Montréal
Série Scientifique
Scientific Series
2001s-27
Bankruptcy Cost, Financial
Structure and Technological
Flexibility Choices
Marcel Boyer, Armel Jacques,
Michel Moreaux
CIRANO
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•École des Hautes Études Commerciales
•École Polytechnique
•Université Concordia
•Université de Montréal
•Université du Québec à Montréal
•Université Laval
•Université McGill
•MEQ
•MRST
•Alcan inc.
•AXA Canada
•Banque du Canada
•Banque Laurentienne du Canada
•Banque Nationale du Canada
•Banque Royale du Canada
•Bell Québec
•Bombardier
•Bourse de Montréal
•Développement des ressources humaines Canada (DRHC)
•Fédération des caisses populaires Desjardins de Montréal et de l’Ouest-du-Québec
•Hydro-Québec
•Imasco
•Industrie Canada
•Pratt & Whitney Canada Inc.
•Raymond Chabot Grant Thornton
•Ville de Montréal
© 2001 Marcel Boyer, Armel Jacques et Michel Moreaux. Tous droits réservés. All rights reserved.
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or its partners.
Bankruptcy Cost, Financial Structure and
Technological Flexibility Choices
*
Marcel Boyer
†
, Armel Jacques
‡
, Michel Moreaux
§
Résumé / Abstract
Nous étudions dans cet article les interactions entre la structure de
financement des firmes et leur choix technologique, en particulier leur flexibilité
technologique. Lorsqu'il existe des coûts de faillite, une firme endettée peut
modifier ses choix stratégiques afin de diminuer sa probabilité de faillite. Nous
montrons, dans le cas où la capacité de la technologie inflexible est faible
(élevée), que l'endettement d'une firme peut conduire cette dernière à choisir une
technologie moins (plus) flexible. Ces effets de l'endettement sur les choix
technologiques peuvent, dans un oligopole, faire l'objet d'un choix stratégique.
Nous montrons qu'il existe des cas où l'endettement est utilisé par les firmes
comme un outil de collusion partielle et d'autres cas où l'endettement améliore la
position stratégique d'une firme au détriment de sa concurrente.
We study the interactions between the capital structure and the
technological flexibility choices of firms in a duopoly. When there are bankruptcy
costs, a leveraged firm may modify its strategic choices in order to decrease its
probability of bankruptcy. We show that, when the capacity level of the inflexible
technology is small (large), debt may induce firms to choose less (more) flexible
technologies. Debt may be used in a strategic way. We show that debt can be used
as a partial collusion tool to increase the expected profits of both firms. We show
also that a firm may use debt as a commitment device to increase its own expected
profit to the detriment of its rival.
Mots Clés :
Endettement, flexibilité, oligopole
Keywords:
Capital structure, flexibility, oligopoly
JEL: L13, G32
*
Corresponding Author: Marcel Boyer, CIRANO, 2020 University Street, 25
th
floor, Montréal, Qc, Canada
H3A 2A5
Tel.: (514) 985-4002
Fax: (514) 985-4035
email: marcel.boyer@cirano.qc.ca
We thank Michel Poitevin, Peter Lochte Jorgensen and participants in the EGRIE meeting (Rome) and in the
microeconomics seminar at Istituto Universitario Europeo (Florence) for their comments. Financial support from the
SSHRC (Canada), CNRS (France) and INRA (France) is gratefully acknowledged.
†
Université de Montréal and CIRANO
According to many businessgurus and commentators, exibilityhasbecome theHoly Grailin
the `new'economic orbusinessenvironment becausedevelopments inglobalization,in
informa-tion technologies and in manufacturing technologies have made themarkets signi cantlymore
volatile. Theincreased exibilityisobtainedthroughreengineering,outsourcing,downsizing,
fo-cusingoncorecompetencies,investingincomputercontrolled exibletechnologies, empowering
keyindividualswithspeci chumancapital,and moregenerally designingmore powerful
incen-tivesystemsandcorporategovernancerulestoensurebetter congruenceofintereststhroughout
the rm. Business International (1991) claims that thesearch for exibilityis theall-inclusive
concept allowinganintegratedunderstandingofmostifnotallrecentdevelopmentsin
manage-menttheory. Itclaimsalsothatreorganizinga rmtoincreaseits exibilityrequiresaconcerted
e ortonmanylevels: introducing atterorganizationalstructures,investinginautomated
man-ufacturing, creating strong butmalleable alliances,introducingdecision and incentive systems
centeredonresults,etc. Inthewordsofeconomictheorists,thismeansharnessingandexploiting
the supermodularityinthesetof strategies.
Wereconsiderheretheseclaimsinacontextofoligopolisticcompetitionunderuncertaintyin
order to clarifytheissuespertainingto the relationshipsbetween exibility, nancialstructure
and bankruptcy costs. As we will see, exibility has both positive and negative features and
thereforethechoiceofitslevelinacorporationraisesmoresubtlestrategicissuesthansuggested
inthegurus'writingandinthemanagementliteratureingeneral. Intermsofinvestment,a
ex-iblemanufacturingsystemcapableofproducingawiderarrayorscopeofproductswilltypically
bemore expensive thanadedicatedmanufacturingsystem, notonlyintermsof theinvestment
costpersebutalsointermsofitsimpactontheinternalorganizationofthe rmandonits
rela-tionswithsuppliersandcustomers. 1
Theevaluationoftheproper exibilityspectrumina rm,
whether this exibility comes from technological, organizational or contractual characteristics
and decisions,requiresan evaluation ofthe netrade-o betweenthevalueand costof changes
in the real options portfolio so created, inthe probability of bankruptcy, inthe probability of
1
SeeGerwin(1982,1993),MensahandMiranti(1989),MilgromandRoberts(1990) andBoyerandMoreaux (1997)for convincingexamples.
and potential, who may be more or less aggressive towards the rm depending on its level of
exibility. Theanalysisoftheseissuesrequiresmodelingstrategiccompetitionwithexplicitand
speci cfeatures relatedto exibility.
Inthatvein,we consideraduopolisticcontext withendogenouscapitalstructuresand
tech-nological exibilitychoices in which rms can fallinto costly bankruptcy. In such a context,
one expects that the debt level can change the technological exibility choice of a rm since
the latter modi esin an important way the distribution of cash ows over thedi erent states
of demand. In turn, it implies rst that debt may be used strategically and second that the
nancial and technological choices ofa rmare simultaneouslydetermined.
BranderandLewis(1986)showthatthedebtlevelmayhaveasigni cantimpactinastrategic
context. Inanoligopolisticmarketunderuncertaindemandconditions,limitedliabilityinduces
rmsto take more riskypositionsasinJensenand Meckling (1976). Thedebt levelworks asa
crediblecommitmentdevice. Byincreasingitsdebtlevel,a rmcan,attheCournotstageofthe
game, decrease theequilibriumproductionlevelof its rivalwhileincreasingits own production
level: debthasastrategicvalue. Withbankruptcycosts, thelink betweendebtand production
ismoreambiguous: BranderandLewis(1988)showthatdebtcaneitherincreaseordecreasethe
competitive positionof the rm. Several otherauthorshavecontributedto clarifyingthee ects
of thecapitalstructureontheproductionlevelofa rminanoligopoly: insomecontexts, debt
improvesthecompetitive positionof the rm butinothers, debtisa sourceof weakness. 2
2
Maksimovic(1988)analysestheimpactofdebtonthepossibilitiestosustaincollusion. Poitevin(1989,1990)
arguesthatdebtmayallowtosignallowproductioncost. Glazer(1994)solvesatwoperiodmodelinwhichdebt isrepaidattheendofthelastperiod;inthesecondperioddebtispro-competitivebut,inthe rstperiod,debt
allows somekindofcollusionbecauseanincreaseintherival'spro tdecreasesitsresidualdebtandmakeitless aggressiveinthelastperiod. Showalter(1995,1999)analysestheBertrand competitioncase; heshowsthat the
optimal strategic debtchoicedependsonthetypeof uncertainty thatexists inthe outputmarket: if costsare uncertain, rmsdonotleveragebut,ifdemandconditionsareuncertain, rmscarrypositivestrategicdebtlevels
inordertosoftencompetition. Inanentryframework,theincumbentwantstocommitcrediblytochoosealow price inorderto deterentry,hencetobeindebtifcostsareuncertainanddebtfreeifdemandisuncertain. In asimilarframework, SchnitzerandWambach(1998)investigatethechoicebetweeninsideandoutside nancing
by risk-averseentrepreneurswho produce withuncertainproduction costs. Parsons(1997) expands themodel of Branderand Lewis (1988) by allowing cornersolutions; with this speci cation, rms may initially have an
incentivetodecreaseoutputlevels iftheytakeonmoredebt. Hughes,Kao andMukherji(1998)showthat the possibility toacquireandshare informationmaydestroyBranderandLewis's(1986)result. DasguptaandShin
(1999) showthat, whenone rmhas better access toinformation, leverage may bea way for the rival rmto free-rideonthe rm'sinformation. InBoltonandScharfstein(1990),debtdecreasestheprobabilitythatthe rm will surviveandthereforeincreasestheprobabilitythatrivalswillpreyonit.
emphasizedbyStigler(1939), rmshavesomedegreesoffreedominchoosingtheircostfunctions.
In thisspirit,Vives(1989), Lecostey (1994)and Boyerand Moreaux(1997)among othersshow
thatawaytocommittoaproductionstrategyinanoligopolisticmarketwithuncertaindemand
conditionsistochooseanin exibletechnology. Thetrade-o inthiscaseisthata rmchoosing
an in exibletechnologycan, ifthe capacity of thein exibletechnology is relatively low[high],
reduce themarketshareof its rivalinstatesoflow[high]demandbutcannot fullyexploit[but
shutsdown in] thestates of high [low] demand. In thepresent paper, we consideroligopolistic
market settings and we analyze the technological choice and the nancial structure as joint
strategic decisions.
The paperis organizedas follows. We present the model insection 2. We derive in section
3 the pro ts of the rms for given technologies and we inferthe debt contracts and the debt
thresholdsofbankruptcy. Insection4,westudytheimpactofdebtonthetechnological exibility
choices. Insection 5,wediscussthestrategicvalueof being indebt andtheexistenceof jointly
optimal capitaland technological structures. We concludeinsection 6.
2 The model
The inversedemandfunctionis assumedto be linear: 3
p=max(0; Q)
whereQistheaggregateoutputand isarandomvariabletakingtwovalues, 1
withprobability
and 2
withprobability1 , with 2
> 1
.
Firmschoosebetweentwoavailabletechnologies: oneisin exible(i)andtheotheris exible
(f). An in exible rm either produces x,where x isthe exogenous capacity, orshutsdown. A
exible rm can choose any positive level of production. The two technologies have the same
average operating costc, butthesunk costsdi er. The sunk cost ofan in exibletechnology is
K;thiscost maybecomposedofproductdesigncosts,landpurchases,plantconstruction costs,
3
Demand linearity and all the other speci c assumptions as constant marginal cost are made only to get
tractableexplicitsolutions. Thereaderwillunderstandthatourassumptionscouldberelaxedatthecostofmore complexityandlesstransparencyintheresults.
Initially, entrepreneur h 2 f1;2g has a capital of A h
. This capital level is exogenous, an
assumption we will relax in section 5. If A h
is less than K orK +H, the entrepreneur must
borrow additional capital from a bank. Banks can observe each rm's technological exibility
choice butneitherthelevelof demandnorthepro tsofthe rms. 4
So adebtcontract speci es
a level of repayment R independent of the level of demand and pro t but dependent on the
technologicalchoicesofboth rms. Ifa rmisunabletorepayR ,itgoesbankruptanditsgross
pro t isseizedbythebank. Formatterofsimplicity,weavoidintroducingincentiveconstraints
in theproblembyassumingthatincase ofbankruptcy,courtscan check thebooks ofthe rm,
ndtheliars and imposeon themharsh punishment. 5
We assumealso thatthe bankingsector
is perfectly competitive and therefore a bank accepts a contract if and only if the expected
repayment is at least equal to the payo which would be obtained in lending at the riskless
interestrate,normalized at zero.
The entrepreneurs have limited liability but bankruptcy generates non-monetary costs for
anentrepreneursincebankruptcysendsabadsignalonhismanagementskills,makingitharder
for him to nda new job or to borrow new capital to nance another project. Furthermore,
bankruptcy generates high transaction costs. These costs are assumed to have a monetary
equivalentvalue B,independentof thelevelof default.
The two entrepreneurs beginthe game with observable amounts of equityA 1
and A 2
. The
timingofthegameisasfollows. First,theentrepreneurssimultaneouslynegotiatedebtcontracts
as functions of the technological con guration to emerge inthe industry. Second, they choose
simultaneouslytheir respective technology. Hence, the debtcontracts and the technologies, or
the exibility levels, are chosen simultaneously within a rm and across rms. Third, they
observe the level of demand and engage in Cournot competition. Finally, rms repay debt or
go bankrupt. Regarding the exogenous capacity level x, we assume that in the high state of
demand, both rmsproduceand avoidbankruptcy at theCournotstage ofthegame whatever
their technological choices, thatis x<( 2
c)=2 . They maygo bankrupt inthe lowstate of
4
Thisassumptionofunobservabilityofpro tsisintroducedsoastomakethestandarddebtcontractoptimal (seeBoltonandScharfstein1990).
5
In other words, pro ts are unobservable by banks but veri able by courts, an assumption which can be justi edbytheinvestigationpowerofcourtsascomparedtobanks.
x2X 1
fxjx <( 1
c)=2 g(smallcapacity): whendemandislow,both rmsproduce
atthe Cournotstage of thegame forany technologicalchoices;
x2X 2 fx j( 1 c)=2 <x <( 1
c)= gg (intermediate capacity): when demandis
low,technologicalcon gurations(f;f)and(f;i)implythesameequilibriaaswhenx2X 1
,
whereas(i;i) impliesthatone rm shutsdownandtheother obtainsits monopolypro t;
x 2 X 3
fx j ( 1
c)= < xg (large capacity): when demand is low, technological
con guration (f;f) impliesthe same equilibriaas above, (f;i)impliesthat the in exible
rm shutsdownwhereasthe exible rm enjoysamonopolypro tlevel, and(i;i)implies
that both rms shut down.
This modelis the simplestpossibletractablestrategic modelcapturing the relevant
character-isticsof the`new'economic orbusinessenvironment asdiscussedabove,oftheinterdependence
between nancial structure and technology choice (endogenous cost function), and of optimal
nancial contracting underasymmetric information(adverseselection) and bankruptcy cost.
3 The expected pro ts as functions of technological choices
Debt levelsplaya crucialrole intheproductcompetitionstage becauseitdeterminesthe
prob-abilityof bankruptcy. We characterize in thissection the debt threshold, over which the rm
cannot repayitsdebtin thebadstate of demand,asa functionof technologicalcon gurations.
Fort;t 0
2fi;fg and any X 2fX 1 ;X 2 ;X 3 g, we shall denote by k (t;t 0 ;X) thepro t of a rm
with technology t facing a rival with technology t 0 when x 2 X and = k 2 f 1 ; 2 g, by E(t;t 0
;X) theexpected pro tof a rmbeforethedemandlevelis revealed, andbyD(t;t 0
;X)
the debt threshold over which the rm goes bankrupt when the demand is low. The Cournot
equilibrium pro ts over operating costs, as functions of the technological choices of the rms,
When demandislow, thegrosspro t ofa exible rm isequalto 1
(f;t 0
;X) which de nesthe
debt threshold 6 D(f;t 0 ;X)= 1 (f;t 0 ;X) (1)
Thus if the debt of the rm is lower than D(f;t 0
;X), the rm never goes bankrupt. The
bankingsectorisperfectlycompetitiveandsotherepaymentR h
isequaltotheamountborrowed
K+H A h . R h =K+H A h : (2)
On the other hand, if the rm's debt is larger than D(f;t 0
;X), the rm goes bankrupt when
demandislow. Inthisbadstate of themarket,the rmrepaysonlyits grosspro t,an amount
lowerthantheamountitshouldrepay. Sointhegoodstate,the rmmustrepayanamountR h
such that the expected pro t of the bank is equal to zero, that is 1 (f;t 0 ;X)+( 1 )R h = K+H A h . Hence,R h asa functionof(f;t 0 ) isgiven by: R h = 1 1 K+H A h 1 (f;t 0 ;X) : (3)
We canobtaintheexpectedpro tasfollows. Forlowdebtlevels,the rm nevergoesbankrupt
and its expected pro t is 1 (f;t 0 ;X)+(1 ) 2 (f;t 0 ;X) R h A h where R h is given by
(2). For large debt levels, the rm goes bankrupt if demand is low; its expected pro t is
( 1 )[ 2 (f;t 0 ;X) R h ] B A h where R h
is now given by (3). Thus, making use of (2)
and (3), weobtainthat theexpected pro t ofthe entrepreneuris given by:
E(f; t 0 ; X)= 8 > < > : d E(f;t 0 ;X); ifK+H A h D(f;t 0 ;X) d E(f;t 0 ;X) B; ifK+H A h >D(f;t 0 ;X) (4) where d E(f;t 0
;X) is theexpected pro t whenthe rmdoesnotgo bankrupt:
d E f;t 0 ;X = 1 (f;t 0 ;X)+( 1 ) 2 (f;t 0 ;X) (K+H): (5) 6
Whena exible rmfacesanin exible rmwithalargecapacity(x2X3),the exible rmmayearnmore pro twhendemandislow,inwhichcasethein exible rmshutsdownandthe exibleoneisamonopolist,than
whendemandishigh,inwhichcase thein exible rmcapturesalarge marketshare. It maytherefore happen that the exible rmavoidsbankruptcywhenthedemandislowbutgoesbankruptwhenthedemandishigh!
valuesof 1
(), D()and d
E ()are given inAppendixA.
3.2 Financial contract and expected pro t of an in exible rm
If eitherx 2X 1 [X 3 and t 0 2fi;fg orx2X 2 and t 0
=f,thegross pro tof an in exible rm
is equalto 1
(i;t 0
;X) which de nesthe debtthreshold
D(i;t 0 ;X)= 1 (i;t 0 ;X) (6)
Ifithasadebtlowerthanthisgrosspro t,itnevergoesbankruptandR h
=K A
h
. Otherwise
itgoesbankruptandthezeroexpectedpayo conditionofthebanktakestheform 1 (i;t 0 ;X)+ ( 1 )R h =K A h ,implyingthat: R h = 1 1 K A h 1 (i;t 0 ;X) : (7)
Its expected pro tis therefore given by
E i;t 0 ;X = 8 > < > : d E(i;t 0 ;X); ifK A h D(i;t 0 ;X) d E(i;t 0 ;X) B; ifK A h >D(i;t 0 ;X) (8) where d E i;t 0 ;X = 1 (i;t 0 ;X)+(1 ) 2 (i;t 0 ;X) K : (9)
Ifboth rmsarein exibleand x2X 2
,onlyone rmproduces ifdemandislow. We assume
that the producing rm is determined randomly with probability1/2. Hence we must de ne
two debtthresholds inthiscase: ^ D(i;i;X
2
)=0if the rm doesnotproduceand D(i;i;X 2 )= 1 (i;i;X 2
)ifitproduces. Each rmgoesbankruptwithprobability1/2ifK A h
<D(i;i;X 2
)
and with probability 1 if K A h
> D(i;i;X 2
). The repayment amount R h
to be paid when
= 2
isgiven intheformer caseby
R h = 1 1 =2 (K A h ) (10)
and inthe lattercase by
R h = 1 1 K A h 1 2 1 (i;i;X 2 ) : (11)
E( i;i;X 2 )= 8 > > > > > < > > > > > : d E( i;i;X 2 ); ifK A h 0 d E( i;i;X 2 ) 1 2 B; if0<K A h D(i;i;X 2 ) d E( i;i;X 2 ) B; ifK A h >D(i;i;X 2 ) (12) where d E(i;i;X 2 )= 1 2 1 (i;i;X 2 )+( 1 ) 2 (i;i;X 2 ) K : (13)
4 The impact of equity on technological choices
A rm'scostofborrowing,expectedpro tandprobabilityofbankruptcyaredeterminedbythe
technologicalcon guration of theindustryand its own levelof equity. Hence the technological
bestreplyofa rmtothetechnologicalchoice ofitscompetitordependsonitsownequitylevel.
To characterize theimpact of equity nancingon thetechnological equilibriumin an industry,
we must rst studyits impact on the technological bestreply functions. We will illustrateour
resultswithexamplesforeachofthethreecasesofsmall,intermediateandlargecapacityofthe
in exibletechnology.
A rm's debt level is given by the cost of the technology it chooses, either K or K+H,
minusitsequityA h
. Foragiventechnologicalcon guration,a rm'sexpectedpro tisaconstant
functionofthedebtlevelprovidedthatthe rmcanmaketherepaymentevenwhenthedemand
is low; when debtis high,theexpected netpro t isreducedbytheexpectedbankruptcy costs.
Bankruptcy allowsastandarddebtcontract tobeanelegant andsimplesolutiontotheadverse
selection problem raised by the unobservability of pro t. Without that agency problem, the
optimal nancingcontractwouldbe apro tsharingcontract underwhichthe rmwouldnever
go bankrupt. If there is no bankruptcy cost, we nd the well known Modigliani and Miller
(1958) result: thecapitalstructureofthe rmisirrelevant,asshownbythebestreplyfunctions
derived inAppendixB.
Proposition 4.1 If there is no bankruptcy costs (B=0), the technological choices are
indepen-dent of the rms' capital structure.
Supposethat a rm chooses the in exibletechnology. To determine the competitor's best
re-sponse,wemustdeterminethevalueofits expectedpro tdi erentialE(i;i;X) E(f;i;X),
forX 2fX 1 ;X 2 ;X 3
g,which foreach X isa stepfunctionof itsequity. Thequalitative
charac-teristics ofthese functions turnoutto be thesame forX 1
and X 3
butdi erforX 2 . 4.1.1 The case X 2fX 1 ;X 3 g
Let A(i;i;X) and A(f;i;X) betheminimumequityrequiredfornotgoing bankruptinthelow
state ofdemandwhen choosingrespectivelythe in exibleand the exibletechnology,thatis:
A(i;i;X) =K D(i;i;X)
A(f;i;X) =K+H D(f;i;X)
(14)
and so, A(i;i;X)<A(f;i;X) i H > 1
(f;i;X) 1
(i;i;X).
If a rm's equity is relatively low [large], the rm [never] goes bankrupt if demand is low
whatever its technology. Hence the technological best response in these two cases will be the
same andindependentoftheexpectedcostofbankruptcyB. Forintermediatelevels ofequity,
that is a levelbetween the critical levels (14), whether or not a rm goesbankrupt in the low
state of demand will depend on its technology and therefore its best response will depend on
the expected bankruptcycost B:
If A(i;i;X)<A(f;i;X) and ifits equityfallsbetweenthose two critical values,that isif
A(i;i;X) <A h
<A(f;i;X),the rm goes bankruptin thelow state of demandi ithas
a exibletechnology.
IfA(f;i;X) <A(i;i;X)and ifA(f;i;X)<A h
<A(i;i;X),the rmgoesbankruptinthe
lowstate of demandi ithas anin exibletechnology.
The formalcharacterization ofa rm'stechnologicalbestreplytothetechnologicalchoiceofits
competitoris giveninAppendixB. From(4) and(8), weobtainthefollowingtwopropositions.
Proposition 4.2 (For x 2 X 2 fX 1
;X 3
g): If A(i;i;X) < A(f;i;X), a switch occurs in the
technological best response to in exibility as equity A h increases i d E (f;i;X) > d E(i;i;X)
( exibility isthe bestresponse underno debt) andB >E (f;i;X) E (i;i;X) (theexpected
cost of bankruptcy is suÆciently high). In such a case, the best response to in exibility is
exibility forlow levelsof equity,in exibility forintermediatelevelsof equity, exibilityfor high
levels of equity.
Proposition 4.3 (For x 2 X 2 fX 1
;X 3
g): If A(f;i;X) < A(i;i;X), a switch occurs in the
best response to in exibility as equity A h increases i d E (i;i;X) > d E(f;i;X) (in exibility
is the best response under no debt) and B > d
E(i;i;X) d
E (f;i;X) (the expected cost of
bankruptcy is suÆciently high). In such a case, the best response to in exibility is in exibility
for low levelsof equity, exibility for intermediate levelsof equity, in exibility for high levelsof
equity.
4.1.2 The case X =X 2
Fortheintermediatecapacitylevelofthein exibletechnology,theanalysisisabitmorecomplex.
Bychoosingthein exibletechnology,a rmfacinganin exiblecompetitorwill,ifdemandislow,
either nevergo bankruptif itsequityis higherthanK (it thenhasno debt), orgoesbankrupt
with probability1/2 ifits equityislowerthanK buthigherthanA(i;i;X 2
)=K D(i;i;X 2
),
or always go bankrupt if its equity is lower than A(i;i;X 2
). If the rm chooses instead the
exibletechnology,theminimumlevelof equitynecessary toavoidbankruptcy inthelowstate
of demandis A(f;i;X 2 ) =K+H D(f;i;X 2 ). Since A(i;i;X 2
) <K, we must now examine
threepossibilitiesdependingonwhetherA(f;i;X 2
)ishigherthanK,betweenKandA(i;i;X 2
),
or lowerthanA(i;i;X 2
). From (4), (8)and (12), we obtainthefollowingtwo propositions.
Proposition 4.4 (For x 2 X 2
): The technological best response to in exibility goes from
ex-ibility to in exibility and to exibility again as equity A h
increases, under two sets of
condi-tions. First, when K < A(f;i;X 2 ) i d E (f;i;X 2 ) > d E (i;i;X 2 ) and B > d E (f;i;X 2 ) d E (i;i;X 2
); second, when A(i;i;X 2 ) < A(f;i;X 2 ) < K i d E (f;i;X 2 ) > d E(i;i;X 2 ) and B >2 h d E(f;i;X 2 ) d E (i;i;X 2 ) i . 7 7
In the rst case, the levels of equity for which in exibility is the best response are given by A h
2
(A(i;i;X2);A(f;i;X2)) or A h
2 (K ;A(f;i;X2)) according to whether c E(f;i;X2) c E(i;i;X2) is lower or higherthan 1 2 B.
2
exibility to exibility and to in exibility again as equity A h
increases, under two sets of c
on-ditions. First, when A(i;i;X 2 ) < A(f;i;X 2 ) < K i d E(i;i;X 2 ) > d E (f;i;X 2 ) and B > 2 h d E (i;i;X 2 ) d E(f;i;X 2 ) i
; second, when A(f;i;X 2 ) < A(i;i;X 2 ) < K i d E(i;i;X 2 ) > d E (f;i;X 2 ) and B> d E (i;i;X 2 ) d E(f;i;X 2 ). 8
4.2 The best response to exibility
Let us de ne A(i;f;X) and A(f;f;X) for X 2 fX 1
;X 2
;X 3
g as the minimum level of equity
required to avoid bankruptcywhen the rm chooses respectivelythe in exibleand the exible
technologywhereasthe other rm isa exible rm,thatis:
A(i;f;X) =K D(i;f;X) ; A(f;f;X)=K+H D(f;f;X): (15)
An argument similarto theargument developed forcharacterizingthe best responseto
in exi-bilityleadsto thefollowing propositions.
Proposition 4.6 (ForX2fX 1 ;X 2 ;X 3
g):WhenA(i;f;X)<A(f;f;X), aswitchoccursinthe
bestresponseto exibilityasA h increasesi d E(f;f;X)> d E (i;f;X)andB> d E (f;f;X) d
E (i;f;X). In such a case, the best response to exibility is exibility for low levels of equity,
in exibility for intermediatelevels, exibility for high levels.
Proposition 4.7 (ForX2fX 1 ;X 2 ;X 3
g):WhenA(i;f;X)>A(f;f;X), aswitchoccursinthe
bestresponseto exibilityasA h increasesi d E(i;f;X)> d E(f;f;X)andB > d E(i;f;X) d
E (f;f;X). Insuch acase,thebestresponseto exibilityisin exibilityforlowlevelsofequity,
exibility for intermediate levels, in exibility for high levels.
4.3 Examples
Thefollowingexamplesshowhowtheabovebestresponsefunctionsgenerateequilibrium
techno-logicalcon gurationsintheindustryasfunctionsoftheequitylevelsofthe rms. Theexamples
are worked outinAppendixC.
8
In the second case, the levels of equity for which exibility is the best response are given by A h 2 (A(f;i;X 2 );K) or A h 2 (A(f;i;X 2 );A(i;i;X 2 )) according to whether c E(i;i;X 2 ) c E(f;i;X 2 ) is lower or higherthan 1 2 B.
1 1 2
We consider rst a commonequitylevel forboth rms, thatis A h
=A forh=1;2 (Figure 1),
before lookingat themore generalcase of asymmetric levels(Figure1 0
).
-FIGURE1 (example 1)
[inY, (f;f) and (i;i)]
A 0 (f;f) 1.2 (f;i),(i;f) 2.4 (i;i) 2.44 Y 3.04 (f;f) 5.00
If the common equitylevel can cover the cost of bothtechnologies (A= 5), both rmschoose
the exibletechnologyinequilibrium. If2:44<A<3:04, therearetwoNashequilibriainwhich
both rmschoosethesametechnology,eitherthe exibleorthein exibleone. Forthose equity
levels, the rms fall into a exibility trap, a coordination failure, as shown in Appendix C. If
2:4<A<2:44, theuniqueequilibriumis(i;i). If1:2<A<2:4,theequilibriumisasymmetric,
(f;i) or (i;f). Finally,if thecommon equity level is small(A<1:2), the equilibrium is again
(f;f).
When theequitylevels aredi erent, newcases appear(see Figure 1 0
).
InsertFigure 1 0
here
There are values for which the unique equilibrium is asymmetric, (f;i) or (i;f). There are
also two sets of values for which there exist no equilibrium in pure strategies. Within these
sets, one rm's best reply is to mimic the technological choice of its rival while for the other,
it is to choose a technology di erent from its rival's. One shouldnotice that the technological
choice of a rm is not a monotonic function of its equity level, given the equity level of its
competitor: for example,if A 1
isinthe interval(0; 1:2), rm 2chooses the exible technology
if its equity level is small, that is, if A 2
2 (0; 1:2), the in exible technology for intermediate
equity levels, that is, for A 2
2(1:2; 2:44), and again the exible technology if its equity level
is large, that is, if A 2
2 (2:44; 5). Also, the technological choice of a rm is not a monotonic
function of the equity level of its competitor, given its own equity level: forexample, if A 1
is small, that is,if A 2
2(0; 1:2),the exibletechnology for intermediate equity levels, thatis,
for A 2
2(2:4; 2:44), and againthe in exibletechnology ifits competitor'sequitylevelis large,
that is,ifA 2
2(3:04; 5).
When rms are totally nanced by equity, they choose the exible technology. This
tech-nology allows rmsto take advantageof theopportunitieso eredwhen demandishigh. Firms
adopt the exibletechnology inspite ofits twodisadvantages: a higher xed cost and alower
pro t whendemandislow. Ifequityisreducedand borrowingnecessary,a exible rmmaygo
bankrupt ifthedemandis low. It can eliminatethis riskifit chooses the in exibletechnology,
allowing a reductionin theamount borrowed and an increase inpro t when demandis lowat
thecostofareductioninpro twhendemandishigh. Theexpectedvalueandvarianceofpro t
decrease. Thesee ects explaintheswitchinequilibriumfrom( f;f) to( i;f) whentheequityof
rm 1 decreases.
But the technological switch of rm 1 may also make the exible technology of the other
rm more risky. When rm 1 becomes in exible,the expected value and variance of pro t for
the exible rm2 increase. Thismaymake the rmbankruptifdemandislow. By choosingan
in exibletechnology,the rmcanreducethevarianceofitspro t. Thisexplainstheexistenceof
twoequilibriainzoneYofFigure1andofauniqueequilibrium(i;i)inthehatchedzone. When
rms have very low equity, a change in technology is insuÆcient to eliminate the probability
of bankruptcy. The previous e ect disappears and rms choose again exible technologies.
Hence,when thecapacityofthein exibletechnologyislow, thepresenceofdebtfavors exible
technologiesbecause theyare lessrisky,thevarianceof pro t being lower.
This example is very instructive. It shows that the technological exibility choices of the
rmsdependontheirlevelofequity. Hence,ontwoperfectlyidenticalmarkets,thetechnological
con gurations may di er if the rms have di erent access to equity nancing. One cannot
predict whichtechnological con gurationwillemerge simply from observingdemandand costs
conditions. Example 2: x 2X 2 ; = 0:5, 1 = 5, 2 =10, x = 2:5, =1, c =0:2, K = 3, H = 0:5,
B =6. Again,weconsider rstacommonequitylevelforboth rms,thatisA h
(Figure2), beforelookingat the more generalcase ofasymmetric levels (Figure2).
-FIGURE2 (example 2)
[inY, (f;f) and (i;i)]
A 0 Y .125 (i;i) .94 Y 2.18 (f;f) 3 Y 3.5
Ifboth rmsareallequity rms, therearetwo equilibria(f;f) and(i;i), sothatthe rmsmay
fall into a exibilitytrap since (i;i) would be more pro table for both of them. If the equity
levels decrease butremain equal to each other, then (f;f) becomes the uniqueequilibrium. If
equity decreases even more, we have again two equilibria(f;f) and (i;i) but, contrary to the
rst situation, pro ts are now higher in the (f;f) equilibrium. The rms may here fall into
an in exibilitytrap. A further decrease inequitylevels brings (i;i) as theunique equilibrium.
Last, if the rmshave close to zero equity, there are again two equilibria(f;f) and (i;i) with
the latterbeingmore pro table forboth rms.
When theequitylevels di er,other equilibriaappear(see Figure 2 0
).
InsertFigure 2 0
here
There exist two sets of equity values for which the rms choose opposite technologies. There
are also equity values for which (f;f) and (i;i) are equilibriabut with no trap since none is
uniformly better for both rms. Again, the observation of demand and cost conditions in an
industry is not suÆcient to predict which technological con gurationwill emerge. If the rms
are totally nanced byequity,there aretwo technological equilibriumcon guration: ( f;f)and
( i;i) . The existence of these two pure strategies equilibria may be explained by the strategic
valueof exibility. Assumethattheinitialsituationis( i;i) . Ifa rmchangesitstechnologyand
chooses exibility,it willbe able to adaptits output levelto thedemandlevel. It willdecrease
its productionwhenthedemandislowandincreaseitwhenthedemandishigh. Thisincreases
the rm's pro t butnotenough to cover thelarger xed cost ofthe exibletechnology. Butif
commitmentinducestheother rm,also exible,todecreaseitsoutputlevelwhenthedemandis
high. Inthiscontext, exibilityhasapositivestrategicvalue. Whendemandislowtheopposite
e ect arises and exibilityhasa negative strategicvalue. Forthe parametervaluesof example
2, the net strategic value of exibilityis positive. When a rm adopts the exibletechnology,
the value of exibilityincreases forthe other rm aswell. Thise ect explainsthe existence of
the two purestrategyequilibria. 9
If one rm hasinitiallyless equity, it must borrowand mayend up bankrupt(with
proba-bility 1/2) ifthe demand is low when the technological con guration is (i;i). By switching to
exibility,the rmalreadyindebtmustborrowadditionalfundsto nancethehigher xedcost
of the exibletechnology. Butits increaseinpro twhen demandis lowismore importantand
eliminates theriskofbankruptcy. Whenthe rmindebtchanges itstechnology,theother rm
isinducedtochangeitstechnologytoo: thereisauniqueequilibriumtechnologicalcon guration
( f;f).
Hence,whenthecapacityofthein exibletechnologyisintermediate,theequilibrium
techno-logicalcon gurationcanevolve towardmore exibilityormorein exibilityasleverageincreases
because the levelof risk linkedto atechnologydependson thetechnology chosen bytheother
rm. Example 3: x 2X 3 ; = 0:1; 1 =4; 2 =15; x =5; = 1;c = 0:2; K =4; H = 0:5,
B = 6. The common equity level case is illustrated in Figure 3 and the more general case of
asymmetric levels inFigure 3 0 . -FIGURE3 (example 3) A 0 (i;i) .89 (i;f),(f;i) 2.9 (f;f) 4 (i;i) 4.5
As inthepreceding two examples,theequilibriumtechnological con gurationischangingwith
the equity levels. When thelevels of equityarethe same forboth rms, A h
=A; h =1;2, the
9
For intermediate equity levels, 2:9 < A < 4, they both switch to the exible technology. For
lowerequitylevels, 0:89<A<2:9,they choose di erenttechnologies andforeven lowerequity
levels, A < 0:89, they both come back to the in exible technology. The case of asymmetric
equitypositionsisillustrated inFigure3 0
.
In this example, the capacity of the in exible technology is so high that a rm using this
technologyalwaysshutsdownwhenthedemandislow. Asaresult,theprobabilityofbankruptcy
of an in exible rm is strictlypositive assoon asits debt isstrictly positive. A leveraged rm
thenprefertoswitchto a exibletechnology,therebyeliminatingtheriskofbankruptcy. When
the rm's debtis larger,choosinga exibletechnology eliminatesthe riskof bankruptcy ifthe
other rm is in exiblebut not if the other rm is exible. Therefore inequilibrium, one rm
switches to the exibletechnology to eliminate its riskof bankruptcy whiletheother keeps an
in exibletechnology anda positiveprobabilityofbankruptcy. Ifequitylevels arevery low, the
real option value of exibility disappears and the rms end up in a (i;i) equilibrium as when
equityis very large.
We can conclude this section 4 by sayingthat the impact of equity nancing on the
tech-nological con guration of an industry is,as illustrated inexamples 1 to 5, a rather subtlenon
monotonous impactcombiningdecisiontheoretice ects,realoptione ectsandstrategice ects.
5 The strategic value of equity
Thefactthatthelevelofequity,assumedtobeexogenoustillnow, canchangethetechnological
bestreplyfunctionssuggeststhatthelevelofequitycouldbechosenstrategically. Notehowever
that the best responses are functions of both the equity level and the bankruptcy cost which
are substitute commitment devices. Hence it is the pair (A h
; B) which has a strategic value.
In order to appreciatethe competitive potentialof an industry,we have to look at what could
be called the industry `commitment index', a function of both the equity nancing and the
IntheprevioussectionweassumedthatA h
,thecapitalinvestedinhisbusinessbyentrepreneur
h, was hisgiven initial wealth and that because of the agency problem,theentrepreneur could
notraiseadditionalfundsthroughexternalequity. Werelaxthatassumptioninthissection. We
willassumethattheentrepreneur'sinitialwealthislargerthanK+Hbutthatinapreliminary
stage 0, the two entrepreneurs choose simultaneouslythe amounts A h
they willinvest in their
respective rms. Iftheinvestedcapitalis lowerthanthecostofthechosentechnology,the rm
mustborrow. We shownext thatthere exist cases inwhichthe entrepreneurs decideto nance
their rms in part through borrowing in order to modify in a credible way their technological
reaction functions.
Let us examineagain example 1 (Figure 1 0
). If the rms are whole equity rms, the
tech-nological equilibrium is (f;f). Each rm's expected pro t is then equal to 1.62 even ifin the
technological con guration (i;i) , their common expected pro t would be higher at 2.6 (See
AppendixC). When the rms are all equity nanced, they play a prisoner dilemma game. If
they decrease theirequity capital,they alterthepayo matrixand they avoid thedilemma. In
example 1,ifboth rmshave anequitycapital ofA=3,they play asubgame admitting(f;f)
and (i;i) as equilibria and they never go bankrupt. For even lower equity capital, the rms
can reach the unique equilibrium con guration ( i;i) which is better for them than (f;f). By
reducingtheirequitycapital,the rmscrediblycommitnotto replytoin exibilityby exibility.
When the rivalisin exible, a exible rm earns a highpro t levelwhen demandis high buta
lowpro tlevelwhen demandislow. Hence,ifthe rmmustborrowa largeamount to buythe
exibletechnology,itgoesbankruptwhendemandislow. Theexpectedbankruptcycostmakes
exibilitylessattractive thanin exibilitywhentheother rmisin exible. Whenthebestreply
to in exibilityswitchesfrom exibilityto in exibility,the rmsavoid theprisonerdilemmaand
playacoordinationgame. Therefore rmscanbothincreasetheirexpectedpro tsbychoosing
strategically theircapital structure: 10
debthasa strategicvaluein thiscontext.
10
The rms would bebetter o eliminatingthecon guration(f;f) asanequilibriumbyreducing evenmore
their equitycapitalbutsuchcapitalstructuresare notequilibriaofthepreliminarystagereducedformgame: a rmwouldbebettero deviatingandincreasingitsequitycapitaltoA
h
=4toinducethecon guration(f;i)as
theuniqueequilibrium. If rmswerechoosingtheir capitalstructuresequentially,aformofcoordinationamong rms, theywouldavoid this problem. Theleader would then choose A
1
=3 and the follower A 2
In example 2 (Figure 2), the best technological con guration for the rms is (i;i) with
nancing mainly through equity A h
> 3. This equilibrium ( i;i) is not unique and there is
a exibility trap here. A lower level of equity would eliminate this trap but one of the two
rms would thengo bankrupt when demand is low. The bankruptcy cost makesthis strategy
unattractive. So the rmswillchoosenotto borrow. However debtmay have astrategic value
asinthefollowingexample4: =0:5; 1
=5; 2
=10; x=4; =1; c=0:2; K =2:5; H=
0:1 and B = 3, with its equilibrium technological con gurations depicted in Figure 4. If the
rmsareallequity rms,theuniqueequilibriumis(i;i),even if rmswouldearngreaterpro ts
in thetechnological con guration (f;f), hencean in exibilitytrap here. If the rms cutdown
their equity capital to A h
= 2:45, the equilibrium of the following subgame becomes ( f;i) or
( i;f) and the sum of pro ts increases. But these equity levels are not an equilibrium of the
preliminarystagegame. A rmwoulddeviatetobeanallequity rm. Ontheotherhand, rms
can increasetheirexpectedpro tsbycuttingdownsharplytheirequitycapitaltosayA h
=0:8;
the subgame then admits two equilibria (f;f) and (i;i). In the latter equilibrium, one rm
goes bankrupt when demand is low. In the former one, rms never go bankrupt. If the two
equilibriahavethe same probability,theexpected payo of rmsincreases. Furthermore,these
are equilibriumcapitalstructures. Debt can again increasetheexpected pro tsof both rms.
InsertFigure4 here
Last, let us consider the following example 5 for the case of a large capacity level of the
in exibletechnology, x2X 3 : =0:3; 1 =5; 2 =18; x =6; =1; c=0:2; K =4; H =
0:75 and B =3, with its equilibriumtechnological con gurations depictedin Figure 5. Inthis
example one rm chooses to bean all equity rm with thein exibletechnology and theother
rm chooses A h
2 (2:2; 4) together with the exible technology. The more pro table rm is
the exible rm. Debt allows the rm to select the most pro table technology. In example 3
(x 2 X 3
), the capital structure could be used strategically to increase the expected pro ts of
both rms. In example 5 (x 2 X 3
), the capital structure is used strategically by one rm to
increaseits expectedpro t at theexpenseof theother. 11
the uniquetechnological equilibriumbeing(i;i). Inthis con guration,the rmsnevergobankrupt. Soraising borrowedcapitalhasnocost.
11
Clearly, whatever the capacity level of the in exibletechnology, there exist subsets of
pa-rameter valuesfor which the equilibriumcapital structures combine equity and debt. In these
equilibria, the debt is used strategically to modify the equilibriumtechnological con guration
of theindustrywhichwouldhave emergedhad theentrepreneurs decidedto nancetheir rms
throughequityonly.
5.2 The strategic increase of bankruptcy costs
We showed above that the capital structure can be used strategically in order to in uence
the technological choice of the rival when the bankruptcy costs are high enough to change
thetechnologicalbestreplyfunctions(propositions4.2to4.7). Areductioninbankruptcycosts
wouldnomoreallowthisstrategicuseofthecapitalstructureandthereforemayindeeddecrease
the expected pro tsof the rms. In these cases, the rms could try to arti cially increasethe
bankruptcy costs. A simple way to do that is, for entrepreneurs, to o er judiciously chosen
assets ascollateralfortheirdebt orinducebanksto ask forthose collateralassets. 12
Thebank andtheentrepreneurmayhave di erentevaluationsofthe collateralassets,some
assets having a greater value for the debtor than for the creditor. In general, this di erence
is ineÆcient and the contracting parties have an interest to choose the assets with the lowest
evaluationdi erence. HoweverWilliamson(1983,1985)arguesthatinsomecontracts,itmaybe
betterthatthecollateralassetshavealowvalueforthecreditor. Thiscanpreventacancellation
ofthecontractaimedatseizingthecollateralassets. Ouranalysisproposesanotherexplanation
for thiskindof behavior. Increasingthe di erenceof evaluation increases the bankruptcy cost
and soincreases thecommitment powerofdebt. 13
sequentially. Ifthetwo rmsareallequity rms,theleaderchooses exibilityandthefollowerchoosesin exibility with payo s of21.35 and 20.78 respectively. However, bychoosingA
2
=3,the followerchangesitsbestreply
to exibilityinthefollowing stage. Iftheleaderchooses exibility,thefollowerthenchooses exibility toowith payo of20.66 forboth. Theleaderthenprefersin exibilityand thefollowerchooses exibilitywithpayo s of
20.78and21.35respectively. Thefollower, byissuingdebt,canoutperformtheleaderintermsofpro t. Thereis anotherperfectequilibriuminwhichtheleaderchoosesA
h
2(2:2; 4)withthe exibletechnologyandthefollower is anall equity rmwiththein exible technology; but,inthe rststage, theleader playsaweakly dominated
strategy. SeeEllingsen(1995)forananalysisofgameswithasimilarstructurealthoughinadi erentcontext. 12
SeeFreixasandRochet(1997,chapters4and5)forreferences. 13
manager to be red in case of bankruptcy. If the control of the rm gives to the manager
enoughprivatebene ts,thenthemanagerwillchoosethetechnologywhich minimizethe rm's
bankruptcyprobability. Inordertoincreasethebankruptcycostsandgivethemstrategicvalue,
shareholderscan providemore privatebene tsto themanager.
6 Conclusion
The bankruptcy costs and the equity levels of rms have signi cant impacts on the
equilib-rium technological con gurations in an industry. These e ects arise because indebted rms,
either exible or in exible, may want to change their technologies to reduce the probability
of bankruptcy. When the capacity level associated with the in exible technology is low, the
equilibriumtechnological con gurationof theindustryismore in exibleif rmshave moderate
levelsofequitythaniftheyarewholeequity rms(Figure1). Whenthatcapacitylevelislarge,
moderatelevelsofequitymakethetechnologicalcon gurationoftheindustrymore exible
(Fig-ure 3). The e ect of equityis not monotonous. An industry may have the same technological
equilibrium forlow and high levels of debt, witha di erent equilibrium forintermediate levels
of debt.
The endogeneity of technological choices is likely to be an important determinant of the
optimalcapital structureand oftherelationshipbetweencapital structureandproductmarket
competition. Our results allow us to take some steps in characterizing the role of endogenous
technological exibilitychoices, whoseanalysis hasbeenneglected intheliterature.
\Shylock:
ThiskindnesswillIshow.
Gowithmetoanotary,sealmethere Yoursinglebond,and,inamerrysport, Ifyourepaymenotonsuchaday,
Insuchaplace,suchasumorsumsasare Expressedinthecondition,lettheforfeit
Benominatedforanequalpound Ofyourfair esh,tobecuto andtaken
Inwhatpartofyourbodypleasethme. Antonio:
Content,infaith-I'llsealtosuchabond, AndsaythereismuchkindnessintheJew."
regroupedunderfourmajorheadings: taxation,informationasymmetriestogetherwithcon icts
of interest, competitive positioningand nallycorporate control. 14
Iftheinterestpaymentsare
tax-deductible while dividends are not, debt has an advantage over equity. Con icts between
shareholders and managers mayarise because managers,when owningonlya smallpercentage
of shares, may end up exerting a suboptimal level of e ort and investing the free cash ows
in perks and acquisitions of low value (Jensen and Meckling 1976, Jensen 1986). Con icts
between shareholders and debtholders arise because the payo of shareholders [debtholders] is
a convex [concave]function ofthe rm'spro t: the shareholderspreferriskierprojects (Jensen
and Meckling 1976). Information asymmetriesbetween managers and outside investors on the
pro tabilityof the rm is a thirddeterminant whose importancedecreases as the rm carries
more debt because the evaluation of the rm's debt is less sensitive to speci c informations
(Myers and Majluf 1984) and the expected bankruptcy costs increase faster for a rm with
lowpro tability(Ross 1977). A rm'scapital structure mayalso modifyits own behaviorand
the behavior of its competitorson productmarkets: managers take more risk or may be more
cooperativewhenthe rmcarriesdebtandthereforedebtcanbeusedasacrediblecommitment
toincreasethelevelofoutput(BranderandLewis1986)ortosethigherprices(Showalter1995).
Finally,the rm's capital structure may modifythe probability of a successful takeover by an
outsideinvestor. Inorder todeterminetheoptimalcombinationbetweendebtandequity, rms
mustconsidersimultaneouslythesedeterminants. Thesigni canceofeachdeterminantdepends
on thespeci cenvironmentof the rm.
Ouranalysisemphasizesthestrategice ectsofcapitalstructurethroughnotonlyamarginal
changeinproductquantityorpricebutalsoinfarreachingtechnologychanges 15
modifyingthe
organization and the market strategy of the rm. This determinant is likely to be even more
importantthantheotheronesinpartbecauseotherlesscostlymeansmaybeavailabletoachieve
the objectivesbehind theother determinants. For instance, con icts betweenstakeholderscan
be soften by more sophisticated managerial contracts and the likelihood of a hostile takeover
14
SeeforinstancetherecentcontributionsofHarrisandRaviv(1991),Hart(1995),RajanandZingales(1995),
LelandandToft(1996). 15
Fazzari, HubbardandPetersen (1988), KaplanandZingales (1997) andCleary (1999) amongothersstudy theimpactofcapitalstructureonthelevelofinvestmentin rmsbuttheydonotconsiderthedi erentspeci c
parameters, debt has a strategic value and increases a rm's expected pro t (see examples 1,
3 and 4 above) but in other contexts debt is a source of weakness for the rm and decreases
its expected pro t. Example 2 illustratesthis last point. In this example, debt can solve the
coordination problemdueto multipleequilibriumtechnological con gurations butmay leadto
the selectionof aPareto-dominated equilibrium.
AccordingtoBranderandLewis(1986),theoutputlevelincreaseswiththedebtlevelwhereas
inGlazer(1994),theoutputleveldecreasesinthe rstperiodandincreasesinthesecondperiod
as debt increases. In Showalter (1995), higherdebt induces lower prices,that is higher output
levels, when costs are uncertain, whilethe oppositee ect holdswhen demandis uncertain. In
our model, the link between debt levels and output levels is more subtle since debt not only
induceschangesinoutputandpricesgiventhetechnologiesbutalsochanges inthetechnologies
themselves. Inexample1 above, a switchfrom ( f;f) to ( i;i)increases outputifdemandis low
but decreasesoutputifdemandis high. Inexample2,the same switchdecreasesoutput inthe
twostates of demand.
It is nevertheless possibleto draw some general results. If the market sizeis high relative
to thecapacity ofthein exibletechnology,debtfavorsin exibleequilibriumtechnological
con- gurations resulting inless variabilityin industryoutput butmore variabilityin prices. If the
marketsizeissmallrelativetothecapacityofthein exibletechnology,oppositee ectsemerge.
In the intermediate case, both situations are possible depending on the industry parameters.
Therefore, thee ects characterized byBrander and Lewis(1986), Glazer (1994) and Showalter
(1995) depend closely on the assumption that a single technology is available. If rms are
al-lowed to choosebetween di erent exibilitylevels,technologicalor organizational, theimpacts
A Cournot equilibria, debt thresholds and expected pro ts
By assumption, the state of demandis observed before the second stage Cournot competition
takes place. For a state of the market , the Cournot reaction function of a exible rm h is
q h = 1 2 ( ( c)= q j ); j6=h. For x 2X 1 (equivalently 1
suÆciently high), that is x <( 1
c)=2 , both rms are always
better o producingthannotand weget:
{ ifboth rmsare exible, theproductionlevel ofeach rm is( k c)=3 and k (f;f;X 1 )=( k c) 2 =9 withD(f;f;X 1 )= 1 (f;f;X 1 )=( 1 c) 2 =9 ;
the expected pro tof each rmis given by(4) with
d E(f;f;X 1 )= 1 9 h ( 1 c) 2 +( 1 )( 2 c) 2 i (K+H)
{ ifone rmis exibleand theother is in exible,theproductionlevelof the exible
[in exible] rmis 1 2 (( k c)= x)[x]; we have k (f;i;X 1 )=( k c x) 2 =4 , k (i;f;X 1 )= 1 2 ( k c x)x withD(f;i;X 1 )= 1 (f;i;X 1 ),D(i;f;X 1 )= 1 (i;f;X 1 );
the expected pro tof the exible[in exible] rmis givenby(4) [(8)]with
d E(f;i;X 1 )= 1 4 h ( 1 c x) 2 +(1 )( 2 c x) 2 i (K+H), d E(i;f;X 1 )= 1 2 [ 1 +( 1 ) 2 c x]x K
{ ifboth rmsarein exible, theproductionlevelof each rmis x;we have
k (i;i;X 1 )=( k c 2 x)x withD(i;i;X 1 )= 1 (i;i;X 1 );
the expected pro tof each rmis given by(8) with
d E(i;i;X 1 )=[ 1 +(1 ) 2 c 2 x]x K Forx2X 2 ,thatis ( 1 c)=2 <x<( 1 c)= ,weget:
{ for (f;f) and(f;i), theequilibriaare thesame asinthecase x2X 1
above
{ for (i;i), if demand is low, one rm shuts down (D(i;i;X 2
) = 0) and the other enjoys a
monopoly position,thatis k (i;i;X 2 )=( k c x)x withD(i;i;X 2 )= 1 (i;i;X 2 );
d E(i;i;X 2 )= 1 2 ( 1 c x)x+(1 )( 2 c 2 x)x K. Forx2X 3 ,thatis ( 1 c)= <x, we get:
{ for (f;f),theequilibriumis thesame asinthecase wherex2X 1
{ for (f;i), the in exible rm shuts down when demand is low (D(i;f;X 3
) = 0) whereas
the exible rm enjoys a monopoly position, that is k (f;i;X 3 ) = ( k c) 2 =4 and D(f;i;X 3 )= 1 (f;i;X 3 );
the expected pro tof the rmsaregiven by(4)and (8) with
d E(f;i;X 3 )= 1 4 h ( 1 c) 2 +( 1 )( 2 c x) 2 i ( K+H) , d E(i;f;X 3 )= 1 2 (1 )( 2 c x)x K
{ for (i;i), both rmsshutdown whendemandis lowand D(i;i;X 3
)=0;
the expected pro tof each rmis given by(8) with
d E(i;i;X 3 )=( 1 )( 2 c 2 x)x K :
B Technological best response
Best reply to in exibility for x 2 X 2 fX 1
;X 3
g : in exibility is the best response to
in exibility
when A(i;i;X)<A(f;i;X) i :
d E (i;i;X) B d E(f;i;X) B; forA h <A(i;i;X) d E(i;i;X) d
E(f;i;X) B; forA(i;i;X) <A h
<A(f;i;X)
d
E(i;i;X) d
E(f;i;X); forA(f;i;X)<A h
when A(f;i;X) <A(i;i;X) i :
d E (i;i;X) B d E(f;i;X) B; forA h <A(f;i;X) d E (i;i;X) B d
E(f;i;X); forA(f;i;X)<A h
<A(i;i;X)
d
E(i;i;X) d
E(f;i;X); forA(i;i;X) <A h
2 when A(i;i;X 2 )<K <A(f;i;X 2 )i : d E (i;i;X 2 ) B > d E(f;i;X 2 ) B; forA h <A(i;i;X 2 ) d E(i;i;X 2 ) 1 2 B > d E(f;i;X 2 ) B; forA(i;i;X 2 )<A h <K d E(i;i;X 2 ) > d E(f;i;X 2 ) B; forK<A h <A(f;i;X 2 ) d E(i;i;X 2 ) > d E(f;i;X 2 ); forA(f;i;X 2 )<A h whenA(i;i;X 2 )<A(f;i;X 2 )<K i : d E (i;i;X 2 ) B > d E (f;i;X 2 ) B; for A h <A(i;i;X 2 ) d E (i;i;X 2 ) 1 2 B > d E (f;i;X 2 ) B; for A(i;i;X 2 )<A h <A(f;i;X 2 ) d E (i;i;X 2 ) 1 2 B > d E (f;i;X 2 ); for A(f;i;X 2 )<A h <K d E(i;i;X 2 ) > d E (f;i;X 2 ); for K<A h When A(f;i;X 2 )<A(i;i;X 2 )<K i : d E (i;i;X 2 ) B > d E (f;i;X 2 ) B; for A h <A(f;i;X 2 ) d E (i;i;X 2 ) B > d E (f;i;X 2 ); for A(f;i;X 2 )<A h <A(i;i;X 2 ) d E (i;i;X 2 ) 1 2 B > d E (f;i;X 2 ); for A(i;i;X 2 )<A h <K d E(i;i;X 2 ) > d E (f;i;X 2 ); for K<A h
Example 1: =0:5, 1 =5, 2 =10,x=2, =1,c=0:2, K=4, H=1and B =2. Pro t levels: 3:04A h E( f;f) = 1:62 > E( i;f) = 1:30 E( f;i) = 3:59 > E( i;i) = 2:60 2:44A h <3:04 E( f;f) = 1:62 > E( i;f) = 1:30 E( f;i) = 2:59 < E( i;i) = 2:60 2:4A h <2:44 E( f;f) = 0:62 < E( i;f) = 1:30 E( f;i) = 2:59 < E( i;i) = 2:60 1:2A h <2:4 E( f;f) = 0:62 < E( i;f) = 1:30 E( f;i) = 2:59 > E( i;i) = 1:60 A h <1:2 E( f;f) = 0:62 > E( i;f) = 0:30 E( f;i) = 2:59 > E( i;i) = 1:60 Example2: =0:5, 1 =5, 2 =10,x=2:5, =1, c=0:2,K =3,H =0:5 andB =6. Pro t levels: 3A h E( f;f) = 3:11 > E( i;f) = 3:00 E( f;i) = 3:82 < E( i;i) = 4:44 2:18A h <3 E( f;f) = 3:11 > E( i;f) = 3:00 E( f;i) = 3:82 > E( i;i) = 2:94 0:94A h <2:18 E( f;f) = 3:11 > E( i;f) = 3:00 E( f;i) = 0:82 < E( i;i) = 2:94 0:125A h <0:94 E( f;f) = 0:11 < E( i;f) = 3:00 E( f;i) = 0:82 < E( i;i) = 2:94 A h <0:125 E( f;f) = 0:11 > E( i;f) = 0:00 E( f;i) = 0:82 < E( i;i) = 2:94
1 2 Pro t levels: 4A h E( f;f) = 17:56 < E( i;f) = 18:05 E( f;i) = 17:47 < E( i;i) = 17:60 2:9A h <4 E( f;f) = 17:56 > E( i;f) = 17:45 E( f;i) = 17:47 > E( i;i) = 17:00 0:89A h <2:9 E( f;f) = 16:96 < E( i;f) = 17:45 E( f;i) = 17:47 > E( i;i) = 17:00 A h <0:89 E( f;f) = 16:96 < E( i;f) = 17:45 E( f;i) = 16:87 < E( i;i) = 17:00 Example 4: =0:5, 1 =5, 2 =10,x=4, =1,c=0:2, K=2:5, H =0:1 andB =3. Pro t levels: 2:5A h E(f;f) = 4:02 < E( i;f) = 4:10 E(f;i) = 1:69 < E( i;i) = 1:90 2:44A h <2:5 E(f;f) = 4:02 < E( i;f) = 4:10 E(f;i) = 1:69 > E( i;i) = 1:15 0:9A h <2:44 E(f;f) = 4:02 < E( i;f) = 4:10 E(f;i) = 0:19 < E( i;i) = 1:15 0:04A h <0:9 E(f;f) = 4:02 > E( i;f) = 2:60 E(f;i) = 0:82 < E( i;i) = 1:15 A h <0:04 E(f;f) = 2:51 < E( i;f) = 2:60 E(f;i) = 0:82 < E( i;i) = 1:15 Example5: =0:3, 1 =5, 2 =18,x=6, =1,c=0:2, K=4, H=0:75and B =3. Pro t levels: 4A h E( f;f) = 20:66 < E( i;f) = 20:78 E( f;i) = 21:35 > E( i;i) = 20:36 2:19A h <4 E( f;f) = 20:66 > E( i;f) = 19:88 E( f;i) = 21:35 > E( i;i) = 19:46 A h <2:19 E( f;f) = 19:76 < E( i;f) = 19:88 E( f;i) = 21:35 > E( i;i) = 19:46
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FIGURE 1
Equilibrium technological con gurations in example 1, x2X 1
;
in hatchedzone, (i;i);
in Y, either (f;f) or (i;i);
in V, (f;i) or (i;f);
in W, no equilibrium in pure strategies.
-6 0 0 A 1 A 2 5:00 3:04 2:44 2:40 1:20 1:20 2:40 2:44 3:04 5:00 (f;f) (i;f) (f;f) W (f;i) V W (f;i) (f;f) (i;f) (f;f) # # # # Y
Figure 2
Equilibrium technological con gurations in example 2, x2X 2
;
in Y, either (f;f) or (i;i);
in Z, (f;f). -6 A 2 3:50 3:00 2:18 0:94 :125 (i;i) (i;f) (i;i) Y Y Y (f;f) Y (f;i) (i;i) 0 :125 0:94 2:18 3:00 3:50 A 1 Y Y Y Y Y Z Z
FIGURE 3
Equilibrium technological con gurations in example 3, x2X 3 ; in V, (f;i) or (i;f). -6 A 2 A 1 4:50 4:00 2:90 0:89 0 0:89 2:90 4:00 4:50 (i;i) (f;i) (i;i) (i;f) (f;f) (i;f) V (i;i) (f;i) (i;i)
Equilibrium technological con gurations in example 4, x2X 2 ; in Y, (f;f) or (i;i); in S, (f;i); in T, (i;f); in V, (f;i) or (i;f);
in W, no equilibrium in pure strategies.
-6 A 2 3:50 2:51 2:44 0:04 0 0:04 0:90 2:44 2:51 3:50 A 1 (i;i) (i;i) (f;i) T W (i;f) (i;f) 0:90 (i;i) (f;i) (i;i) Y W S V
Equilibrium technological con gurations in example 5, x2X 3 ; in V, (f;i) or (i;f). -6 A 2 4:75 2:20 0 2:20 4:00 4:75 A 1 V (f;i) V (i;f) (f;f) (i;f) V (f;i) V
