Product differentiation

Transcription

1 differeniaion Horizonal differeniaion Deparmen of Economics, Universiy of Oslo ECON480 Spring 010 Las modified: The exen of he marke Differen producs or differeniaed varians of he same produc Quesions Ouline How far does he marke exend? Which firms compee wih each oher? Wha is an indusry? s are no homogeneous Excepions: Gasoline, elecriciy Sill, some producs are more equal o each oher han o oher producs in he economy. These producs consiue an indusry wih differeniaed producs. Bu where do we draw he line? Examples: beer vs. soda? soda vs. milk? beer vs. milk?

2 Two kinds of produc differeniaion Quesions Ouline 1 Horizonal differeniaion Ex: Differen locaion of sores Differen ime slos for airline deparures Consumers differ in heir preferences over he produc s characerisics (as color, ase, locaion of oule). The opimal choice for idenical s depends on consumer preferences. Covered here. Verical differeniaion Ex: Cars of differen qualiy and in differen segmens s differ in some characerisic (called qualiy) in which all consumers agree wha is bes. For equal s, all prefer he varian wih higher qualiy. Theopimalchoiceishesameforeveryone. For differen s, consumer make differen choice (e.g. due o differences in income). Covered nex ime. Horizonal produc differeniaion Posiive quesions Quesions Ouline Pricing behavior for given number of firms and given locaions. How does produc differeniaion influence he firms compeiion? Locaion choice for given number of firms. How do firms differeniae heir producs o weaken compeiion? Enry decisions.

3 Horizonal produc differeniaion Normaive quesions Quesions Ouline Is he produc variaion oo large in equilibrium? Too much produc differeniaion? Are here oo many varians in equilibrium? Too many firms ener? Ouline Quesions Ouline wih differeniaed producs Spaial compeiion The linear ciy The circular ciy and informaional produc differeniaion Informaive? Persuasive?

4 wih differeniaed producs (1) Srucure: (1) Prices se () Demand deermines quaniies Firms 1 and have consan uni cos c 1 and c and se s p 1 and p simulaneously. Sales are given by D i (p i, p j ), which is he coninuous demand funcion for firm i. max p i (p i c i )D i (p i, p j ) Why does a coninuous demand funcion mean ha producs are differeniaed? Resul Le c 1 = c = c. If D 1 (p 1, p ) > 0 when p 1 min{c, p } and D (p, p 1 ) > 0 when p min{c, p 1 },heninanynash equilibrium (p1, p ) we have ha (p 1, p ) (c, c). wih differeniaed producs () Proof. To be shown: (p 1, p ) is no a Nash equilibrium if min{p 1, p } c. Case 1: min{p 1, p } < c. A leas one firm i has negaive profi. Non-negaive profi by seing p i c. Case : min{p 1, p } = c. If p i = c and p j c, henby assumpion D i (p i, p j ) > 0, and firm i s profi is zero. Since D i (, ) is coninuous, firm i can aain posiive profi by seing p i = c + ε for ε>0 sufficienly small. Hence, differeniaed producs solve he paradox, in he sense ha i leads o exceeding marginal cos.

5 The linear ciy wih linear ransporaion coss (1) Linear ransp. coss Quadraic ransp. coss Following Hoelling (199), consider a linear ciy of lengh 1 wih consumers uniformly disribued along his inerval. Also, assume ha firm 1 is locaed a 0 and firm is locaed a 1. For a consumer locaed a x ( [0, 1]) he cos o buy from firm 1isp 1 + x and he cos o buy from firm is p + (1 x). Every consumer buys one uni from a firm wih lowes cos. Indifferen consumer x: p 1 + x = p + (1 x), which implies x = p p 1 + D i (p i, p j )= and 1 x = p 1 p + 1 if p i p j p j p i + if p i (p j, p j + ) 0 if p i p j + The linear ciy wih linear ransporaion coss () Linear ransp. coss Quadraic ransp. coss max (p i c) p j p i + p i [p j,p j +] FOC if p i (p j, p j + ): p j + c + p i =0 p i = p j if p j c +3 p j +c+ if p j (c, c +3) p j + if p j c Unique Nash equilibrium, (p1 c, pc )saisfies: p1 c = pc = c +. Hence, exceeds c. Do firms maximize produc differeniae o relax compeiion? Problemaic o discuss choice of produc differeniaion wih linear ransporaion coss. Why? Wha produc differeniaion maximizes welfare?

6 The linear ciy wih quadraic ransporaion coss () Linear ransp. coss Quadraic ransp. coss Assume ha firm 1 is locaed a a and firm is locaed a 1 b, where 0 a < 1 b 1. For a consumer locaed a x ( [0, 1]) he cos o buy from firm 1isp 1 + x and he cos o buy from firm is p + (1 x). Srucure: (1) Firms choose locaions a and b () Given locaions, firms choose s p 1 and p (3) Demand deermines quaniies Maximal produc differeniaion o weaken compeiion: a =0andb =0 Less produc differeniaion would have maximized welfare: a = 1 4 and b = 1 4 Wha abou enry? Beer o analyze in he circular ciy. The circular ciy and firm enry Presenaion of enry Socially op. enry Srucure: (1) Firms choose wheher o ener; locae symmerically around a circle (lengh 1) () Given enry and locaions, firms choose s; we assume maximal differeniaion (3) Demand deermines quaniies f : Fixed cos of enry (p i c)d i f :Firmi s (ex ane) profi Assume linear ransporaion coss. Ask: How many firms will ener?

7 The circular ciy and firm enry Demand for i s produc, given ha he compeiors is p. Assume ha firm i only compees wih his neares compeiors. Indifferen consumer x: p i + x = p + ( 1 n x), which implies: enry Socially op. enry D i (p i, p j )= x = p p i + n max(p i c) p p i + n p i f FOC if p i (p n, p j + n ): p + c + n p i =0 Find he symmeric equilibrium by seing p i = p: p = c + n The profi margin (p c) is reduced if greaer enry (larger n) The circular ciy and firm enry enry enry Socially op. enry How many firms will ener? Demand for each: 1 n maximize n subjec o (p c) 1 n f = n f 0 n c f and n c +1> f p c c + f Higher ranspor coss (larger ) weakens compeiion, increases, and leads o greaer enry (larger n). In equilibrium: Toal cos of enry: Toal ransporaion cos: f f = f / 4 f = 4 1 f Toal cos: 5 4 f

8 The circular ciy and firm enry Socially opimal enry enry Socially op. enry Consumpion is given (p > c does no lead o efficiency loss). Hence, social planner wishes o minimize he sum of enry coss and ransporaion coss: [ ( 1 n [ ] min nf + n xdx =min nf + n 0 n 4n n = 1 f = 1 nc Too many firms in equilibrium Privae moivaion for enry: Business sealing Social moivaion for enry: Saving ransporaion coss In social opimum: Toal cos of enry: 1 Toal ransporaion cos: / (4 1 Toal cos: f f f = 1 f ) = 1 f f The circular ciy and firm enry Discussion enry Socially op. enry Maximal produc differeniaion is assumed. Can his be endogenized hrough a 3 sage game Economides (1984) Simulaneous enry is assumed Wha abou sequenial enry? Presco & Visscher (1977) Each firm produces only one brand (one produc varian) Wha if each firm can produce muliple brands? Then hey can aach heir compeiors from more han one direcion. Leading o muli-brand monopoly raher han one-brand oligopoly?

9 Maximal or minimal differeniaion? Argumens for less differeniaion enry Socially op. enry Locaing where demand is. Posiive exernaliies beween firms. Ex.: A paricular ype of sores is locaed in he same sree. The consumers know where o go and can compare more easily producs ha are differeniaed from oher characerisics han locaion. No compeiion (Hoelling, 199). Ex.: Commercial TV companies wishing o maximize heir audience, ransmi similar programs in he same ime slo. Poliical paries approach he cener (median voer). Relaed o he posiive demand effec. Informaional produc differeniaion Model Informaive: focus here Persuasive: shifing consumers preferences Consider a linear ciy of lengh 1 wih consumers uniformly disribued along his inerval. Also, assume ha firm 1 is locaeda0andfirmislocaeda1. For a consumer locaed a x ( [0, 1]) he cos o buy from firm 1isp 1 + x if informed of firm 1 and he cos o buy from firm is p + (1 x) ifinformedoffirm.aconsumerbecomes informed of firm i by receiving adverising from firm i. Fracion of consumers receiving adverising from firm i: ϕ i coss: A i = A(ϕ i )= a ϕ i

10 Model of informaional produc differeniaion Model Poenial marke for firm 1: ϕ 1 Ou of hese consumers, afracion1 ϕ have no received informaion from firm The res, a fracion [ ϕ ou of ϕ 1 (, know abou boh firms D 1 = ϕ 1 (1 ϕ )+ϕ 1 + p p 1 Firms simulaneously & independenly choose adverising & [ ( max(p 1 c)ϕ 1 (1 ϕ )+ϕ 1 p 1,ϕ 1 + p p 1 a ϕ 1 FOCs [ ( p 1 : ϕ 1 (1 ϕ )+ϕ 1 + p p 1 (p1 c) ϕ 1ϕ =0 p 1 = p +c + ϕ ϕ 1 : (p 1 c) [ ( (1 ϕ )+ϕ 1 + p p 1 aϕ1 =0 ϕ 1 = p [ ( 1 c a (1 ϕ )+ϕ 1 + p p 1 Model Find he symmeric equilibrium by seing p 1 = p = p and ϕ 1 = ϕ = ϕ: p = p+c + ϕ a p = c + ( ϕ 1) = c + = c + a ϕ = p c [ a (1 ϕ)+ ϕ] = a( ϕ 1)( 1 ϕ ) ϕ = q (which requires a) 1+ a Π= a ϕ a = ( 1+ q ) a p a > 0, ϕ a < 0, Π > 0, Π a > 0. An increase in adverising coss increases firms profis A direc negaive effec. An indirec posiive effec: a ϕ p