1 Industrial Organization Product Differentiation Univ. Prof. dr. Maarten Janssen University of Vienna Summer semester Week 12

2 What is product differentiation? Products differ in their characteristics and attributes. It is useful to distinguish between:  1. HORIZONTAL: Consumers do not agree in the ranking they give to the goods some people prefer blue jeans while others prefer black jeans People prefer different supermarkets because of their location  2. VERTICAL. Consumers give the same ranking to the goods (almost) everyone prefers a color printer over a b&w printer (almost) everyone prefers a BMW over a SEAT

3 Hotelling's linear city model: 2 issues: Competition over location Competition over location and price Firm 0 Firm 1 Mass of consumers=M x t(1-x) tx

4 Competition over location only: The principle of minimum differentiation For two firms, equilibrium locations exhibit minimum differentiation: Can a location choice like this be equilibrium?

5 The principle of minimum differentiation with more than two firms For four firms, equilibrium locations do not exhibit minimum differentiation strictly speaking but bunching

6 Welfare maximizing product choices For any number of firms N: locate the firms equidistantly so that there are 1/2N half-market lengths of equal distance. For two firms: For four firms:

7 Suppose firms locate at the end-points of the city: differentiation is maximal. Assume consumer x’ utility is U=V - t d 2 (x,i) - p i For a pair of prices (p A,p B ), there is a consumer x 0 indifferent between the two varieties: V - t d 2 (x 0,A) – p A = V - t d 2 (x 0,B) - p B Competition over location and prices: the principle of maximum differentiation A B x t(1-x) 2 tx 2

8 Consumer x 0 is x 0 = ( p B – p A )/2t + 1/2. Consumers to the left of x 0 prefer to buy from A while consumers to the right of x 0 prefer to buy from B. x0x0 A=0 B=1

9 To find the NE in prices, we derive the best-response functions: Maximize π A = ( (p B – p A )/2t + ½) p A wrt p A p A = (p B +t) / 2 By symmetry p B = (p A + t) / 2 Solving yields p A =p B =t π = t / 2 Prices are above marginal costs the degree of product differentiation

10 Consider firms relocate to a distance x from their respective initial end-points locations. x0x0 x1x1 A B The new indifferent consumer is x 1, with: It is useful to compute demand elasticity: Following the same steps as above, the new NE is p=t (1-2x) and profits π = p / 2 This shows how location affect equilibrium prices and profits

11 Consider a two-stage game: Stage 1: Firms locate their products Stage 2: Firms compete in prices The observations above suggest that there are two effects to take into account: A demand effect: firms have an incentive to move towards the center to increase the size of their captive markets The strategic effect: firms have an incentive to move towards the end-points of the city to minimize price competition with the rival. The principle of maximum differentiation In the quadratic cost example discussed here, the 2nd effect dominates and firms end up locating the furthest possible from their rival’s location (see next slides).

12 Strategic location choice I Firm 1 locates at a > 0; firm 2 at 1-b  Not necessarily symmetric  So far, a = b D 1 = a + (1-a-b)/2 + (p 2 -p 1 )/2t(1-a-b) Price equilibrium p 1 = t(1-a-b)(1+[a-b]/3) and p 2 = t(1-a-b)(1+[b-a]/3) Π 1 (a,b; p 1 (a,b),p 2 (a,b)) Location choice  ∂Π 1 /∂a + ∂Π 1 /∂p 1 ∙∂p 1 /∂a + ∂Π 1 /∂p 2 ∙∂p 2 /∂a = 0  Second term is 0, because of envelope theorem  First term is direct effect (= ∂D 1 /∂a; third term is strategic effect (= ∂D 1 /∂p 2 ∙∂p* 2 /∂a).

13 Strategic location choice II ∂D 1 /∂a = D 1 = 1/2 + (p 2 -p 1 )/2t(1-a-b) 2 ∂D 1 /∂p 2 ∙∂p* 2 /∂a = 1/2t(1-a-b) ∙ t[-4 + 2a]/3 Substituting the subgame perfect equilibrium prices it follows that dΠ 1 /da < 0 Maximal differentiation Optimal from a social welfare perspective?  Minimize transportation cost  Socially optimal to have a = b = ¼.

14 Bertrand Equilibrium p 1 * maximizes firm 1’s profits, given that firm 2 charges p 2 * p 2 * maximizes firm 2’s profits, given firm 1’s price is p 1 * No firm wants to change its price, given the rival’s Beliefs are consistent: each firm “thinks” rivals will stick to their current price, and they do so! p2Bp2B p1Bp1B p2p2 p1p1 d/2e R 1 (p 2 ) R 2 (p 1 ) Bertrand equilibrium d/2e

15 Salop’s circular city model - entry When consumers are uniformally distrbuted Firms locate equidistant from each other: with n firms, distance is 1/n How many firms will enter?  Entry cost f For n firms, symmetric equilibrium price p Demand for firm i if others charge p, determine indifferent consumer whose location is x from firm i : p i + tx = p + t(1/n –x) Demand is 2x = (p + t/n –p i )/t

16 Salop’s circular city model II Maximize profits to get price p = c + t/n Profits (p-c)/n –f = 0 (free entry)  N = √(t/f) Is there too little or too much entry?  Social optimum where transportation costs + overall fixed cost are minimized  Min { nf + t ∙ 2n ∙ ∫ 1/2n 0 x dx } = nf + t/4n  Socially optimal to have n = ½√(t/f)  Too much entry! Too many varieties!

17 Vertical product differentiation Products differ in ‘quality’ Quality can be ‘observable’ or ‘unobservable.’  Goods whose quality is observable are called search goods  Goods whose quality is unobservable before the purchase are called experience goods.  There are goods whose quality is (almost) never observed: credence goods. Here we discuss questions pertaining to search goods: Does the market offer the right quality?  Questions that pertain to experience goods have a larger scope, including the effects of warranties and signaling  Later in the course

18 Quality and competition I Consumers have preferences U= θs – p if they buy quality s at price p. No utility if they do not buy. They buy at most a single unit of the product. Buyers differ in the valuation they place on quality θ; e.g., θ is uniformly distributed over the set [0, 1]. Competition develops over two stages. 1st stage: firms choose quality s; 2nd stage: firms compete in prices to sell their products.

19 Quality and competition: price competition For given qualities s 2 > s 1, indifferent consumer θ where θs 2 – p 2 = θs 1 – p 1  D 1 = (p 2 – p 1 )/(s 2 – s 1 ) – p 1 /s 1  D 2 = 1 - (p 2 – p 1 )/(s 2 – s 1 ) Equilibrium prices and profits  P 1 = s 1 (s 2 – s 1 )/(4s 2 – s 1 ); P 2 = 2s 2 (s 2 – s 1 )/(4s 2 – s 1 );  π 1 = s 1 2 (s 2 – s 1 )/(4s 2 – s 1 ) 2 ;  π 2 = 4s 2 2 (s 2 – s 1 )/(4s 2 – s 1 ) 2 ; High quality firm charges higher prices, gets more demand and receives more profits

20 Quality and competition: quality choice Which qualities will be chosen?  Note that profits are 0 when firms produce the same quality (Bertrand competition) Both firms benefit from quality differentiation  Even the low quality firm, although less so Highest quality will choose maximal quality and lower quality keeps away from it (although will not choose lowest possible quality)!  Look at first-order derivatives of profits wrt quality choices

21 Conclusion Horizontal and vertical product differentiation  Firms have an incentive to differentiate to avoid severe price competition Horizontal differentiation  Hotelling: too much differentiation – under quadratic transportation cost  Salop: excessive entry / too much variety Vertical differentiation  Both high and low quality firm benefits from differentiation  But high quality firm benefits most and makes more profits