Download Profit Maximization and Product Quality in Markets with Imperfect Information and more Exercises Market economy in PDF only on Docsity!
WORKING
PAPERS
CONSUMER INFORMATION, PRODUCT QUALITY AND SELLER REPUTATION
Carl Shapiro*
WORKING PAPER NO. 42
July 1980
nc Bureau fi Ecooomks working papers are preliminary materials circulated to stimulate discussion and critical COIIllllelll AD data cootained in them are in the
pablic tl the authors aod do IHidomain. Tbis includes ioformation obtained aecessarily reflect the vim of by * Commisoo whidl has become part other members of the Bureau rl Economics, other Commissioo staff, of public monl. ne aalyses oraod the coocluions set Commission itself.forth are thoseUpon
request, single copies of tie paper will be provided. References iu pablicajoas to FfC Bureau of Ecooomia working papers by FfC erooOIIIQs (other than
acknowledgement by a writer that be has atttSS to such unpublished materials) should be cleared with the author to protect the tentative character of these papers.
BUREAU OF ECONOflCS
FEDERAL TRADE COMrtflSSION
WASHINGTON, DC 20580
Table of Contents
Intro:luction 1
General1-bnop::>list Fonrulation of OJality Ch:::>ice by a Under Imperfect Information 11
Once arrl For All Q.lality Ch:::>ice: General Fesults 14
Welfare Implications
Personal Learning: An Exten:led &le 2 9
A Continuous T .ime Example of Once arrl for All QJ.ality
Choice 43
Product Q.lality Ch:::>ice Over ·General Results T irre: REmarks and 48
A continuous Time M::x:lel with Variable QJ.ality 56
Conclusion 63
lbtes 64
Ap_p:mdi.x
Ec onomi s t s a r e becoming i n c r e a s in g l y aware o f how impe r f e c t i n f o rma t i on c a n c a u s e a w i d e range o f ma r k e t impe r f e c t ion s. A g r e a t d e a l o f e f fo r t h a s gone into c a r e f u l anal y s i s o f unc e r ta inty a bo u t the v a r i o u s p r i c e s a t wh i c h a homogenous p roduc t i s be i n g o f f e r ed for s a l e. 1 Ye t un c e rta inty about p r i ce is r e l a t ive l y minor and inexpe n s ive to e l imi n a t e i n c ompa r i so n w i th unc e r t a inty about o t h e r p roduct c h a r a c te r i s t i c s ( e. g. , durab i l i t y , s a f e t y o r t a s te ). Th i s pape r i s concerned w i th per fo rmance i n ma rke t s whe r e the p ro d uc t s sold cannot b e f u l l y a n d a c cur a t e l y eva l ua t e d p r i o r to purch a s e. The a n a l y s i s wi l l center on how a pro f i t -maximi z in g f i rm choo s e s product qua l i t y i n an envi r onme nt whe re c on s ume r s c annot o b s e rve qua l i t y p r i or to purch a s e. I am pa r t i c u l a r l y i n t e r e s ted i n how t he qua l i ty o f produc t s p rovided depend s on the mann e r and speed with whi ch c o n s ume r s gath e r i n f o rma t i o n abo u t prod uc t s a n d e n t e r a n d l e ave the ma rke t. Qua l i ta t i ve unc e rta i n ty i s a w i d e s p r e a d and i mpo r t a n t f e a t u r e o f ma rket s for mo s t f i rms ' good s a nd s e rv i c e s. Vi r tua l l y a l l s e r v i c e s are impo s s i b l e t o eva l uate un t i l they are u s ed. Th i s inc l ude s llte d i c al a n d l e g a l s e rv i c e s , auto mob i l e r e p a ir , p l umb i n g and e l e c t r i c a l work , e t c. Ano t h e r impor t a n t c l a s s o f produ c t s who se qua l i t y c anno t eas i l y be j udged prior to pur c ha s e a r e con sumer d urab l e s. I n fa c t , when a new mod e l a u tomob i l e come s o u t , t h e re s i m p l y i s no way o f knowing wha t i t s repair r e c o r d wi l l look l ike. A s a f ina l cla s s o f e xamp l e s , t h e r e a re many produc t s whi c h we buy
q u i t e f r eq ue n t ly wh i ch have unob s e rvab l e a t t r i b u t e s : r e s t au r a n t mea l s ( ta st e ) and c l o t h i ng ( wi l l i t fade o r s h r i nk ) a r e two e x ampl e s. The r i se in bot h the comp l ex i ty o f p ro duc t s ( c o n s i d e r h i f i equ i pme nt o r e t h i c a l d r ug s ) and t h e f r a c t i o n o f income spent on s e rv i c e s ha s i n c r e a sed the impo rtance (^) of the s e i n f o r mational prob l e m s. The per forman c e o f the marke t in such a s e t t ing i s e s s en t i al to t he eval u a t i o n o f a wide var i e ty o f r e g u l atory initiatives. The s e^ i n c l ud e^ o c cupat ional^ l i c e n s i n g^ (o r^ min imum qual i ty s t andard s in g e n e r al ) , oc c upat ional h e al t h r e g u l a t i o n s ( th e wor ke r t aking t h e r o l e o f the c o n s ume r ) , a utomo b i l e s a fety r u l e s , and a w i d e r ange o f r e g u l at i o n s b y t he Food and Drug Admin i s t r at i on , F e de r al Tr ad e Commi s s ion , and Con sume r Product S a f e ty Commi s s ion. Rec ent a c t i o n s such a s the FTC ' s p ropo s ed u s e d c a r r u l e ar e d e s i gned p r e c i s e ly to improve the informat ion in the marke t and thereby enhan c e per f orman c e. I t i s paramoψn t , t h e re f o r e , to de s c r i be marke t p e r f o rmanc e in t h e ab s e n c e o f po l i c y i n t e r f e renc e to be ab l e t o eva luate t h e wo r t h ine s s o f e i ther mandato ry s tandards or pub l i c p rov i s io n o f in format ion. The analy s i s i n th i s pape r i s r e s t r i c t e d to t he c a s e whe re a monopo l i s t c o n t ro l s t he quan t i ty a s we l l a s q ua l i t y o f t h e g o o d in que s t ion. S i nce impe r fe c t i n fo:L.Ii.latie7.t'• gene ra l l y l e ad s t o s ome marke t powe r , t h i s anal y s i s i s a n e c e s sary p r e r e quis i te to s tudy i n g many s uppl i e r s in the pre sence o f
Qua l i ty
Qua l i ty Dynam i c
σhoτ
P ro du c t Cha r a c t e r i s t i c s and S in c e t h e i s su e s d e s c r ib e d above r evo lve a round product c ho i c e by a s e l l e r r a t h e r than s imp l y p r i c in g or output d e c i s i on s for a g iven p r o du c t , it i s ve r y u s e f u l to adopt L an c a s t e r s ' f r amewo r k and v i ew produ c t s as b und l e s o f c h a r a c te r i st i c s. When produ c t s a r e v i ewed in th i s wa y , one que s t ion whi c h a r i s e s i s whe ther o r not the ma rket prov i d e s t h e s oc i a l ly opt imal m i x o f p roduct c ha r a c t e r i st ic s. 2 S i n c e I wi sh to fo c u s o n product qu a l i ty a s o ppo sed to p r o duc t va r i e t y , I r e s t r i c t qua l i ty to a s i ng l e d imen s ion. T hi s shou l d be thoug h t o f a s some prod u c t a t t r ibute wh i c h i s d i f f i cu l t o r impo s s i b l e to o b s erve p r i o r t o purcha s e , but wh i c h con sume r s a l l l ike to have mor e o f. Examp l e s inc lude durab i l i ty , sa f e ty ( p robab i l i ty o f no acc ident}, o r speed o f s e r v i c e. The r e s t r i c t ion o f qua l i ty to one d i men s ion imp l i e s , i n pa r t i c ul a r , t h a t a ny two c on s umer s wi l l a g ree wh i c h o f two produc t s i s pre f e r r e d a l though they may d i s a g re e a s to how much the added qua l i ty i s wo r t h.^3
Enodenous Cho i c e : A P rob l em To under s t a nd the p rob l ems wh i c h o c c u r when produ c t qua l i ty i s unob s e rva b l e p r i o r to pur cha s e , i t i s impo r t ant to d i s t ingu i s h the c a se whe re s e l l e r s product qua l i ty f rom the c a s e whe r e t he r e i s an exogenous s upp l y o f p rodu c t s o f d i f f e rent qua l i t i e s. T h e l a t t e r c a se i s t h e o n e i n t roduced
by Ake r l o f i n h i s s emin a l a r t i c l e U97 0 ]. Un fortuna t e ly , mod e l s wi t h exogenous q ua l i t y supp l y a r e o f l im i t e d u s e f u l ne s s i n product ma rk e t s. I f t h e p r i c e o f fe red d e pende d on l y on ave rage q ua l i ty in the ma r ke t , a n d h i g her qua l i ty i t ems a re mor e co s t l y to produce , then i n a one-shot mod e l t h e r e i s n o inc ent i ve f o r a g ive n prod u c e r t o provide any t h i ng o t h e r t h a n min imal qua l ity. Con s equen t l y ,^ the^ ma rke t^ w i l l^ be^ o ve r r un^ by mln lma^.^.^1 qua 1 'lty^ ltems..^4 The s ame r e s u l t o c c u r s in a dynamic mod e l i f c o n s ume r s do not l e a rn about the qua l i ty of i n d i vi d u a l f i rm s o ve r t ime. The inc ent i ve to prod u c i ng h i gh qua l i ty i tems i s that h i gh e r qua l i ty today wi l l c a u s e the demand cu rve i n the f u t u r e to s h i f t o ut. So p ro d u c t quali t y cho i c e s by s e l l e r s a re f und amenta l l y dynami c.
I n fo rma t i on Flows It is appa r ent f rom the s e con s i d e r a t i on s that the t e c hn o l og y o f i n f o rmat ion f l ow w i l l b e e s s e nt i a l to a n y s t o ry o f ma rk e t e q u i l ib r i um. I t^ i s^ conve n i e n t^ to^ d i s t i n gu i s h^ three^ f a c e t s^ o f th i s t e c hno l o gy : ( 1) How i n forma t i on f l ow s among con s umer s , ( 2 ) How muc h a con sume r l e a r n s a bo u t the p roduc t 's qua l i ty
f rom u s i ng i t , a nd ( 3) how con s ume r s en t e r and l e a ve the
mar k e t. Bo th the n a t u r e o f the p roduct a nd the i n s t i tut ion s s ur r o und i n g the ma r k e t for the good i n f lue n c e the way i n wh i c h i n f o rma t i on f l ows r e ga rd i ng e a c h f i rm' s p roducts.
e xpe c t a t i on s
i n thi s^ context^ to^ t hink^ o f^ t h e^ c o n s ume r^ a s^ o b s e rv i n g^ s ome outcome wh i c h depends o n bo t h the q ua l i ty o f the prod u c t and
some unob s e rv a b l e r andom va r i a b l e. 6 In the c a r s a f e ty e xamp l e ,
i f a c a r h o l d s up we l l^ in^ an^ a c c i d e n t^ i t^ i s not c l e a r whe th e r t h e m i n ima l^ dama ge^ i s^ due^ to^ the^ type^ o f^ a c c i d e n t^ o r^ the^ way the c a r wa s made. A s imi l a r l a c k o f o b s ervabi l i t y h o l d s t rue fo r d r ug s , s e r vi c e s , e t c. I f a l awye r l o s e s a c a s e i t i s h a r d to (^) know i f he wa s b a d o r the c a s e wa s we ak. On e way to i nco rpo r a t e l e a rn i n g i n to c o n s ume r cho i ce i s
t o a s sume that qua l i ty i s po s i t ive ly r e l a t ed to the p robab i l i t y o f repe a t pur c ha s e. Th i s approa c h ha s been taken i n Schma l e n s ec [ 1 97 8 ] and Sma l lwood - Co nl i s k 11979]. One prob l em w i t h i t i s t hat i t g i v e s no i n s i ght a s to how c o n s umer s re spond to pri c e.^7 I have taken a d i f f e r en t approa c h i n wha t fo l l ow s. At any po i n t in t ime a c o ns um e r ha s some r e g a rd i ng p roduc t qua l i ty. Thi s^ d e t e rmine s^ the^ po s i t ion^ of^ h i s^ demand c urve.^ The^ l e a rn ing^ then^ c o r r e s pond s^ t o^ a d j us t in g^ e x p e c t e d qua l i ty towa r d s t rue qua l i t y. Produc t s for w h i c h qua l i ty i s ha rd to o b s e rve even a f ter u s e wi l l d i sp l a y s l ow o r l a gged a d j u s tment of co n s ume r e xpe c t a t i on s. I t sh0u l d b e n o t e d t h a t t h e ab i l i ty o f con sume r s to d r aw in f e r en c e s a bout the f i rm ' s qua l i ty from u s i n g the produc t i s not sol e l y techno l o g i c a l l y determined. To the ext e nt t h a t f i rms have imp e r f e c t qua l i ty con t r o l a c on s umer who g e t s a bad i tem may have d i f f i c u l t y
I n t e r pe r sona l Lea r n ing
Repo r t s ,
knowing whether i t s poo r qua l i ty i s r e p r e se n t a t ive o f that f irm o r not. For the purpo s e s o f t h i s d i s cu s s ion , I w i l l avo i d t h i s p ro b l em by a s s uming that^ a l l^ the^ produ c t s^ a^ f i rm^ s e l l s^ on^ a g iven d a t e have un i fo rm q ua l i t y.
and the Ma r k e t f o r I n fo rma t io n The re a r e q u i t e a f e w potent i a l sourc e s o f i n f o rmat ion about p r o du c t qua l ity in add i t io n to p e r sona l expe r i e nc e. The se ar e (1) Exp e r i e n c e o f f r i e nd s , ( 2 ) P ub l i c a t i o n s , 0ithe r pub l i c o r p r ivate , s uc h a s
Adve rt i s ing , and (4) P o t en t i a l s i gna l s of qua l i ty such a s
p r i c e , warran t i e s , o r adve rt i s ing. If the ma r k e t for in forma t i o n about product a tt r ibut e s worked we l l , t h e i n f orma t i on a l prob l ems i n t h e ma rke t s for final good s a n d s e r v i ce s wou l d be s ub s t an t i a l ly r e d u c e d or e l imina t e d. T he r e are seve r a l r e a s o n s why the in forma t io n ma r k e t c annot be expe c t e d to wor k we l l , howe v e r. The f i r s t two r e a sons r e l a t e to the pub l i c good nature o f i n forma t io n. The f i r s t i s that i t i s d i f f i c u l t to prevent r e s a l e of i n f o rma t io n. A p r i va t e f i rm that s e l l s informat ion may not be able to surv ive even though the r e is a sub stant i a l v a l u e t o the in forma t i on , b e c a u s e there wou l d b e n o re s t r i c t i on s o n i n d i v idua l s who b uy t h e in forma t ion pa s s ing i t a l ong ( f r e e l y ) to non-buye r s. The s e cond r e a son i s due to the φos i t i ve e xt e rna l i ty c re a t e d by in forme d b uye r s wh i c h bene f i t s u.in f o rmed b uy e r s t hroug h ra i s ing qua l it y ( s imi l a r t o what
C on s ume r 8 (3)
wa rran t i e s. T h i s i s b e c a u s e the manu f a c t urer c a nn o t mon i tor ma i n t e na n c e or i n t en s i ty of u s e. S u c h mora l h a z a rd and advers e s e l e c t ion pro b l ems a re i n e v i t a b l e b arri ers t o t h e a b s o r pt i on o f pro d u c t q ua l i ty ri s k s b y t h e produc er. I n t h e e xamp l e o f l e g a l s e rv i c e s , i t i s po s s ib l e t o wri t e inc en t ive c on trac t s , b u t adve rs e s e l e c t ion l imi t s t h e i r s c o pe.^9 F i na l l y , i n th i s paper I do not inc l ude advert i s ing , a l though i t s v i rt u e s a s we l l a s f a ul t s mu s t b e ana l y z ed in the context o f impe rf e c t in forma t ion. Advert i s ing c a n b e v i ewed as a l tering c o n s umer ' s e x pe c t a t i o n s of q u a l i t y. S i nce there i s an obv i o u s i n c e n t ive for produc e rs to over ra te the ir produc t , the key que s t i o n h e re i s why con s umers pay any a t t e n t ion to such c l a ims. The ab i l i ty o f advert i s in g to c onvey i n f orma t io n abo ut pro duc t qua l i ty i s some t h ing I hope to t reat in the future. I have t r i e d i n t h i s s e c t i on t o i d e n t i fy f a c tors wh i c h i n f luence t he spee d o f l e a rn ing b y c o n s ume rs. T h e ana l y s i s be low foc u s e s o n t h e re l a t io n s h i p b e tween t h a t s pe e d and the q ua l i ty o f pro duct c ho s e n b y the mo nopo l i s t. I n e xampl e s whe re t h e o n l y l ea rn ing i s person a l l e a rn ing , i t i s po s s ib l e to b e q u i t e expl i c i t about how the f i rm ' s demand c urve s h i f t s i n re s po n s e t o l e arn i ng. Such e x ampl e s p l a c e a n uppe r bound o n t h e in fo rma t i ona l pro b l ems i n t h e ma rk e t , s i n c e th ere a re in f a c t add i t iona l informa t ion sourc e s , as d i s c u s s ed above.
Qua l i ty b y (^) Monopo l i s t I mpe rf e c t
Gen e r a l F o rmu l a t i o n o f Cho i c e a Un de r In forma t ion Con s i de r the prob l em f a c ed b y a f i rm i n s e t t i ng i t s q ua l i ty , q. At a n y^ po i n t^ i n^ t ime^ the^ f i rm^ c a n^ r e a p^ e x t ra^ pro f i t s^ b y c u t t ing qua l i ty ; t h e re w i l l b e n o l o s s i n revenue s unt i l c on s ume r s c a n r e s pond to t he q ua l i ty change. S i n ce the probl em i s e s s e nt i al l y dyn ami c , let t d e no te t ime an d c a l l p ( t ) the pr i c e at t ime t , q ( t ) the q u a l i ty , a n d x ( t ) s a l e s. The re i s a l s o a c o s t f un c t ion c ( x , q ) i n quan t i t y a n d qua l i t y. There may a l s o be c o s t s to c h a n g i n g qua l i ty i. e. , o n c e a n d f o r a l l c o s t s to i n t ro d uc i n g a new q ua l i ty l i ne. I^ i gn o r e th e s e^ for^ the^ mo s t^ pa r t ,^ e xc e pt^ to^ note^ t h a t^ they^ j u s t i fy the a t t en t i on pa i d to o n c e - and- f o r - a l l gua l i ty c ho i c e s b e l ow. I n f a c t we do not u s ua l l y o b s e rve f requent qua l i ty c han g e s b y s e l l e r s ; pr i c e c ha n g e s o c cur much mo re r api d l y. Th i s i s further j us t i f i c a t i o n for the t r e a tme n t i n t h e fo l l ow i n g s e c t io n. Pro f i t s a t t ime t a r e g iven by
TI ( t )^ =^ p ( t ) x ( t ) -^ c ( x ( t ) ,^ q ( t ) ).
The c ru c i a l que s t ion i s how x ( t ) d e pe n d s on p ( t ) and pre v i o u s qua 1. 1ty c h o1c e s .. 10 One approach i s to t r e a t x ( t ) a s t h e s t a t e va r i ab l e r e pr e senting a l o y a l s e t o f pa tron s. Then the i n f l ow of n e w custom e r s and the o u t fl o w o f d i s sa ti s f i ed c u s tome r s wi l l i n ge ne r al d e pend on qua l i ty , pr i c e , and thP rtoc k of c u s tome r s itself. Small wood and Conl i sk [ 1 97 9 ] took
r e puta t ion,
wha t t o e xp e c t. I n st e a d , e v i de n c e on c o n sumer beha v i o r sug g e s t s st rong l y t h a t consume r s e xt rapo l a t e f rom r e cent e xp e r i en c e t o p r e di c t future p roduct p e r f o rma n c e .1 3 Vi ewin g^ a^ f i rm's^ r eput a t i on^ a s^ t h e^ sta t e^ var i a b l e^ i n^ t h e dynam i c se t t i ng out l i ne d above , t h e f i rms prob l em i s : 00 maxx ( t ) 1 q ( t ) e - r t( X ( t ) p ( X ( t ) 1 t=O
R ( t ) ) - C ( X ( t ) , q ( t ) )) dt
sub j e c t to .R ( t ) = f ( x ( t ) , q ( t ) , R { t ) ). R ( O ) g i ven. He r e the i nv e r se deman d c u rve t h e f i rm f a c e s a t t ime t i s p ( x ( t ) , R ( t ) ) ; it s l o c a tion de pends o n n o t^ qua l i ty a t t ime t ( si n c e that wil l not b e o b s e rv e d unt i l l a t e r ). Now co nsumer l e a r n i n g wi l l be e mbo di e d in the f ( x , q , R ) f un c t i o n. T h e discussi o n above about i n format ion sour c e s in f l ue n c e s f i rm be havio r t hrough f. Con s equen t l y , i t wi l l be v e ry impo r t a n t t o (^) se e how t h e opt ima l c hoice o f q ( t ) a n d x ( t ) depend o n t h e spe c i f i c a t i on o f f.
Qua l i t y
o p t i m i z ed
c hange s ove r t ime a r e permi t ted , Rt wi l l d epend on previ ous qual i ty a nd sa l e s (^) cho i c es by the (^) f i rm i t se l f.
To r ema i n p e r f e c t l y (^) g e n e ra l , denote (^) the (^) present va l ue
on ce an d for A l l C ho i c e : Gene r a l Resu l t s I n this se c t ion I sha l l c onsi der t h e prob l em f a c e d by a monopo l i st when he i s c hoosing once and for a l l wha t qua l i ty produc t to produc e. I t i s best thoug h t o f a s i n troduct io n o f a new product , bu t app l i e s a t a n y po i n t whe r e a l o n g - r un qua l i ty cho i c e i s b e i n g mad e. Suppose consume r s a l l e xpe c t t h e qua l i ty produc e d t o b e R 0 •^ That^ i s ,^ suppose^ t h e^ f i rm^ h a s^ a n^ i n i t i a l^ reput a t i o n^ o f R 0 ( R^ and^ q^ a re^ me a sured^ i n^ t he^ same^ un i ts ).^ F o r^ now^ I^ t ak e R 0 a s^ beyo n d^ the^ control o f the f i r m. (^) I f a dve r t i si ng (^) i s pe rm i t t e d , i t ma y we l l ope r a t e t hrough a l te r i n g R 0 • One c o u l d st udy how muc h the f i rm wou l d a dvert i se t o i n f l ue n c e R 0 f avorab ly. O f course , suc h a dve rt i s i n g need n o t b e i n fo rma t ive. R 0 may a l so depend on t he qua l i ty o f pro duc t s a l re a dy i n the ma r k e t ( more o n t h i s be l o w ). I n the fu l l mo de l whe r e qua l i ty
Suppose , g iven in i t i a l reputa t io n R 0 the f i rm e l e c t s to produce a pro du c t o f qua l i ty q. It t h e n c hoo s e s a n op tima l. pr i c i n g pa t h ( a n d c o r r e spond i ng sa l e s p a t h ) over t ime to ma xim i z e the p r e se n t va l ue of i t s pro f i t s t r eam. Wha t suc h a p a t h (^) looks l ike w i l l depend on how l ea r n i n g o c c urs b y (^) consume r s.
