Lender liability in the Consumer Credit Market

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■♥❝❧✉✐ ❜✐❜❧✐♦❣r❛❢✐❛✳

Lender liability in the Consumer Credit Market

¤

Elisabetta Iossa

and Giuliana Palumbo

January 10, 2002

A bst r act

In many count ries consumer credit legislat ion provides for t he ex-t ension of liabiliex-ty for producex-t failure ex-t o ex-t he …nancial insex-t iex-t uex-t ion ex-t haex-t advances credit t o t he consumer. In part icular, lender liability is im-posed on t hose credit grant ors who closely operat e wit h t he supplier of t he good.

T his paper provides a rat ionale for lender-responsibility in t he con-sumer credit market . It shows t hat , when judicial enforcement is in-e¢ cient or t here is risk of seller liquidat ion, lender-liability helps t o prot ect consumers who syst emat ically underest imat e t he probability of product failure and overest imat e t he ext ent t o which t hey can ob-t ain compensaob-t ion.

Keywords: consumer credit , lender liability, mispercept ion, product failure.

J.E.L. classi…cation: D18, G28, K13.

¤_{For helpful comment s, we wish t o t hank Giuseppe Bert ola, John Bennet t , Philip Davis,}

M arco Pagano, Bruno Parigi, Jean Charles Rochet , seminar part icipant s at Birbeck Col-lege, Brunel University, Ent e Luigi Einaudi, European University Inst it ut e, London School of Economics, University of Helsinki, University of Salerno and conference part icipant s at EEA 2000 and RES 2001.

Financial support from Findomest ic S.p.A and Cet elem and Brunel University (Brief A ward) is grat efully acknowledged.

y_{Respect ively, Brunel University, Get ulio Vargas Foundat ion and European}

1

I nt r oduct ion

When a consumer purchases a good on credit she ent ers two cont ract ual re-lat ionships: t he sale or main cont ract wit h t he supplier of t he good and t he credit cont ract wit h t he grant or of credit . An issue which has been highly debat ed is whet her t he obligat ions assumed by t he part ies under each con-t raccon-t should be independencon-t of each ocon-t her or racon-t her be conneccon-t ed by vircon-t ue of t he link between t he purchase of t he good and it s …nancing. In part icular, in t he event of default or incomplet e performance of t he sale cont ract , should t he consumer keep ful…lling her obligat ions wit h t he lender and address her claim exclusively against t he supplier or should she be ent it led t o a similar claim against t he lender?

A brief examinat ion of regulat ions across t he Unit ed St at es and t he Eu-ropean Union Member St at es shows t hat t he legislat or has been favorable t o t he ext ension of t he liability t o t he lender in all sit uat ions where t he credit is advanced under an agreement between t he supplier of t he good and t he credit grant or. T his principle was …rst int roduced in t he Unit ed Kingdom by t he Consumer Credit Act 1974. T he Brit ish example was t hen followed by ot her count ries and it s principles appear in t he Federal Trade Commis-sion Holder Rule (196) of t he Unit ed St at es and in t he European Direct ive EEC/ 102/ 87.1 Not ice t hat an “ agreement ” arises whenever a supplier ar-ranges a loan for a cust omer and t his can also include t he case where t he cust omer buys t he good using a credit card.2 In t hese sit uat ions, t he …nance company shares liability wit h t he supplier. Inst ead, if a cust omer obt ains credit independent ly of t he supplier t hrough her own bank for example -t he credi-t gran-t or does no-t bear any liabili-ty. Nor is a credi-t card company liable if t he cust omer uses her credit card t o obt ain cash and pay for her purchases.

T he main mot ivat ion for ext ending liability t o t he lender is consumer prot ect ion. As emphasized by t he Brit ish legislat or, “ where a transaction involves a connected loan, it would be unfair and insu¢ cient for the con-sumer as debtor to have remedy only against the supplier, his obligation to continue repaying the lender remaining una¤ected” . The keys t o consumer prot ect ion are essent ially two. One is t he possibility of approaching t he

1_{T he European Direct ive int roduces subsidiary liability when t he credit is provided on}

t he basis of a pre-exist ing agreement where credit is made available “ exclusively” by t hat grant or of credit t o cust omers of t hat supplier. However, in most count ries, it is common j urisprudence t o recognize lender-responsibility also for non exclusive agreement s.

2_{T he regulat ion of credit cards agreement s varies across count ries. In UK for example,}

lender when t he seller is unable or refuses t o sat isfy t he consumer’s claim. T he ot her is t he accordance t o t he consumer of t he right t o suspend t he repayment of t he loan unt il t he good object of t he cont ract has been deliv-ered. However, t he e¤ect ive “ prot ect ion power” of t his measure cannot be assessed wit hout simult aneously considering t he behavior of all t he part ies act ing in t he market . In t his regard, one argument adduced against joint liability is t hat t he higher cost s in‡ict ed on credit ors will be t ransferred t o consumers, in one of t he following two forms. Eit her credit grant ors will refuse t o sign agreement s wit h t he suppliers in order t o avoid t he liability or t hey will charge higher int erest rat es t o rest ore t heir pro…tability.

In t his paper we invest igat e t hese issues and provide a rat ionale for t he exist ence of volunt ary agreement s where t he credit grant or accept s co-responsibility for inadequat e performance of t he seller. Furt her, we show t hat t he present legislat ion has posit ive e¤ect s on consumer welfare when consumers are poorly informed about risk.

We consider a simple economy composed of two market s: a monopolist ic good market and a perfect ly compet it ive credit market . Consumers are risk neut ral and decide whet her t o buy one unit of t he good; t he good is defect ive (or more generally, t here is lack of conformity wit h t he sale cont ract ) wit h exogenous and posit ive probability and may cause damage. Depending on t heir init ial endowment of wealt h, two classes of consumers are ident i…ed: poor consumers, who must borrow money t o …nance t heir purchases and rich consumers who can buy for cash if t hey wish. Following a st rand of lit erat ure dat ing back t o Spence (1977) and relat ed empirical evidence (see e.g. Eisenberg 1995), we assume t hat , wit hin each class, consumers are a¤ect ed by mispercept ion, and in part icular, t hey overest imat e t he expect ed value of t he good t hey are purchasing.3 _{In our set t ing opt imism result s}

from t he combinat ion of two e¤ect s: consumers bot h underest imat e t he risk of product failure and overest imat e t he ext ent t o which t hey can obt ain compensat ion. T he lat t er in t urn may be due t o misinformat ion about t he e¤ect iveness of t he judicial enforcement and/ or t he likelihood t hat t he seller is st ill in business at t he t ime t he consumer addresses her claim.4

We argue t hat joint liability helps mit igat e t he loss t hat consumers su¤er because of t heir mispercept ions. Crucial t o t his result is t hat t he prot ect ion grant ed by joint liability cannot be fully t ransferred by t he seller int o higher prices (or int erest rat es). T his is because, as a direct consequence of t heir

3_{Recent development s in market ing t echniques such as int ernet sales, door-t o-door}

selling and dist ance selling oft en raise a concern of compet it ion aut horit ies.

4_{It has been est imat ed t hat in England 95% by volume of t he claims under Sect ion 75}

being opt imist ic, consumers undervalue t he bene…ts t hey obt ain from joint liability.

Joint liability prot ect s consumers in two ways. First , t hey have t he right not t o repay t heir debt t o t he lender whenever t he seller does not ful…ll his obligat ions. T his reduces t he loss t hat consumers su¤er from misperceiving bot h t he probability of product failure and t he compensat ion t hey can obt ain t hrough t he judicial syst em. Second, t hey are ent it led t o obt ain remedies against t he lender in case t he seller goes out of business. T his prot ect s consumers against t heir underest imat ing t he risk of seller bankrupt cy. In bot h cases consumer welfare is enhanced because t he price t hey are willing t o pay for t he prot ect ion is lower t han it s e¤ect ive value.

T hat joint liability reduces t he rent t hat can be ext ract ed out of t he mispercept ion of consumers implies t hat joint liability per se would never be volunt ary undert aken. However, it is undert aken when it is a condit ion sine qua non for coordinat ion of price and int erest decisions which allows t he seller t o price discriminat e between rich and poor consumers. This argument provides a rat ionale for rest rict ing joint liability t o t hose sit uat ions involving an agreement between t he seller and t he lender, as is t he case under t he exist ing legislat ion. In t his regard, joint -liability can be viewed as a means t o redist ribut e some of t he gains from coordinat ion t owards t he consumers. To our knowledge t he desirability of ext ending t he liability for product failure t o t he lender is an issue as yet st ill unexplored. On t he one hand, lender liability has mainly been analyzed in t he …eld of environment al regu-lat ion, where banks may be considered liable for t he environment al damage creat ed by t he …rms t hey …nance. (See for example, Pit chford 1995, and Boyer and La¤ont 1997). On t he ot her hand, t he lit erat ure on liability for product failure mainly rest rict s at t ent ion t o seller-only responsibility regula-t ion and focuses on regula-t he e¤ecregula-t s of di¤erenregula-t liabiliregula-ty rules on risk disregula-t riburegula-t ion and on t he incent ives of t he buyer t o exert product care and of t he seller t o provide quality.5 _{In cont rast , our paper st udies t he e¤ect s of volunt ary}

provision of lender and seller liability and it abst ract s from risk and moral hazard considerat ions. Moreover, none of t hese papers allows for any sort of consumers’ mispercept ion. In t his respect , our paper is most ly relat ed t o a st rand of lit erat ure dat ing back t o Spence (1977), who consider t he loss consumers may su¤er when t hey underest imat e t he probability of product failure.6

5_{See for example, Green (1976), Spence (1977), Epple and Raviv (1978), Polinsky and}

Rogerson (1983) and Daughety and Reinganum (1995).

T he rest of t he paper is organized as follows. Sect ion 2 out lines t he model. Sect ion 3 present s two relevant benchmarks: t he case of fully rat ional consumers (Sect ion 3.1) and t he case where t here is consumers’ mispercep-t ion, bumispercep-t mispercep-t he seller and lender are free mispercep-t o coordinamispercep-t e mispercep-t heir decisions wimispercep-t houmispercep-t t his implying t he undert aking of joint responsibility (Sect ion 3.2). Sect ion 4 st udies t he e¤ect s of int roducing joint liability, while Sect ion 5 discusses ot her means of prot ect ing consumers from t heir mispercept ions. It shows t hat full prot ect ion from mispercept ion requires liability rules t hat make t he ut ility in t he bad st at e higher t han t hat in t he good st at e. It furt her shows t hat joint liability may work as a device t hat induces t he seller t o give up t he rent he can make on t he irrat ionality of consumers in order t o be able t o serve also rat ional (and pessimist ic) consumers. Sect ion 6 concludes.

2

T he m odel

T he economy consist s of a monopolist ic good market and a perfect ly com-pet it ive …nancial market . Consumers may decide t o buy a unit good from t he seller and have access t o credit from t he …nancial market . T he good is wort h B t o each of t hem. However, wit h exogenous probability d; where 0 · d · 1; t he sale cont ract is inadequat ely honored: t he good is defect ive or not delivered or it is not in conformity wit h t he st andards speci…ed in t he init ial cont ract . In t his case t he value of t he good t o t he consumers is zero if t here is no damage, and ¡ D if damage occurs.

In most of t he paper, we t ake a posit ive approach t o liability legislat ion and assume t hat t he ext ent of t he seller liability is equal t o D + B : Furt her, we assume t hat resort ing t o t he legal syst em is cost ly (due t o legal fees or t o non-monet ary unrecoverable cost s of t he t ime wast ed) or, analogously, t hat t he judicial enforcement is ine¢ cient (lengt hy t rials, incompet ent judges). Finally, we consider t he possibility t hat aft er t he good is purchased and before t he consumer is able t o go t o court , t he seller goes bankrupt . We account for t he ine¢ ciency of t he judicial syst em by assuming t hat if t he seller does not ful…l his obligat ions and t he consumer goes t o court , she can recover only a fract ion ® of her claim, where 0 · ® · 1:7Furt her, we denot e by º wit h 0 · º · 1 t he probability t hat t he seller is st ill in business at t he t ime t he consumer lays her claim.

T here are two classes of consumers, rich and poor; all of t hem are risk

7_{® could also be int erpret ed as t he probability of winning t he lawsuit . Not e, t hat all}

neut ral. Rich consumers have su¢ cient money t o purchase t he good for cash if t hey wish; alt ernat ively t hey may purchase on credit . Poor con-sumers have no cash, and, t herefore, if t hey are t o purchase t he good, t hey must use credit . T he number of rich and poor consumers is given by nr and

np; respect ively. In most of t he paper we focus on consumers who are

inher-ent ly opt imist ic for t hey syst emat ically overest imat e t he value of t he good. T he assumpt ion of opt imism has been a st andard feat ure of t he lit erat ure on consumers’ behavior (see e.g. Spence 1977, Polinsky and Rogerson 1983, Shapiro 1982) and is mot ivat ed by t he exist ence of signi…cant empirical evi-dence in favor of consumer opt imism (see e.g. Eisenberg 1995 and references t herein). In our set t ing, opt imism result s from consumers underest imat ing bot h t he risk of product failure and of seller bankrupt cy and overest imat ing t he compensat ion t hey can obt ain in court when t he seller refuses or is un-able t o honor t he cont ract . Formally, let bd; bº and b® denot e t he consumers’ imprecise est imat es of t he probability of product failure (d), t he risk of seller bankrupt cy (1 ¡ º ) and t he ine¢ ciency of t he judicial enforcement (1 ¡ ®). We assume t hat bd · d; bº ¸ º and b® ¸ ®; wit h d® ¸ bdb®:8

T he supplier of t he good and t he credit grant or may operat e indepen-dent ly or may decide t o sign an agreement in order t o coordinat e t heir price and int erest rat e decisions. Let R 2 f r; i g denot e t he int erest rat e on credit , where r and i are t he int erest rat e under independence and under coordi-nat ion, respect ively. Thus t he e¤ect ive price, denot e by P paid by t he consumers is equal t o p if t he consumer buys for cash and t o (1+ R)p if t he consumer buys on credit .

When t he seller and t he lender act independent ly, a regime of seller liability applies, where t he discovery of a defect ive good does not a¤ect t he consumers’ right s and dut ies wit h t he lender. In t his case, t he real surplus derived from t he consumpt ion of t he good is

US(P ) = (1 ¡ d)(B ¡ P ) + d(¡ D ¡ P + º ®(D + B ))

= (1 ¡ d (1 ¡ º ®))B ¡ P ¡ d (1 ¡ º ®) D (1) Not ice t hat , under seller-only responsibility, when t he good is defect ive, t he consumer can pursue her remedy only against t he seller. Hence, she can recoup t he damage and a new unit of t he good (or it s money equivalent ) only if t he lat t er is st ill in business.9 Moreover, due t o t he ine¢ ciency of

8_{We shall ret urn on t his assumpt ion in Sect ion 4.2 .}

9_{T hat consumers receive a new unit of t he good (or it s money equivalent ) when t he}

t he judicial syst em, only a port ion ® of her claim will be sat is…ed.

However, consumers are a¤ect ed by mispercept ion. Their perceived ut il-ity is t hen given by

b

US(P ) = (1 ¡ bd(1 ¡ bº b®))B ¡ P ¡ bd(1 ¡ bº b®)D (2) When t he seller and t he lender coordinat e t heir decisions, t he lat t er be-comes co-responsible wit h t he seller t owards t hose consumers t o whom he has supplied credit . T his joint liability has a twofold e¤ect . First , t he con-sumer pays P = (1 + i )p only if t he good is not defect ive or her claim is sat is…ed. Second, if t he good is defect ive she can resort t o t he lender and obt ain a fract ion ® of t he damage in‡ict ed t o herself, if t he seller has gone int o liquidat ion.10 _{Thus, under joint liability, t he real ut ility is}

UJ (P ) = (1 ¡ d)(B ¡ P ) + d(¡ D + º ®(D + B ¡ P ) + (1 ¡ º )®D ) = (1 ¡ d (1 ¡ º ®)) (B ¡ P ) ¡ d (1 ¡ ®) D (3) T he perceived ut ility is

b

UJ(P ) = (1 ¡ bd (1 ¡ bº b®)) (B ¡ P ) ¡ bd (1 ¡ b®) D (4) T he monopolist ic seller aims t o maximize expect ed pro…ts, t aking int o account t he amount of responsibility he bears if t he good is defect ive. De-not ing by n (P; ¢) t he number of consumers served, his expect ed pro…t when he act s independent ly is given by

¼SI (p) = [p ¡ dº ®D ] n ¡ K (5) where for simplicity we have assumed no product ion cost s and posit ive …xed cost K :

On t he credit market , t he supply of loans ent ails posit ive average t rans-act ion and management cost F if t he seller and t he lender operat e indepen-dent ly, and Fc if t hey coordinat e, wit h Fc · F . This lat t er assumpt ion is meant t o capt ure t he reduct ion in t he lender’s management cost s t hat result from t he possibility of using t he facilit ies o¤ered by t he seller t o manage t he supply of loans t o his cost umers. For simplicity we let Fc = 0: T he credit grant or faces a perfect ly elast ic supply of funds at an exogenously det er-mined int erest rat e, which we normalize t o zero. Since perfect compet it ion forces t he credit grant or t o break even on his loans, under independence, t he int erest rat e he must charge is given by r = F .

10_{Clearly, we are referring only t o t hose consumers who seek credit from t he connect ed}

Suppose now t hat t he seller and t he lender coordinat e t heir decisions and as a result accept co-responsibility in case of product failure. Let nJ

be t he number of consumers who buy on credit from t he lender connect ed t o t he seller, and n ¡ nJ be t he number of consumers who eit her buy cash or buy on credit from an independent lender. Any agreement between t he seller and t he lender will have t he property t hat t he price and int erest rat e will be set so as t o maximize t he t ot al expect ed pro…ts of t he two agent s. T he cont ract will t hen specify a monet ary t ransfer t t hat allocat es t he gains from coordinat ion among t he two part ies. Given t hat t he seller has all t he bargaining power, in equilibrium t he t ransfer will be equal t o t he level t hat maint ains t he lender on his reservat ion pro…t of zero. This yields t = i l + (1¡ º )®D nJ _{where l = pn}J _{is t he amount of loans and (1¡ º )®D n}J

is t he amount of responsibility t hat t he lender bears in case t he seller goes bankrupt and for which he will have t o be compensat ed ex ant e. Hence, t he expect ed pro…t of t he seller is

¼J = [(1 ¡ d (1 ¡ º ®)) p ¡ d®D ] nJ + [p ¡ dº ®D ]¡n ¡ nJ¢+ i l ¡ K (6) Not e t hat under joint responsibility, t he seller receives t he price p only if t he consumer receives a non-defect ive good, which occurs wit h probability (1 ¡ d (1 ¡ º ®)) ; moreover, he bears t he liability for damage wit h probabil-ity 1, due t o t he compensat ion he needs t o o¤er t o t he lender.

Finally, not ice t hat if coordinat ion did not involve any change in t he responsibility regime t hen t he seller’s expect ed pro…t when he cooperat es wit h t he lender would be given by

¼SC = [p ¡ dº ®D ] n + i l ¡ K (7) wit h t = i l:

3

B enchm ar ks

3.1

N o m isp er cept ions

In t his sect ion we consider t he benchmark where consumers are not af-fect ed by mispercept ion. For simplicity we shall refer t o t hem as “ rat ional” consumers:

Rich consumers do not need t o borrow t o purchase t he good. T herefore t heir reservat ion price, from (1), is given by

On t he cont rary, poor consumers must resort t o credit t o …nance t heir pur-chase. Since t hey have t o borrow p; and r = F > 0; t heir reservat ion price is lower t han t heir rich count erpart and equal t o_{1+ F}pS . Therefore, t he pro…t opport unit ies of a seller who relies on a independent lender t o provide credit t o his cust omers are as follows. The seller can set p = pS _{and sell only t o}

t he rich consumers or he can set p = _{1+ F}pS and supply t he ent ire market at a lower price. We assume t hat F is su¢ cient ly high t hat it is opt imal t o sell only t o t he rich consumers. Then, t he seller’s pro…t, ¼SI ¡_pS¢_{, is given by}

¼SI ¡pS¢= ¦ nr ¡ K (9)

where ¦ ´ [(1 ¡ d (1 ¡ º ®))B ¡ dD ].

Now suppose t hat t he seller can coordinat e his decisions wit h t he lender wit hout t his implying any changes in t he responsibility regime (i.e. t here is seller-only responsibility). Coordinat ion increases t he pro…t opport unit ies for t he seller since he can choose t he price and int erest rat e t hat maximize his pro…ts (net of a t ransfer t o t he lender). In part icular, by charging pS and set t ing i = 0; t he seller can at t ract t he poor consumers wit hout having t o reduce t he price below t he willingness t o pay of t he rich ones. T his is clearly t he opt imal st rat egy since it allows t he seller t o ext ract t he ent ire consumer surplus. Subst it ut ing for pS; i = 0; n = (nr + np) and l = npint o

(7), yields

¼SC¡pS; i = 0¢= ¦ (nr + np) ¡ K (10)

Not ice t hat ¼SC¡pS; i = 0¢> ¼SI ¡pS¢, t hat is, it is always in t he int erest of t he seller t o coordinat e his decisions wit h t he lender, since he can at t ract t he poor consumers wit hout reducing t he pro…ts he can make on t he rich ones.11

Let us assume now t hat a regime of joint liability applies t o any agree-ment between t he seller and t he lender.

P r op osit ion 1 When all consumers are rational, joint liability is ine¤ec-tive.

T his result is not surprising. The rat ionality of consumers, coupled wit h t heir neut rality t owards risk implies t hat addit ional prot ect ion is irrelevant . T his is because, when consumers are rat ional t he seller can always repli-cat e t he same sit uat ion as wit h coordinat ion and seller-only liability by

t ransferring t he addit ional liability int o higher prices. In part icular, t he seller charges a price equal t o t he willingness t o pay of t he rich consumers, pJ _{= B ¡} d(1¡ º ®)

(1¡ d(1¡ ®))D ; and set s i = 0: T his yields: ¼J

¡

pJ_{; i = 0}¢_{= ¼}SC¡_pS¢

and UJ ¡pJ; i = 0¢= US¡pS¢= 0:

3.2

M isp er cept ions and seller -only r esp onsibi lit y

We now allow for consumers’ mispercept ion and analyze t he seller’s choice when a regime of seller-only responsibility applies. The e¤ect s of int roducing joint liability legislat ion will be invest igat ed in Sect ion 4.

T he willingness t o pay for t he good of a rich and opt imist ic consumer, from (2), is given by

b

pS = B ¡ P ¡ bd (1 ¡ bº b®) (B + D ) (11) At t his price t he real ut ility of t he consumer is

US¡pbS¢= h

b

d (1 ¡ bº b®) ¡ d (1 ¡ º ®) i

(B + D ) < 0 (12) T hat is, when consumers are a¤ect ed by mispercept ion and t he seller set s t he price equal t o t heir willingness t o pay, t hey su¤er a loss in real t erms. T he reason for t his is t hat bpS _{is great er t han t he real expect ed value of t he}

good, which is given by what rat ional consumers would be willing t o pay, i.e. pS_{: Assuming again t hat under no coordinat ion it is never opt imal t o}

sell t o poor consumers (F su¢ cient ly high), t he seller will charge bpS _{and his}

expect ed pro…t will be

¼SI ¡pbS¢= £¦ ¡ US( bps)¤nr ¡ K (13)

Not e t hat t he loss t hat consumers make due t o t heir mispercept ion, US( bps) ; becomes addit ional pro…ts t o t he seller. Conversely, when t he seller and t he lender coordinat e t heir decisions, t he following result s obt ains.

L em m a 2 When seller-only responsibility applies to coordination, the seller always prefers to coordinate and i = 0: Moreover, he sells to all consumers and his pro…t is given by

¼SC¡pbS; i = 0¢= £¦ ¡ US¡pbS¢¤(nr + np) ¡ K

4

Joint L iabilit y

In t his sect ion we consider t he case of a legislat ion t hat imposes a joint liability regime t o t hose sale cont ract s where t he consumer obt ains credit from a lender connect ed t o t he seller.

A measure of t he ext ent by which consumers can be harmed by t heir mispercept ion is given by t he di¤erence between t heir perceived ut ility and t heir real ut ility, for t he great er t his di¤erence t he more a consumer will be incorrect ly evaluat ing t he bene…ts from consumpt ion. Under seller-only responsibility, bUs(¢) ¡ Us(¢) ; as given respect ively by (2) and (1), amount s t o

b

US(¢) ¡ US(¢) = h

d (1 ¡ º ®) ¡ bd (1 ¡ bº b®) i

(B + D ) > 0: whereas, under joint liability, from (4) and (3), we obt ain

b

UJ(¢) ¡ UJ (¢) = h

d (1 ¡ º ®) ¡ d (1 ¡ bb º b®) i

(B ¡ (1 + i )p) +

h

d (1 ¡ ®) ¡ d (1 ¡ bb ®) i

D ¸ 0

St raight forward calculat ions show t hat , for any given p and i such t hat b

UJ(¢) ¸ 0

b

Us(¢) ¡ Us(¢) > bUJ (¢) ¡ UJ(¢) (14) T wo main implicat ions follow from expression (14). First , t he seller can-not fully t ransfer t he addit ional liability int o higher prices, t hat is, he can never replicat e t he same sit uat ion as wit h coordinat ion and seller-only lia-bility. T his is because opt imist ic consumers underest imat e t he value of t he addit ional prot ect ion given by joint liability and t herefore are not willing t o pay t he price t hat re‡ect s t he t rue value of t he bene…ts t hey obt ain.12 T hus, if t he seller increases t he price and/ or t he int erest rat e so as t o leave t hem indi¤erent between t he two liability regimes ( bUs _{= bU}J _{= 0); t heir}

real ut ility increases (UJ > US). This is a crucial point for it suggest s t hat joint liability may help prot ect consumers from t heir mispercept ion and t hat Proposit ion 1 does not ext end t o t he case where consumers are irrat ional.

12_{In fact , since d > bd consumers underest imat e t he probability t hat t he bad st at e occurs.}

A second implicat ion of expression (14), which is st rict ly relat ed t o t he pre-vious point , is t hat it is in t he int erest of t he seller t o minimize t he number of consumers who borrow from a connect ed lender. T his means t hat t he bene…cial e¤ect s of joint liability t o t he poor consumers may not ext end t o t he rich ones. Indeed, as we shall see, t he seller will use joint liability as a market -segment at ion t echnique: by appropriat ely choosing t he price and t he int erest rat e, he will cont inue t o ext ract a rent from t he rich consumers by giving t hem incent ives not t o swit ch t o credit .

To illust rat e bot h point s, as a …rst st ep, t ake t he case where consumers incur no loss for damage when t hey purchase from a connect ed seller under a regime of joint liability. T his can happen eit her when D = 0 or when t he judicial syst em works e¢ cient ly and t he consumers know it : b® = ® = 1. Indeed, from (3), when b® = ® = 1 t he mispercept ion on t he risk of seller bankrupt cy plays no role under joint liability, since consumers can resort t o t he lender. As an example of a sit uat ion where D = 0 one can t hink of t he case where t he seller does not deliver t he good or delivers a good which is of no use t o t he consumer. T he assumpt ion b® = ® = 1 works well for count ries wit h a well est ablished t radit ion for prot ect ing consumers’ int erest s or where consumers associat ions are st rong enough t o ensure t hat consumers are fully compensat ed for t he damages t hey su¤er.

> From expressions (3) and (4), when D = 0 or b® = ® = 1; t he real and perceived ut ility of a consumer who purchases t he good seeking credit from a connect ed lender are respect ively given by

UJ(¢) = (1 ¡ d (1 ¡ º ®)) (B ¡ (1 + i )p) b

UJ(¢) = (1 ¡ bd (1 ¡ bº b®)) (B ¡ (1 + i )p)

T hese expressions suggest t hat when consumers su¤ers no loss for damage under joint liability, t here does not exist a couple (p; i ) such t hat t hey receive a negat ive real ut ility, since for any p; i such t hat UJ ¸ 0; we have bUJ ¸ 0: T he int uit ion lies in t he fact t hat consumers pay for t he good if and only if t hey receive B , and enjoy zero ut ility ot herwise. Since consumers will never buy if t he e¤ect ive price is great er t han t he value of t he good, B ; t he real ut ility can never be negat ive: This leads us t o t he following result .

served; the poor ask for credit to the connected lender and obtain zero utility; the rich buy for cash and are fooled.

Proposit ion 2 can be underst ood as follows. T he opt imal policy for a seller who signs t he agreement wit h a lender is t o charge bpS _{as de…ned in}

(11) and iJ = d(1¡ bb ®bº )

1¡ bd(1¡ b®bº ). T his ensures bU

S_{( bp}S_{) = bU}J_{( bp}S_{; i}J_{) = 0. T hus, all}

consumers are willing t o ent er t he market : poor consumers ask for credit t o t he connect ed lender while t he rich ones buy for cash. Moreover, since joint liability enables t he seller t o price discriminat e among poor and rich consumers, it is always in his int erest t o sign t he agreement . The seller’s pro…t under t his policy is given by

¼J¡pbS; iJ¢= ¡¦ ¡ US¡pbS¢¢nr + ¦ np¡ K

T he e¤ect of joint liability on consumer welfare is posit ive. More precisely, joint liability fully prot ect s poor consumers (UJ( bpS; iJ) = 0) and has no e¤ect on t he welfare of t he rich ones who st ill receive US¡_pbS¢_{< 0.}

Comparing ¼SC¡pbS¢and ¼J¡pbS; iJ¢, an immediat e consequence of Propo-sit ion 2 is as follows.

C or ollar y 4 When product failure entails no damage (D = 0) or judicial enforcement is e¢ cient ( b® = ® = 1), joint liability hurts the seller, for it redistributes some of his pro…ts to the consumers.

T he above corollary suggest s t hat sellers and lenders would never volun-t arily o¤er joinvolun-t liabilivolun-ty, because ivolun-t reduces volun-t heir gains from coordinavolun-t ion (¼J ¡_pbS_{; i}J¢ _{< ¼}SC¡_pbS¢_{). However t hey do undert ake joint responsibility}

when t his is a condit ion sine qua non for coordinat ion, i.e. t o price discrim-inat e between rich and poor consumers. In fact ¼J ¡pbS; iJ¢> ¼SI ¡bpS¢: In t his respect , joint liability can be viewed as a means t o redist ribut e some of t he gains from coordinat ion t o t he consumers.

Now, let us t urn t o t he case where product failure leads t o damage, D > 0 and b® > ®: In t his set t ing, while t he inequality in (14) st ill holds, it is no longer t rue t hat consumers under joint liability can never su¤er a negat ive real ut ility. Indeed, from (4), t he willingness t o pay for t he good, inclusive of int erest (i.e. (1 + i )p), under joint responsibility is

b

PJ = B ¡ ³ d (1 ¡ bb ®) 1 ¡ bd (1 ¡ b®bº )

wit h associat ed real ut ility equal t o (from (3))

UJ( bPJ) = h

b

d (1 ¡ b®) ¡ d (1 ¡ ®) i ³

1 ¡ bd (1 ¡ b®bº )

´ D < 0 (16)

where

US( bpS) < UJ( bPJ) < 0 (17) Hence, consumers can st ill be fooled by t heir mispercept ion. T his is because when D > 0; and b® > ® consumers overest imat e t he level of prot ect ion given by t he judicial syst em and t heir ut ility in t he bad st at e will be negat ive. However, US_{( bp}S_{) < U}J_{( bP}J_{) implies t hat t he ext ra rent t hat t he seller can}

make on irrat ional consumers is lower t han under seller-only responsibility. T his underlies t he following Proposit ion.

P r op osit ion 5 When product failure entails damage (D > 0) and judicial enforcement is ine¢ cient ( b® > ®), joint liability redistributes the gains of coordination from the seller to the poor irrational consumers. However, poor consumers are not fully protected from their misperceptions.

Not ice t hat t he seller can st ill price discriminat e between t he two classes of consumers. It su¢ ces t hat he chooses bpS _{and adjust s t he int erest rat e}

so as t o obt ain bPJ = (1 + iJ) bpS as given by (15). This yields bUS( bpS) = b

UJ( bPJ) = 0: Thus rich consumers buy for cash while poor consumers buy on credit from t he connect ed lender. Consequent ly, as in Proposit ion 2, rich consumers receive no bene…t from joint liability. Poor consumers are bet t er o¤ since t he ext ra rent t hat t he seller can make on irrat ional consumers is lower under joint liability (from (17)). However, cont rary t o Proposit ion 2, t hey are not fully prot ect ed (from (16)). More precisely, t he seller obt ains

¼J( bpS; iJ) = nr(¦ ¡ US( bps)) + np(¦ ¡ UJ( bPJ) ¡ K (18)

where iJ = d(1¡ bb ®bº )

1¡ bd(1¡ b®bº ):

In t he next sect ion we shall discuss ot her fact ors t hat may help t o deal wit h consumers’ mispercept ions.

5

Ot her m eans t o deal wit h m isper cept ion

5.1

T he ext ent of liabilit y

increase consumer welfare, but not t o ensure full prot ect ion when t here is damage and t he judicial syst em does not work perfect ly. This conclusion raises t he quest ion of whet her consumers could be made bet t er-o¤ by a di¤erent choice of t he ext ent of liability. To answer t his quest ion, consider t he perceived and real ut ility of a consumer for a given liability L ; under seller-responsibility (similar result s are obt ained under joint responsibility)

b

US(p; L ) = B ¡ P ¡ bd (B + D ¡ bº b®L ) US(p; L ) = B ¡ P ¡ d (B + D ¡ º ®L )

It follows t hat at t he price bP such t hat bU( bP ; L ) = 0; t he real ut ility of t he consumers is given by

US( bP ; L ) = ¡ (d ¡ bd)(B + D ) + (dº ® ¡ bdbº b®)L

which is increasing in L since d® ¡ bdb® > 0 (which implies dº ® ¡ bdbº b® > 0), and is equal t o zero for13

L¤= (d ¡ bd)(B + D ) dº ® ¡ bdbº b® :

T hus, t he opt imal ext ent of liability is larger t han B + D . The int uit ion is t hat opt imist ic consumers always bene…t from an increase in t he level of prot ect ion since t he price t hey are willing t o pay for t he prot ect ion is lower t han it s e¤ect ive value. Not ice also t hat L¤is great er t han t he value of L t hat equat es ut ilit ies across st at es, which is given by (B + D )_{º ®} : Equal real ut ilit ies across st at es result s in t he consumer overest imat ing t he value of t he good since t he perceived ut ility in t he bad st at e is great er t han t he real ut ility: T herefore, in order t o fully prot ect consumers from t heir mispercept ions, t he ut ility in t he bad st at e needs t o be higher t han t hat in t he good st at e.14

Unfort unat ely, such a solut ion would be di¢ cult t o implement as it would require t he regulat or t o possess informat ion on t he ext ent of consumers’ mispercept ion which may be rat her expensive t o acquire.

13_{Not ice t hat if d® ¡ bdb® (respect ively dº ® ¡ bdbº b®) were negat ive, t hen under seller-only}

responsibility (respect ively j oint responsibility) consumer prot ect ion would be ensured by set t ing t he seller liability equal t o zero.

14_{T his result di¤ers from t hat obt ained by Spence (1977) where a liability rule t hat}

5.2

T he pr esence of well infor m ed consum er s

Cont rary t o t he previous sect ions, let us assume t hat , wit hin each class (t he rich and t he poor) a fract ion ¹ of consumers is not a¤ect ed by mispercept ion. For simplicity we shall refer t o t hese consumers as ‘rat ional’ and t o t hose a¤ect ed by mispercept ion as ‘irrat ional’. Rat ional consumers value t he good correct ly and t heir willingness t o pay under seller-only responsibility is given by pS _{from (8) wit h p}S _{< bp}S_{. The pro…t opport unit ies for t he seller under}

seller-only responsibility are t he following. Eit her he set s bpS and serves only t he irrat ional consumers, or he set s pS and at t ract s bot h rat ional and irrat ional ones. In t he former case, he gains t he ext ra rent US¡_pbS¢_{on each}

of t hem. In t he lat t er, he serves a higher segment of t he market but cannot ext ract t he rent US¡pbS¢ from t he irrat ional consumers. T his reasoning suggest s t hat t he presence of rat ional consumers may work as a prot ect ion device t hat gives incent ives t o t he seller t o give up t he rent on mispercept ion in order t o increase t he market demand. Clearly, whet her t he seller …nds t his pro…table depends on how large t he proport ion of rat ional consumers is.

Let ¹S and ¹J be t he cut -o¤ value such t hat t he seller prefers t o keep rat ional consumers out if and only if ¹ · ¹S _{under seller-only responsibility}

and ¹ · ¹J under joint liability when D > 0 and b® > ®.

P r op osit ion 6 When product failure entails damage (D > 0) and judicial enforcement is ine¢ cient ( b® > ®), ¹J < ¹S : joint liability increases the welfare of all irrational consumers, where the poor ones are fully protected by their misperception.

P r oof. See Appendix.

Proposit ion 4 suggest s t hat under joint liability t he number of rat ional consumers t hat is needed in order t o induce t he seller t o supply t he ent ire market is lower t han under seller-only responsibility: This is because joint liability reduces t he rent t hat can be ext ract ed from t he irrat ional consumers (Proposit ion 3) and t hus increases t he seller’s incent ives t o serve t he rat ional ones. Not e t hat serving t he (poor) rat ional consumers requires UJ(:) = 0: Hence, once t he rat ional consumers are served, t he poor irrat ional ones are fully prot ect ed. Moreover, price discriminat ion between rich and poor con-sumers becomes more di¢ cult . Indeed, det erring irrat ional rich concon-sumers from swit ching t o credit implies bUS_{(:) = bU}J _{(:) ; which is always posit ive}

seller charges pS < pR < bpS which st ill enables him t o ext ract some rent but

leaves t he rich irrat ional consumers bet t er o¤.

R em ar k 1 For the presence of rational consumers to act as a protection de-vice, it is necessary to monitor the behavior of the seller and impede practices that may allow the seller to price discriminate among the di¤erent degrees of rationality. I ndeed, the seller can try to o¤er di¤erent types of contracts in order to induce the consumers to self-select. One way to achieve this is through optional warranties. Suppose that the seller charges a price for the good equal to the reservation price of the irrational consumers and o¤ers an optional warranty at a price that leaves the rational consumers with zero util-ity. Contrary to rational consumers, irrational consumers have no incentive to buy the warranty, since their willingness to pay for the protection is lower than the willingness to pay of the rational consumers

³

since d® > bdb® ´

: This self-selection mechanism allows the seller to attract rational consumers with-out losing the rent that can be extracted from the irrational ones.

T he above considerat ions can easily ext end t o t he case where some con-sumers are pessimist ic. Indeed, pessimist ic concon-sumers underest imat e t he value of t he good and, in t he absence of price discriminat ion devices, t heir ent ry can be bene…cial t o t he opt imist ic consumers. Furt her, t hey suggest t hat government policy devot ed t o increase t he proport ion of informed con-sumers can be e¤ect ive even if not all concon-sumers are made informed.

6

Conclusion

in-st it ut ions connect ed wit h suppliers of goods and services. We have shown t hat lender liability is an e¤ect ive, t hough not perfect , device t o increase consumer prot ect ion and t o redist ribut e some of t he gains t hat result from t he coordinat ion of price and int erest rat e decisions away from t he seller (lender) t oward t he consumers. Speci…cally, joint liability yields t he full prot ect ion of t hose consumers who buy on credit in each of t he following sit -uat ions: (i) product failure ent ails no damage (ii) t he judicial enforcement is e¢ cient , (iii) t he proport ion of informed consumers is su¢ cient ly high. In t he remaining cases, it helps but is not su¢ cient ; neit her does joint liability fully prot ect t hose consumers who can a¤ord t o buy for cash and do not underst and t he bene…t of buying on credit from a connect ed lender.

We have considered a perfect ly compet it ive …nancial market and a mo-nopolist ic product market . Our result s ext end t o more general set t ings pro-vided t hat on eit her market t here exist s some degree of monopoly power t hat makes advant ageous t he coordinat ion of price and int erest rat e decisions .15

T his paper has t aken a posit ive approach t o joint liability rules, rat her t han a normat ive one, alt hough some suggest ions have been provided as t o how t o design t he opt imal liability rule. In part icular, we have shown t hat when consumers not only underest imat e t he probability of product failure but also overest imat e t he probability of seeing t heir claim sat is…ed, t hen liability rules need t o ensure a ut ility in t he bad st at e t hat is higher t han t hat in t he good st at e. A more det ailed normat ive analysis could const it ut e an int erest ing object ive for furt her research. Similarly, new insight s could be gained by endogenizing t he probability of product failure.

15_{Spence (1977) shows t hat mispercept ion may raise an issue of consumer prot ect ion}

7

A pp endix

P r oof of P r op osit ion 4. Suppose t hat ¹ ¦ · ¡ (1 ¡ ¹ )US¡_pbS¢_{; which}

holds for ¹ · ¹s where

¹S= ¡ U

S¡_pbS¢

¦ ¡ US_{( bp}S₎

T his implies t hat under seller-only responsibility, t he seller prefers t o set b

pS > pS; his pro…ts, under independence and coordinat ion, will be respec-t ively

¼SI ¡pbS¢ = £¦ ¡ US¡bpS¢¤(1 ¡ ¹ )nr ¡ K

¼SC¡pbS; i = 0¢ = £¦ ¡ US¡bpS¢¤(1 ¡ ¹ ) (nr + np) ¡ K

where US¡_pbS¢_{< 0 is given by (12).}

Now consider t he case where joint liability is imposed on seller-lender agree-ment s. If t he seller chooses t o serve all consumers, pro…t maximizat ion is achieved when t he cash price and int erest rat e charged are such t hat bUJ_{(¢) =}

b

US(¢) and UJ(¢) = 0. Not ice t hat UJ(:) = 0 is necessary t o induce t he poor and t he rich rat ional consumers t o ent er t he market , whereas bUJ(:) = bUS(:) is required t o det er rich irrat ional consumers from swit ching t o credit . Sim-ple algebra shows t hat t his yields: pR =

³

1 ¡ bd (1 ¡ b®) ´ ³

B ¡ _{1¡ d(1¡ ®)}d(1¡ ®) D ´

and iJ = d(1¡ bb ®)

1¡ bd(1¡ b®) where 0 < p S _{< p}

R< bpSand 0 > US(pR) > US

¡ b

pS¢: t he rich and irrat ional consumers are also bet t er o¤ t han under no coordinat ion. In t his case, t he seller’s pro…t is given by

¼J ¡pJ_R; iJ¢= (1 ¡ ¹ )nr(¦ ¡ US(pR)) + (¹ nr + np)¦ ¡ K (19)

By cont rast , if t he seller decides t o supply only irrat ional consumers, pro…t maximizat ion ent ails bpS and iJ = d(1¡ bb ®)

1¡ bd(1¡ b®) such t hat bU

S¡_pbS¢ _{= 0 and}

b

UJ( bpS; iJ) = 0, wit h (1 + iJ) bpS = bPJ: Rich consumers buy for cash while poor consumers buy on credit from t he connect ed lender. Bot h groups are fooled. Under t his policy, t he seller only supplies a fract ion of t he market , but ext ract s an ext ra rent from bot h t he rich and poor irrat ional consumers. T his yields

¼J¡pbS; iJ¢= (1 ¡ ¹ )nr(¦ ¡ US

¡ b

pS¢) + (1 ¡ ¹ )np(¦ ¡ UJ( bpS; iJ) ¡ K

Comparing (20) wit h (19) t he seller will supply t he ent ire market i¤ ¹ < ¹J where

¹J = ¡ nr(U

S¡_pbS¢_{¡ U}S_(p

R)) ¡ npUJ( bpS; iJ)

¡ nr(US( bpS) ¡ US(pR)) ¡ npUJ( bpS; iJ) + (nr + np) ¦

(21)

Not e t hat ¹J _{from (21) can be rewrit t en as ¹}j_{(A) =} ¡ (nr+ np)Us( bps)+ A

(nr+ np)(¦ ¡ Us( bps))+ A;

wit h A = nrUS(pR) + np

¡

Us¡_pbS¢_{¡ U}J_{( bp}S_{; i}J₎¢_{< 0: Since ¡} @¹J_{(A )}

@A < 0

and ¹J(0) = ¹S; it follows t hat ¹J < ¹S:

R efer ences

[1] Boyer, M. and J.J. La¤ont (1997). Environment al Risk and Bank Lia-bility. European Economic Review, 41(8): 1427-1459.

[2] Daughety, A and Reinganum, J (1995). Product Safety: Liability, R&D, and Signalling. American Economic Review, 85(5):1187-1995.

[3] Eisenberg, M. A. (1995). T he Limit s of Cognit ion and t he Limit s of Cont ract s. Stanford Law Review, 47: 211-259.

[4] Epple, D. and A. Raviv (1978). Product Safety: Liability Rules, Market St ruct ure And Imperfect Informat ion. American Economic Review, 68: 80-95.

[5] Green, J. (1976). On t he Opt imal St ruct ure of Liability Laws. Bell Jour-nal of Economics, 7: 553-574.

[6] Pit chford, R (1995). How Liable Should a Lender Be? T he Case of Judgement -Proof Firms and Environment al Risk. American Economic Review, 85(5): 1171-1186.

[7] Polinsky, A M. and W.P. Rogerson (1983). Product s Liability, Consumer Mispercept ions, and Market Power. Bell Journal of Economics, 14(2): 581-589.

[8] Shapiro, C. (1982) Consumer Informat ion, Product Quality, and Seller Reput at ion. Bell Journal of Economics 13: 20-35.