  Coca-Cola’s price > Pepsi-Cola’s price Departamento de Estructura Económica

  42. p1= p2=p p=1 p=1 a’ a L-b Q1= 53.565 Q2= 53.565 Q1= 45.44 Q1= 61.69 4. Application: Coca-Cola vs. Pepsi-Cola: optimal prices determination (V) • Demand asymmetries Q1=63.42 -1.73p Q2=49.52 -4.08p Q1=63.42 - 3.98 p1+ 2.25 p2 Q2=49.52 - 5.48 p2+ 1.40 p1 • Graphic analysis  normalize p=1 • Q1= 61.69 y Q2=45.44 • Q=Q1+Q2=107.13 1. Symmetric Eq. a=b  Q1=Q2 2. Aymmetric Eq. a’>b  Q1>Q2 Departamento de Estructura Económica

  43. 4. Application: Coca-Cola vs. Pepsi-Cola: optimal prices determination (VI) • The higher Coca-Cola’s price is due to: • Higher marginal cost (cost asymmetries) • Demand asymmetries that favour Coca-Cola Departamento de Estructura Económica

  44. 4. Application: Coca-Cola vs. Pepsi-Cola: optimal prices determination (VII) • Do these asymmetries have any additional impact?  price-cost margin • The price-cost margin of Coca-Cola is higher than the Pepsi-Cola’s one • Demand asymmetry in favour of Coca-Cola • Higher market power for Coca-Cola Departamento de Estructura Económica

  45. 5. Concluding Remarks • Product differentiation solves the Bertrand paradox: • It allows firms to set price above marginal cost • It allows firms to obtain positive profits • Firm will intend to differentiate their products (from those of its competitors) as much as possible, the aim is to reduce the intensity of price competition: • Actual product differentiation • Perceived product differentiation: increase consumers’ preference for the products of the firm Departamento de Estructura Económica

  46. Departamento de Estructura Económica

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