Corporate taxes with unobservable profits

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Cuadernos de economía

ARTICLE

Corporate taxes with unobservable profits ^夽

Manel Antelo

DepartmentofEconomics,FacultyofEconomicsandBusinessAdministration,UniversityofSantiagodeCompostela, CampusNorte,s/n,15782SantiagodeCompostela,Spain

Received4November2015;accepted13May2016 Availableonline22June2016

JEL

CLASSIFICATION H21;

D82

KEYWORDS Corporatetaxes;

Signalling;

Revenue-raising government;

Separating equilibrium;

Poolingequilibrium;

Welfare

Abstract Usingatwo-periodtax-signallingmodel,astudyisperformedonthebehaviourofa revenue-raisinggovernmentinsettingprofit-basedcorporatetaxesforacompanywithprivate informationonitspotentialprofitability.Inaseparatingequilibriuminwhichboththehigh-and low-profitcompanyproduceapositiveamountinperiod1(separatingequilibriumS2),thetax setforthatperiodislowerthanthatofthesymmetricinformation,resultingininformational renttothehigh-profitcompanyinthatperiod,butnotinperiod2.Asresult,taxesincreasewith time.Inaseparatingequilibriuminwhichonlythehigh-profitcompanyproduces(separating equilibriumS1orshut-downequilibrium),noinformationalrentgoestothehigh-profitcompany ineitherperiod,butatthecostthatthelow-profitfirmexitsthemarket.Finally,inapooling equilibrium,taxesaretime-invariantandchargedinsuchaway thatperiod-1informational renttothehigh-profitcompanyislowerthaninS2,butpersistsinperiod2.Consequently,the governmentcanmaximizetaxrevenuebynotforcinginformationdisclosure.Theimpactof governmentbehaviouronwelfareisalsoexamined.

© 2016 Asociaci´onCuadernos de Econom´ıa. Publishedby Elsevier Espa˜na, S.L.U. All rights reserved.

CÓDIGOSJEL H21;

D82

PALABRASCLAVE Impuestos

corporativos;

Se˜nalización;

Impuestodesociedadescuandolosbeneficiosnosonobservables

Resumen Esteartículoexamina,atravésdeunmodelodese˜nalizacióndedosperíodos,el comportamientodeungobiernorecaudatorioalahoradefijarelimpuestodesociedadesauna empresaconinformaciónprivadasobresupotencialderentabilidad.Enunequilibrioseparador enelquetantolaempresamuyrentablecomolapocorentableproducenunacantidadpositiva enelperiodo1(equilibrioseparadorS2),elimpuestofijadoparadichoperíodoesinferioralde informaciónsimétrica,loqueresultaenrentasinformacionalesalaempresarentable,aunque

夽 Theauthor thanksLluís Bru and MikelPérez-Nievas for theirinputand feedback that resultedin substantial improvementto the manuscript.Anyremainingerroristheauthor’sresponsibility. MyacknowledgementisalsototheXuntadeGaliciafor fundingthrough projectGPC2013-045.

E-mailaddress:[email protected] http://dx.doi.org/10.1016/j.cesjef.2016.05.002

0210-0266/©2016Asociaci´onCuadernosdeEconom´ıa.PublishedbyElsevierEspa˜na,S.L.U.Allrightsreserved.

Gobiernoque maximizala recaudación;

Equilibrioseparador;

Equilibrioagrupador;

Bienestar

estasrentasdesaparecenenelperiodo2.Comoresultado,elimpuestocrececoneltiempo.En unequilibrioseparadorenelquesololaempresarentableproduce(equilibrioseparadorS1),el gobiernoahorracualquierrentainformacionalaestaempresaenambosperiodos,peroacosta dequelaempresapocorentablesalgadelmercado.Porúltimo,enunequilibrioagrupador,el impuestoesinvarianteeneltiempoyfijadodeformaquelarentainformacionaldelaempresa rentableenelperíodo1esmenorqueenS2,peropersisteenelperiodo2.Enconsecuencia, elgobiernopuedemaximizarlosingresosfiscalesnoforzandoladivulgacióndeinformación.

Tambiénseexaminaelimpactoquelacitadaconductadelgobiernotieneenelbienestar.

© 2016Asociaci´onCuadernos deEconom´ıa. Publicado porElsevier Espa˜na,S.L.U. Todoslos derechosreservados.

1. Introduction

Inmosteconomies,taxrevenuesprovideasubstantialpor- tionoffundsaimedatfinancingpublicservicesorenabling governments to redistribute resources. Firms contribute to tax revenues through input, output and profit taxes.

In fact, the directtaxation of businesses is a widespread practiceworldwide.Sincefirmsarelegalentitiesseparate fromtheir owners,thejustification for thiscorporatetax remains rather unclear, as the government could just as easilydirectlytaxownersbymeansofanincometax.The literatureonpublicfinancedescribesthreepotentialjusti- ficationsfortaxingcorporategains.First,acorporatetaxas atax onpure profitscauses lessdistortion. Second, since corporate status provides protection in bankruptcy situa- tionsitseemsreasonabletopayforthisprivilegethatisnot availabletoindividuals.Finally,myopicownerswhodonot perceivethemselvesaspayingthecorporatetaxwillmore readilyacceptthistaxthananincometax;therefore,ifthe governmentwants tomaximizevotes,itwilltendtoseta corporatetax(BachettaandCaminal,1991).

Thefactremainsthatgovernmentstaxbusinesses.Taken together,personalandcorporateincometaxesarethemost importantsourcesofrevenuesforpublicspendinginalmost half ofallOECDcountries(OECD, 2012),andeventhough personalincometaxestypicallyrepresentthelargest por- tion of total tax revenues, corporate taxes are also an importantsource.AccordingtoOECDdata,in2010thecor- porateshare oftax revenueswasaround10%onaverage, althoughwithwidevariationsacrosscountries,fromalow of 3%in Icelandand Hungary toahigh of 24% in Norway, withrates forGermany,France,theUK,theUSAandAus- traliaappliedat4.2%,6%,8.8%,10.8%and19%,respectively.

(SeealsoDevereuxetal.[2002]andDevereux[2012],among others.)

Apart from other factors, a government’s ability to obtainmoreorlesscorporatetaxrevenuesreliesonfirms’

behaviour regarding correct reporting of earnings. In a context of perfect information, the government is obvi- ouslyinthebestpositiontooptimallycalibratecorporate taxes according to a firm’s profits. However, it is more logical to assume that the government has----at least in some periods----less information on the firm’s profits or entrepreneurialabilitythanfirmsthemselves, and,conse- quently,on tax-paying capacity. Therefore,a government

dilemmais determiningwhetherinformationdisclosureby firmsispreferabletonon-disclosure.

AsKlingerandMcFate(2013)arguecorporatetaxdisclo- surehasgrownincreasinglyopaque.Adecadeago,theSEC imposeduniformdisclosurestandardsforexecutivecompen- sation.Asresult,allpubliccompaniesreportthesameCEO paydatainacommonformat,makingcomparisonsofone firmtoanotherbotheasyandstraightforward.Incontrast, corporate tax disclosure has no uniformity. Corporations presentrudimentaryinformationonthetaxestheyexpect topayinagivenyear,butmanyarequicktocomplainthat thesearenotthe‘‘real numbers’’when theyarecitedin themedia.Corporationsshoulddisclosehowmuchtheypay inincometaxesandtowhomthosetaxesarepaid.

Putdifferently,improvedtaxdisclosurewouldhelppol- icymakersandtaxcollectorstoseewhichcorporationsare reporting billions of dollars of profits in small tax haven countrieswheretheyhavenosales,employees,orphysical assets.Themagnitudeofoffshoretaxabusewouldbeplain toseeandcreatethepoliticalwilltoaddresstheproblem (KlingerandMcFate,2013,p.18).

This paper develops a simple model of asymmetric informationwithadverseselectionthatconsidersarevenue- raising government and a single firm that can be either high-profitorlow-profit.Thegovernmentwantstosetatax onprofitsintwoperiodsinsuchawayastomaximizeitsrev- enue.Thefirmhasprivateinformationconcerningitsprofit potential(highor low),whereasthe governmentcanonly makeapriorprobabilityassessment.Atwo-periodmodelis developedin which the firm’speriod-1 outputmay trans- mit(ornot)informationtothegovernmentconcerningfirm profitability.

Entrepreneurial ability is an unobservable input that cannotbedirectly taxed(Moresi,1998).Output,however, ispubliclyobservableandenablesthegovernmenttoinfer (or not)the firm’s profits. In thiscontext, the high-profit firmwouldliketohideitsprivateinformationandconvince the government that it is a low-profit firm and so pay lower taxes. For reported output to be a credible signal oflow profittheremust bea costassociatedwithoutput under-reporting. The model developed below addresses thefollowingissues:Howshouldthegovernmenttaxfirms to maximize tax revenues? Does the government prefer toinduce thetaxed firm todisclose itsinformation? How does optimal taxation affect social welfare? Under what

conditions is government’s behaviour socially optimal?

Real-life taxation situations seem quite similar to the simpleframeworkdescribedhere.

Themain contributionofthispaperistoshowthatthe governmentfacesatrade-offwhensettingcorporatetaxes under asymmetric information. On one hand, by observ- ing the firm’s output in period 1 (in a perfect Bayesian separating equilibrium), it can elicit information on the firm’stax-paying potential.¹ Inthiscase, itneedstooffer anincentivetothe taxedfirmtofully discloseitsprivate information, resultingin thehigh-profit firm obtaining an informationalrentinperiod1.Ontheotherhand,thegov- ernmentneednotgrantanyinformationalrentinperiod2 becausecomplete information is restoredfor this period.

Thehigh-profit firmwillwanttoreducethe informational contentofitsoutputreporttoincreasetheprobabilitythat itisperceivedasalow-profitfirm.Conversely,alow-profit firmwillwanttoenhancetheinformationalcontentof its outputreporttoensurethatthepayabletaxcoincidesmore closely with the tax corresponding to complete informa- tion.Derivedthusistheseparatingequilibrium(S2)forthe two-periodtax-signallinggameinwhichbothfirmtypesare producing, with the result that the low-profit firm must distortitsperiod-1outputbelowthecomplete-information profit-maximizingleveltoconvincethegovernmentthatit isgenuinelylow-profit.Theoptimalperiod-1taxforthegov- ernmentisconsequentlylowerinthepresencethaninthe absenceofsignalling,andsuchtaxistime-increasing.

Alternativelythegovernmentcanopttoelicitthefirm’s informationbyobservingitsperiod-1outputand,further,by preventingthehigh-profitfirmfromobtaininginformational rentin either period. This is separatingequilibrium S1or shut-downequilibrium,inwhichthecosttothegovernment ofnotgrantinginformationalrenttothehigh-profitfirmis thatthelow-profitfirmdoesnotproduceatall.

Yetanotheralternativeisforthegovernmenttorefuseto updateitsfirm-typeinformationandallowbothfirmtypes toproduce.Thisisapoolingequilibrium,inwhichbothfirm typesproduce thesame output in period1.The informa- tionalrent that the government grants to the high-profit firminthisperiodislowerthaninS2,butunlikeinS2,this rentpersistsinperiod2.

In S2 equilibrium of the game, the government sets period-1 tax for the high-profit firm in such a way that informational rent is sufficiently large for this firm not tomisrepresentitself.This rentis, however,restricted to period1,thatis,informationalrentnolongerholdsinperiod 2.InS1equilibrium,thegovernmentalsoidentifiesthefirm typebutprovides noinformationalrenttothe high-profit firm,althoughatthecostofthelow-profitfirmexitingthe market.Inpooling equilibrium,the governmentgivesless informationalrentinperiod1tothehigh-profitfirmthanin S2,but,unlikeinS2,thisrentpersistsinperiod2.

Ingeneral,thegovernmentprefersfirmstodisclosetheir ability tomake (more or less) profits, becausedisclosure

1Anequilibriumissaidtobeperfectlyinformativeifitcommu- nicatesthefirm’stypewithprobability1onthe(period-1)output reportdate.Contrariwise,anuninformativeequilibriumisdefined asan equilibriumin which thegovernmentcannot usereported (period-1)outputtoupdateitspriorassessmentofthefirm’stype.

results in higher tax revenue than non-disclosure. In par- ticular, if the ratio of high-profit firms is small enough, thepoolingequilibriumoutcomeisthebestoption forthe government, even though the high-profit firm obtains an informationalrentinbothperiods(higherinperiod2thanin period1).Iftheratioofhigh-profitfirmsismoderate,given thelevel ofefficiencyoflow-profitfirms,thegovernment preferstoimposeS2,withtheresultthatinformationalrent tothehigh-profitfirmishigherthaninpoolingequilibrium, butisonlygrantedinperiod1.Finally,iftheratioofhigh- profitfirmsishighenough,informationalrenttothehigh- profitfirmwouldbesolarge(bothinpoolingequilibriumand S2)thatthegovernmentwouldprefertoimposeseparation byensuringthatonlythehigh-profitfirmproducesandthat itobtainsnoinformationalrentineitherperiod.

Theintuitionbehindthisresultisasfollows.Inasymmet- ricinformationcontext,this(lump-sum)taxdoesnotdistort thefirm’sbehaviour(AtkinsonandStiglitz,1980).However, inanasymmetricinformationcontextevenalump-sumtax as corporation tax can be distorting. And the aim of the governmentwishingtomaximizerevenuesistoreducedis- tortionasmuchaspossible.Thus,whenthereisasmallratio of high-profitfirms,thegovernmentprefersnottodistort theperiod-1outputofthelow-profitfirmbuttodistortthat ofthehigh-profitfirm,because,inthisway,itreducesthe informationalrentgrantedtothelatter. Infact,theratio ofhigh-profitfirmsis sosmallastoresultinasmallinfor- mationalrentinexpectedterms.However,whenthereisa moderateratioofhigh-profitfirms,thegovernmentprefers disclosuretoholdevenifthisresultsinsomedistortionfor thelow-profitfirminperiod1.Consequently,period-1infor- mationalrentforthehigh-profitfirmisincreasedrelativeto thepoolingequilibriumsituationand,inreturn,neitherfirm obtainsinformationalrentinperiod2.Finally,whenthereis averyhighratioofhigh-profitfirms,theoptimalbehaviour for the governmentis toassume that thefirm has a high tax-payingpotential.Inthiscase,itrenouncesrevenuesif thefirmis,infact,low-profit(aratherunlikelyscenario), but instead fullyeliminates theinformational rent tothe high-profitfirm.

From a social standpoint, the incentives of a govern- mentthatsetscorporatetaxestomaximizetaxrevenueare notgenerallyalignedwithsocialincentives.Inducingdisclo- suregenerallymaximizessocialwelfare:aggregatewelfare is only maximized when the government opts for pooling equilibriumandinasmallregionwhereS2holds.Otherwise government incentives are not aligned with social incen- tives. From a social perspective, for example, when the governmentimposesS2,poolingequilibriumissociallyopti- mal, and when thegovernment imposesS1, S2is socially optimal.

For an environment in which entrepreneurs chose between risky projects(higher potential profits) and safe projects(lowerpotentialprofits),BeckerandFuest(2007) examined the relationship between limited liability and corporate taxation, showing that a corporate tax on all entrepreneurs with limited liability is optimal when entrepreneurs can offsetpotential lossesin asituation of asymmetricinformationconcerningprojectqualities.Fora similarcontext,Miglo(2007)confirmedthatentrepreneurs’

abilitytooffsetlossesandthepresenceofasymmetricinfor- mationmayaffecttaxpolicy,althoughtheoptimaltaxation

policy differed from that suggested by Becker and Fuest (2007).

The remainderof the paperis organizedinto fivesec- tions. Section 2outlines the model. Section3 derives, as a benchmark, taxation on profits under symmetric infor- mation. Section 4 analyses the optimal taxation strategy underasymmetricinformationanddiscussesthecorrespond- ingdistortionsingovernmentandfirmbehaviours.Section5 examinesthewelfareimplicationsofgovernmentbehaviour.

Finally,Section6concludesthepaper.

2. The model

Aneconomywitharevenue-raisinggovernmentthatcharges corporatetaxtoafirmovertwoperiodsisconsidered.Firm activityis restrictedtothissinglecountry,² andcorporate tax amountsto 100% of capital gains. Assumptions areas describedasfollows.

Assumption1. Thetaxedfirmfaceslinearmarketdemand pt(qt)=1−qt in each period t, t=1, 2, for qt<1 and pt(qt)=0forqt≥1,whereptdenotesunitpriceinperiod twhenqtunitsofthegoodaresold.(1denotesthemarket parameter.)

Asymmetricinformationischaracterizedbythefollowing assumption:

Assumption2. Thedistributionforthefirm’sprofitiscom- monknowledge,butonlythefirmknowsitspotentialprofit.

Thatis, the firm privately knowswhether itspotential profitability is high or low (i.e., whether its potential to paytaxesishighorlow)because,betterthanthegovern- ment,itknowsthedemandlevelanditsownefficiencylevel.

Twopossible profitabilityvaluesderivefromthefollowing assumption:

Assumption 3. The intercept term for the demand describedinAssumption1,netofcosts,cantakeoneoftwo values,1and1−c,with0<c<1,dependingonwhether thefirm’smarginalproductioncostiseither low(equalto zero)orhigh(c>0).

Thehigh-profitfirmandlow-profitfirmarelabelledHand L,respectively.Profitlevelsovertwoperiodsarethesame.

Assumption4. Thepriorprobabilityassessmentofahigh- profitfirmis,0<<1.

Theonlyinformationavailabletothegovernmentatthe beginningofthegameistheprobabilityofafirmbeinghigh profit or low profit. However,the firm’s potential topay taxes maybe then inferredby the government(in a per- fect Bayesian separating equilibrium)or not (in aperfect Bayesian pooling equilibrium) after observing the output producedbythefirminperiod1.

2Ifthefirmproducedinthecountryaswellasinothercountries, wewouldneedtoweightreportedprofitsbythecountrysalesto totalsalestoapproximatetheprofitgeneratedinthecountry.

Finally,thediscountfactorbetweenperiodsisassumed tobe1,allplayersareassumedtoberisk-neutral³andthe governmentis assumed to seek to maximizetax revenue throughoutbothperiodsofthetaxgame.

3. Symmetric information

Inasymmetricinformationscenario,allplayersareassumed toknowthefirm’spotentialtopaytaxes,inwhichcasethe taxgameproceedsasfollows.

Period 1. At the beginning of period1, Naturechooses thefirm’sabilitytomakeprofitsandthisabilityispublicly observable.Forthisperiod,thefirmpays(lump-sum)corpo- ratetaxT1^∗k4asafunctionoftypek,k∈{H,L}andproduces outputlevelq1^∗k.

Period 2. Corporate tax and output in period 2 arethe sameasforperiod1,namelyT2^∗k=T1^∗kandq2^∗k=q^∗1k.

Inthiscontext,thefollowingresultisachieved.

Lemma1. Underincompletebutsymmetricinformation, ineachperiodt,t=1,2,thegovernmentsetscorporatetax T_tH^∗ =1/4forthehigh-profitfirmandT_tL^∗ =(1−c)²/4forthe low-profitfirm.

In expected terms, the tax paid by the firm in each periodt amounts to T_t^∗=[1−(1−)(2−c)c]/4, t=1, 2, anddecreasesastheprobabilityofthefirmbeinghigh-profit typeincreasesand/or asthedisparity betweenprofitsfor bothtypesoffirmincreases.Thefirm’sequilibriumoutput ineach periodamounts to1/2 whenthe firm is Hand to (1−c)/2 ifitisL.Governmentalrevenuesover bothperi- ods are 1/2 for the firm if it is H, and (1−c)²/2 if it is L.The government’s expectedrevenue over both periods thusamountstoR^∗=2T_t^∗,i.e.,thegovernmentobtainsthe firm’swholeper-periodprofit.Needlesstosay,thepresence of(lump-sum)taxesdoesnotinanywaydistortthefirm’s behaviourundersymmetricinformation.However,thissit- uationnolongerholdswheninformationisasymmetric.In thiscase, taxeswilldistortfirm behaviour, despite ofthe factthatsuchtaxesarelump-sum.

4. Asymmetric information

Wenowreturntotheoriginalcontext,whereinformationis asymmetric.Afirmthatisbetterinformedthanthegovern- mentconcerningitstax-payingpotentialwilltrytobenefit fromthisadvantagebyrepresentingitselfasafirmwithlow tax-payingpotential. This incentivederives fromthe fact that the corporate tax set by the government for period 2----when it believes the firm is low-profit----is lower than thetax setwhenthegovernmentbelieves thatthefirmis high-profit.InaseparatingBayesianequilibrium----wherethe governmentinferstypefromobservingperiod-1output----the governmentwill try tomitigate opportunism by setting a

3Riskneutralityisastandardassumptionformodelsofthistype.

4Asteriskdenotessymmetricinformation.

period-1taxforthatinducesthefirmtodisclosethekindof privateinformationthatwouldenablebettercalibrationof period-2tax.Conversely, inapoolingBayesianequilibrium thegovernmentwouldbeunabletoupdateitspriorproba- bilityassessmentconcerningfirmtypefromperiod-1output;

hence,taxinperiod2wouldbethesameasinperiod1.

4.1. PerfectBayesianseparatingequilibrium Thetaxgamewhenseparatingequilibriumholdsunfoldsas follows.

Period1. At thebeginning of period1, the government announcesandcommitstoperiod-1corporatetaxT1^S(super- scriptS denotesseparation)for thefirm,givensomeprior probabilityassessmentthat thefirm is high-profit. Atthis stage,thefirmknowsitstax-payingpotential,whereasthe governmentonlyhas impreciseinformation. However,the distribution of firm type is common knowledge. The firm chooses,inperiod1,anoutputlevelaccordingtoitstype andtheimpactofitsoutputonupdatedbeliefs.Giventhe priorprobabilityassessmentthatthefirmishigh-profitand thattaxisT1^S,thefirmchoosesperiod1outputtomaximize profit.At theend ofthisperiod,thegovernmentobserves period-1outputandusesthisinformationtoupdateitsprob- abilityassessmentregardingthefirm’stax-payingpotential.

Period 2. At the beginning of period 2 (when complete informationhas been restored), given its updated proba- bilityassessment,thegovernmentannouncesandcommits toperiod-2corporatetaxT2^∗k,thistimedifferentfor each firmtypeandequaltothatsetinconditionsofsymmetric information.Giventhistax andthegovernment’supdated probabilityassessment,thefirmchoosesperiod-2outputto maximizeprofits,andthegameends.

Soughtasasolutionforthistaxgameistheseparating pure-strategy perfectBayesian-Nash equilibrium.Compar- ing the period-2 net profits of each firm type in the equilibriumandoff-equilibriumpaths,thefirmisfound to beinterestedinbeingperceived aslow-profitbythe gov- ernment.

Inperiod1thegovernmentcannotdistinguishonefirm typefromanother,sothetaxchargedinthisperiodmustbe thesameforboth.However,separatingequilibriumimplies that the output for each firm type in this periodwill be different.Thus,thegovernmentwillupdateitspriorprob- ability assessment after it observes period-1 output and detectsthetruefirmtype.Inthesecircumstances,thebest the high-profit firm can do in period 1 is toproduce the outputlevelofamyopicprofit-maximizingmonopolist,i.e., q1^mH= 1

2 (1)

(the m superscript stands for myopic monopolistic behaviour), who makes the corresponding gross profits

^m1H=1/4. Togetherwithperiod-1output levelq1^SL forthe low-profitfirm,theperiod-1outputgiveninEq.(1)forms part of the separating equilibrium if the corresponding

incentive-compatibility conditionsaresatisfied.In sum,in period1thegovernmentsolvesthefollowingproblem:

max T1

s.t.

⎧⎪

⎨

⎪⎩

(1−c−q^S1L)q1^SL+^m2L−T2^∗L≥^m1L+2^mL−T2^∗H

(1−q^S1L)q1^SL+^m2H−T2^∗L≤1^mH+^m2H−T2^∗H

T1≤min{1H(q1^SH),1L(q1^mL)}

(2)

where,byvirtueofLemma1,T2^∗L=2^mLandT2^∗H=2^mH.The firstrestrictioninEq.(2)isaself-selectionconstraint,which states thata low-profitfirm, inperiod1, wouldpreferto produceoutputq^S1L(alevelthatmaydifferfromtheprofit- maximizingamount)andtobeperceivedbythegovernment asalow-profitfirmratherthanasahigh-profitfirmbypro- ducinganamountotherthanq1^SL.Thesecondrestrictionin Eq.(2)istheincentive-compatibilityconstraintforahigh- profitfirm,whichstatesthat,inperiod1,ahigh-profitfirm wouldprefertoproduceq^m_1Handtobeperceivedbythegov- ernmentasahigh-profitfirmratherthanasalow-profitfirm andbeforcedtoproduceq1^SL.Finally,thethirdrestrictionin Eq.(2)summarizestheparticipationconditionofbothfirm types.

In the abovementioned separating equilibrium, both types of firm produce in period 1 (and also in period 2).

Forthisreason,wecallthissituationS2.However,another wayforthegovernmenttoinducedisclosureistosetatax inperiod1(andalsoinperiod2)thatisonlyacceptableto thehigh-profitfirm.Inthiscase,theperiod-1outputforthe low-profitfirmwillbezero,q^S1L=0.Oncethegovernment observesapositiveperiod-1output,itinfersthatthefirmis ofhigh-profittype.WecallthissituationS1.

Thesolutionforproblem(2)andthepossibilityofiden- tifying firm typeby forcing thelow-profit firm out of the marketisasfollows,wherethesuperscript2(resp.,1)indi- catesthatbothfirmtypes(resp.,onlythehigh-profitfirm) produceapositiveoutput.

Proposition1.

(i) (Separating equilibriumS2)Intheleast-costseparat- ing equilibrium in which both types of firm produce, thegovernmentcharges,inperiod1,thecorporatetax T1^S2={1−c[4−c−2

c(2−c)]}/4tobothfirmtypes.

Thefirmthusproducesq^S21H=1/2ifitishigh-profitand q^S21L=[1−

c(2−c)]/2ifitis low-profit.Thegovern- ment’sposteriorbeliefsare(q^S21H)=1and(q^S21L)=0.

Hence, in period2, both taxesand outputs areas in Lemma1.

(ii) (SeparatingequilibriumS1)Intheseparatingequilib- riuminwhichonlythehigh-profitfirmproducesoutput, the government charges, in period 1, the corporate tax T1^S1=1/4. The firm thus produces q^S11L=q2L=1/2 if itis high-profit (andq1^S1L=0if itis low-profit).The government’supdatedbeliefsare(q1=1/2)=and

(q1 /=1/2)=1. Hence, in period 2, q^S12H=1/2 and q^S1_2L=0.

Proof. SeeAppendix.

Separationoftypeswhenbothproduceiscostlybecause the high-profit firm finds it optimal toapply a low-profit

firm’sreportingpolicyunderasymmetricinformation.Thus, to prevent the high-profit firm from projecting itself as a low-profit firm, in period 1 the low-profit firm needs to produce an output below the symmetric-information profit-maximizinglevel.Thisreducesitsgrossprofits⁵and, consequently,the corporatetaxacceptable toboth firm’s types decreases relative to the situation where no high- profit firm exists. In fact, when comparing taxes in both informationcontexts,itfollowsthatT1^S2<T1^∗,i.e.,thegov- ernment reduces period-1 corporate tax as regards that expectedly imposed in a symmetric information context.

Thisperiod-1taxreductionamountsto:

T1^S2−T1^∗=−c[2−2

c(2−c)+(2−c)]

4 . (3)

Thepresenceofalow-profitfirmbenefitsthehigh-profit firmbecausethelatterobtainsnetprofitsasfollows:

^S21H−T1^S2= c[4−c−2

c(2−c)]

4 (4)

Thisrepresentsitsinformationalrentinperiod1(infor- mationalrentatthetop).Thelow-profitfirm,ontheother hand,obtainsnoinformationalrent,i.e.,^S21L−T1^S2=0(no informationalrentatthebottom).Insum,thegovernment facesa trade-off.Forthelow-profitfirmtoacceptpaying the proposedperiod-1tax, the governmentneeds topro- videaninformationalrenttothehigh-profitfirminperiod 1;in contrast,the governmentappropriatesallprofitsfor period 2, irrespectiveof firm type.In separating equilib- rium,insum, time-increasing taxationwouldbeobserved asinformationevolvedfromasymmetrictosymmetric.

Alsocostlyisthesituationinwhichthegovernmentsets corporatetaxasT1^S1=1/4inperiod1andidentifiesthehigh- profitfirmasacceptingthistaxandconsequentlyproducing.

Infact,thegovernmentdoesnothavetograntinformational renttothehigh-profitfirmineitherperiod1or2,butatthe costofthelow-profitfirmnotproducingineitherperiod.

Dependingonthegovernment’spriorprobabilityassess- ment concerningfirm type,will choosethe corporatetax thatmaximizes taxrevenue. This is formallydescribed as follows.

Proposition 2. Given the value of parameter c, let us define 2=2[1−3c+c²+c

c(2−c)]/(2−2c+c²), where0<2<1forallc.Then:

(i) If ∈ (0,2), thegovernmentprefers toidentify the typeofthefirmbymakingbothproducedifferentout- putsinperiod1(S2).

(ii) If ∈ (2,1), thegovernmentprefers toidentify the type of the firm by making both produce different outputsinperiod1and,particularly,byforcingthelow- profittypedroppingoutofthemarket(S1).

5Thatis,inspiteofthetaxbeinglump-sum,thefactthatthey arechargedinacontextofasymmetricinformation----asopposed tosymmetricinformation----leadstoaproductivedistortionforthe low-profitfirminperiod1,withareductioninoutputamountingto q^S21L−q1^∗L=[c−2

c(2−c)]/2.

1.0

0.8

0.6 Separating equilibrium S1

Separating equilibrium S2 0.4

Production cost difference, c

0.2

0.0

0.0 0.2 0.4

Probability of a good realization of costs, µ

0.6 0.8 1.0

Figure 1 The preference ofa revenue-raising government regardingseparatingequilibria.

The result of Proposition2 is very intuitive.Given the valueofparameterc,whentheprobabilityofthefirmbeing high-profitissufficientlylow,thegovernmentoptstomain- tainbothtypesoffirmproducing.Otherwise,itprefersnot tograntinformationalrenttothehigh-profitfirm,butatthe costofforcingthelow-profitfirmtoexitthemarket.This resultisillustratedinFig.1.

4.2. PerfectBayesianpoolingequilibrium

Whenbothtypesoffirmproducethesameoutputinperiod 1,thetax-signallinggameproceedsasfollows.

Period1. AfterNaturehaschosenthefirm’stype,thegov- ernmentsetsthesamecorporatetaxT1^P (thePsuperscript denotespooling)forbothtypes.Inperiod1,bothfirmtypes producethesameoutputlevel,q1H=q1L=q^P1,fromwhich noadditionalinformation concerningtax-paying potential canbeinferred.

Period2. Thegovernmentcontinuestouseasitsprob- ability assessment that the firm is high-profit. Thus, the governmentcontinuestoannounceandcommittothesame corporatetaxforbothfirmtypes,whichequalsthetaxpre- viouslyappliedinperiod1,namely,T2^P=T1^P.

Onlyonecorporatetaxlevelcanformpartofthepooling equilibriuminperiod1,namely,T1^P=(1−c)²/4,chargedin period1(andalsoinperiod2).Bothfirmtypesacceptthe taxandproduceq1^P=(1−c)/2inperiod1.Thisequilibrium is supported by the government’s beliefs (q1=q1^P)= and(q1 /=q1^P)=1,inwhichcaseT2^P=1/4.Thisisformally describedasfollows.

Proposition3. Inthepoolingequilibrium,thegovernment charges corporate tax T_t^P=(1−c)²/4 to both firm types ineachperiodt.Bothfirmtypesproduceq^P1L=q1^PH=q1^P= (1−c)/2inperiod1.Thegovernment’supdatedbeliefsare

(q1^P)=and(q1 /=q^P1)=1.Hence,inperiod2thefirm’s

outputisq^P2H=1/2ifitishigh-profitandq^P2L=(1−c)/2if itislow-profit.

However,thedisadvantageofthisequilibriumtothegov- ernmentis thatthe high-profit firm obtains informational rentineachperiod,amountingtoc(1−c)/2inperiod1and c(2−c)/4inperiod2.⁶

4.3. Toinduceornottoinduceinformation disclosure?

Regarding period 2, the government always prefers the taxedfirmtodiscloseinformationbecausethegovernment’s revenueissuchthatT2^S2=T2^∗>T2^P.This isduetothefact thatnoinformationalrent inthisperiodis grantedtothe high-profitfirm----ashappenswhenasymmetricinformation prevailsin the poolingequilibrium. Incontrast, whenthe firm is induced to disclose rather than withholdinforma- tion,period-1taxislower,i.e.,T1^S2<T1^P<T1^S1.Takingboth periodsintoaccount,theresultofProposition4holds.

Proposition 4. For a givenvalue of parameter c,letus define 1=2[1−

c(2−c)]/(2−c), and 2=2[1−3c+ c²+c

c(2−c)]/(2−2c+c²),where0<1<1,0<2<

1,and1<2forallc.Thegovernment’sbehaviourunder asymmetricinformationdependingonitsprior probability assessmentisasfollows:

(i) If ∈ (0,1),thecorporatetaxT1^P ischargedtoboth types of firmsin period 1 (andalso in period 2)and theprivateinformationisnotdisclosed.Thehigh-profit firmthusobtainsaninformationalrentinbothperiods.

(ii) If ∈ (1,2),thecorporatetaxT1^S2ischargedtoboth typesof firmin period1andinduces thefirm todis- closeitsinformation.Thehigh-profitfirmthusobtains aninformationalrentinperiod1,butnotinperiod2.

(iii) If ∈ (2,1),thecorporatetaxT1^S1ischargedtoboth typesoffirmsinperiod1(andalsoinperiod2).Infor- mationisdisclosedbecausethelow-profitfirmdoesnot produce.Thehigh-profitfirmdoesnotobtaininforma- tionalrentineitherperiod1orinperiod2.

Proof. SeeAppendix.

Proposition 4 (i)states that, giventhe earnings of the low-profit firm, if there is a small enough ratio of high- profitfirmsthegovernmentpreferstorenounceidentifying firmtypebecauseseparationwouldimplygrantingtoomuch informationalrenttothehigh-profitfirm.Instead,thegov- ernment reduces corporate tax in each period compared

6Theperiod-1informationalrent wouldbeeven greaterinthe caseofanaïvegovernmentunabletoobservetheperiod-1output ofthefirm(orthemarketpriceofthegood).Inthiscase,thegov- ernmentwouldchoosethetaxT_t^P=(1−c)²/4ineachproduction periodandthehigh-profitfirmwouldproduceq1H=1/2inperiod 1rather than producethesamequantity asthelow-profitfirm, q1L=q1H=q^P=(1−c)²/2.Asaresult,theperiod-1informational rentwouldamounttoc(2−c)/2.Insum,boththefirmandcon- sumersarebetteroffifthegovernmentcannotobservethefirm’s period-1output.

1.0

0.8

0.6 Separating equilibrium S1

Pooling equilibrium Separating equilibrium S2 0.4

Production cost difference, c

0.2

0.0

0.0 0.2 0.4

Probability of a good realization of costs, µ

0.6 0.8 1.0

Figure 2 The preference of a revenue-raising government regardingidentifyingfirmtypeornot.

to the tax set under a symmetric information scenario, T_t^P−T_t^∗=−c(2−c)/4<0,t=1,2.Hence,bothfirmtypes canproduceandthehigh-profitfirm receives,asinforma- tionalrent,c(1−c)/2inperiod1andc(2−c)/4inperiod 2.In contrast,Proposition4 (ii)states thatifthe ratioof highlyprofitablefirmsismoderate,thegovernmentimposes S2, whereby the high-profit firm obtains an informational rent inperiod1but notinperiod2.Finally,Proposition 4 (iii) states thatwhen theratio of high-profitfirms is high enough, the governmentcharges such a high tax in each periodthatitisonlyacceptabletothehigh-profitfirm(the low-profit firm refuses to pay). This high tax means that thehigh-profit firmreceivesnoinformationalrent.This is the S1 situation, where per-period corporate tax is well above that expectedly set under symmetric information, T_t^S1−T_t^∗=(1−)c(2−c)/4>0, t=1, 2. This is because per-period output diminishes relative to per-period out- put as expectedunder symmetricinformation, q_t^S1−q^∗_t=

−(1−)(1−c)/2<0;hence,thepriceofthegoodtocon- sumersincreases.

ThisresultisillustratedinFig.2.

Meanwhile,thetaxedfirmwouldpreferthegovernment tochoosepoolingequilibriumratherthanS1orS2,because itsinformationalrentsoverbothperiods,IR^P=c(4−3c)/4, IR^S2=c[4−c−2

c(2−c)]/4and IR^S1=0, aresuch that IR^P>IR^S2. Finally, the government obtains less revenue underasymmetricinformationthanundersymmetricinfor- mation,regardless ofwhether ornotit induces thetaxed firm todisclose itsprivateinformation, namely,T^S2<T^∗, T^S1<T^∗,T^S1<T^∗andT^P<T^∗.

5. Welfare

The analysissofar hasexamined thegovernment’sincen- tives to induce or not information disclosure. Welfare implicationsof suchbehaviourarenowexaminedinorder to ascertain whether or not the incentives of a revenue- raising government are aligned with social interests. To

thisend,(expected)welfareisdefinedastheun-weighted sumofconsumersurplus,thefirm’sinformationalrentsand government-collectedtaxrevenue.Consumersareassumed tohavethesame priorprobabilityassessmentasthegov- ernmentregarding thefirm’spotentialtomakeprofit and paytaxes.

Proposition5.

(i) Ifarevenue-raisinggovernmentinducesthetaxedfirm todiscloseitsinformation,thenW^S2<W^∗intheregion where both types of firm produce a positive output, andW^S1<W^∗whenonlythehigh-profitfirmproduces apositiveoutput.

(ii) Ifthegovernmentchoosesnottoinducethetaxedfirm todisclose itsinformation,social welfareis suchthat W^P<W^∗.

Proof. SeeAppendix.

Whenthefirmdisclosesinformation,itsperiod-1output islowerthanthatprevailinginasymmetric-informationsce- nario.Thus,consumerspaymoreforthegoodinthisperiod (lump-sumcorporatetaxescauseinflationwheninformation isasymmetricasopposedtosymmetric)andtheconsumer surplusdecreases.Inaddition,expectedprofits(somegoing tothegovernmentastaxrevenueandsomeretainedbythe high-profit firm asinformational rent) alsodecrease rela- tivetowhathappensinasymmetric-information context.

Takingintoaccountthewelfarelevel inperiod2andthat welfaredistributionbetweenthegovernment,thefirmand consumers is as under symmetric information, the result W^S2<W^∗holds. In contrast,whenS1prevailsin period2 aswellasperiod1,firmoutputislowerthanundersymmet- ricinformation, consumers have topaya higherpricefor goodsandsocialwelfareisdecreased.

Ifpoolingequilibriumprevails,inperiod1thefirm’sout- put decreases relative tothat expected under symmetric information, resultingin a lower welfare level. In period 2 the firm produces the same output as expected under symmetricinformation,sowelfareremainsthesame.How- ever, welfare distributionamongplayers shifts relativeto thedistributioninthesymmetricinformationscenario.

Insum,althoughgovernmenttaxsetinbothsymmetric andasymmetricinformationcontextsisalump-sumtax,the factthat thegood’sexpectedpriceis higherinthelatter contextleadstolowersocialwelfareintheformercontext, regardlessofwhetherornottheinformationisdisclosed.

Welfareoutcome underasymmetricinformationis now comparedasa function of the government’sbehaviour in maximizingitsrevenue,renderingthefollowingproposition.

Proposition 6. For each value of parameter c a prior probability assessment 3 exists, 3=[2c²+(2− 4c)

c(2−c)]/[2c+3c²+(2−4c)

c(2−c)], where 0<

3<1,forallc,forwhichthefollowinghold:

(i) If ∈ (3,1),socialwelfareismaximizedwhenthefirm disclosesitsinformation(inS2).

(ii) If ∈ (0,3),socialwelfareismaximizedwhenthefirm doesnotdiscloseitsinformation.

1.0

0.8

Welfare is maximized under separating equilibrium S2

Welfare is maximized under pooling equilibrium 0.6

0.4

Production cost difference, c

0.2

0.0

0.0 0.2 0.4

Probability of a good realization of costs, µ

0.6 0.8 1.0

Figure3 Equilibrium thatwould maximize expectedsocial welfare.

Proof. SeeAppendix.

ThecontentofProposition6maybeillustratedinFig.3.

The tax-inducingS1isnot sociallydesirable,sinceitis dominatedbythetaxthatinducesS2.Infact,thelow-profit firmproducesnooutputin S1,sothedistortioncausedby thatfirminperiod1is greaterthaninS2, wherethisdis- tortionalsoemerges.Thus,ineachperiodthepricepaidby consumersishigherinS1thaninS2, andsocialwelfareis consequentlylowerinS1.

Likewise, when comparing S2 and poolingequilibrium, inducingseparationisonlysociallyefficientwhen----giventhe earningsofthelow-profitfirm----there isasufficientlyhigh ratioofhigh-profit firms.The sociallyoptimaloutcome in period2isthatthereisseparation,becausecompleteinfor- mationisrestored.Ontheotherhand,theoutputdistortion in period 1 that leads to separation, and hence reduces welfare,is morepronouncedinseparatingthaninpooling equilibrium.Overall,thewelfareincreaseinperiod2caused byS2relativetopoolingequilibriumoutweighsthewelfare reductioninperiod1.

Bearinginmindtheratioofhigh-profitfirms,iftheprofits of the low-profit firm are not very small,a large period- 1outputreductionisrequiredtoseparatethelatter from theformer. The government thus setsa verysmalltax in period1sothatitisacceptabletothelow-profitfirm,but thismakesinformationalrentverylargeforthehigh-profit firm.Inthiscase,noseparationissociallypreferable.The oppositeholdswhenthenumberoflow-profitfirmsissmall (Fig.4)

Thus,arevenue-maximizinggovernmentthatleadsthe taxedfirmnottoinducedisclosureinalsomaximizessocial welfare in all the region of the pooling equilibrium. The government’sbehaviouralsomaximizesaggregatewelfare whenitencourages,troughseparatingequilibriumS2,the firm to reveal its information. However, in this case the government and social objectives are only coupled in a very small separating equilibrium region. Finally, a tax- maximizinggovernmentthatchoosestoinducefirm’stypes

The government does not maximize welfare

The government maximize welfare

0.0 1.0

0.8

0.6

0.4

0.2

0.0

0.2 0.4

Probability of a good realization of costs, µ

0.6 0.8 1.0

Production cost difference, c

Figure 4 The revenue-raising government’s alignment and non-alignmentwithsocialwelfare.

separationdoes notmaximizesocial welfarein theentire S1separatingequilibriumregionaswellasinmostoftheS2 separatingequilibriumregion.

6. Conclusions

Thispaperexaminesthebehaviourofarevenue-raisinggov- ernment when charging corporate taxes to a firm better informedthan thegovernmentconcerning itsprofitability and,hence, its tax-paying potential. In a two-period sig- nalling model in which the government interacts with a singlefirm,thegovernment’staxpolicyofinducingthefirm todiscloseitsinformationisfoundtobegenerallydesirable inordertomaximizerevenue.

Inparticular,whenthepriorprobabilityassessmentofthe governmentabouthavingahigh-profitfirmishighenough, thegovernmentprefersthefirmtodiscloseitsprivateinfor- mation,althoughthecostisthatthelow-profitfirmdoesnot produceatallandnotaxesfromthisfirmarecollected.In thiscase, thegovernmentsavestheinformationalrent to thehigh-profitfirminperiod2aswell asinperiod1.The disclosureapproachis alsothebestpolicyfor thegovern- mentwhen,given theearningsof thelow-profit firm,the government’spriorprobabilityassessmentthatthefirmhas ahightax-payingpotentialismoderate.Inthiscase,thegov- ernmentreducesperiod-1taxrelativetothatwhichwould expectedlybepaidundersymmetricinformation.Thegov- ernmentis thus obliged togrant an informationalrent to thehigh-profitfirminperiod1;however,therestorationof completeinformationmeansthat,inperiod2,taxrevenue isincreasedtothepointthatinformationalrentisreduced tozero.Finally,ifthegovernment’spriorprobabilityassess- mentislowenough,thegovernmentprefersnottoidentify thefirm typebutprefers insteadtoseta period-1corpo- ratetaxthatreducesthisperiod’sinformationalrenttothe high-profitfirm relativetoseparation, althoughthe infor- mationalrentpersistsinperiod2(andevenincreaseswith respecttoperiod1).

From a social viewpoint, the strategy of a revenue- raisinggovernmentinthissignallingcontextisgenerallynot aligned withsocial interests,especiallywhen thegovern- mentinducesseparation,asthisleadstothelow-profitfirm exitingthemarket.Yetitissociallydesirabletohavesep- arationwithbothfirmtypesproducing,asconsumerprices wouldbelowerinbothperiods.Likewise,whengovernment- inducedseparationresultsinpositiveoutputinperiod1for bothfirmtypes,aregionofparametersexistsinwhichnon- disclosure of informationis sociallydesirable, given that, in welfare terms, disclosure is toocostly relative tonon- disclosure.

As Klinger and McFate (2013) pointed out ‘‘companies (inthe U.S.)canmake profits,pay taxesonthoseprofits, andcreatejobs.Ensuringthatallcorporationspaytaxeson theirprofitswillprovidethenationalgovernmentwiththe revenueneededtoinvestinmodernizingthetransportation, information,communications,andenergyinfrastructurethe economyneedstogrow.Demandingthat corporateactors that benefit from operating in America help pay for the publicsystemsthatenabletheirsuccesswillensurefuture generationsofAmericansareabletocompeteintheglobal economyandthrive’’(p.19).Andtheroleofobtainingthe necessaryinformationiscrucialtothatend.

Conflict of interest

Theauthordeclaresnoconflictofinterest.

Appendix.

ProofofProposition2.

(i) SeparatingequilibriumS1.Theincentive-compatibility conditionsoftheproblemstatedin(3)particularizein (1−c−q1^SL)q^S1L≥(1−c)²

4 − c(2−c)

4 (A1)

and

(1−q1^SL)q^S1L+c(2−c)

4 ≤ 1

4, (A2)

respectively. The tworoots that solveinequality (A1) taken asan equalityarer^+,−=[1−c±

(2−c)c]/2, soinequality (A1)issatisfiedwheneverq^S1L ∈ [r⁻,r⁺].

On the other hand, the tworoots that solve inequal- ity (A2) as an equality are s^+,−=[1±

c(2−c)]/2, inequality (A2) is satisfied whenever q1^SL ∈ [0,s⁻]∪ [s⁺,∞].Takingintoaccount thatr⁻<s⁻,any output level q1^SL ∈ [r⁻,s⁻]revealsthat thefirmis low-profit.

Bearinginmindthats⁻<(1−c)/2≡q^m1L,weconclude that, of these output levels, the least costly for the government is q^S1L=s⁻. In sum, the period-1outputs thatformpartoftheseparatingequilibriumareq^S1L= [1−

c(2−c)]/2forthelow-profitfirmandq^m1H=1/2 for the high-profit firm. Finally, of the twocorporate taxes that the government may set in t=1, namely T1^S=^S1LorT1^S=^S1H,thetaxthatallowsbothfirmtypes totakepartinthetaxgameisT1^S=1^SL.Thistaxleads theincentive-compatibilityconstraintforthelow-profit

firmtobebinding,whereasthatofthehigh-profitfirm is not binding and this firm consequently may obtain informationalrent.

(ii) SeparatingequilibriumS1.Thisariseswhenthegovern- mentchargesthetaxT1^S=^S1Htobothtypesoffirmin period1.Itisclearthatthelow-profitfirmwouldreject thistax,sotheonlyfirmthatacceptstopaythetaxand produceswouldbethehigh-profitfirm.Fullinformation isthusrestoredinperiod2.

ProofofProposition4. Whentaxrevenueovertwoperiods inS2equilibriumandpoolingequilibriumarecompared,it followsthat T1^S2−T1^P=−c[1−

c(2−c)]/2<0, whereas T2^S2−T2^P=c(2−c)/4>0.Overall

T^S2−T^P=−2[1−

c(2−c)]

2−c , (A3)

i.e., tax revenue under S2 equilibrium is higher (lower) thanunderpoolingequilibriumwheneverthegovernment’s priorbeliefregardingthefirmashigh-profitislarge(small) enough. On the other hand, when tax revenue under S1 equilibrium and pooling equilibrium are compared, we have T1^S1−T1^P=[−(1−c)²]/4>0 and T₂^S1−T₂^P=[− (1−c)²]/4>0,bywhich

T^S1−T^P= −(1−c)²

2 . (A4)

Likewise, when tax revenue under S2 equilibrium and S1equilibriumarecompared,itholdsthatT1^S2−T1^S1=[1−

−c(4−c−2

c(2−c)]/4,whichmaybepositiveornega- tive,whereasT2^∗−T2^S1=(1−)(1−c)²/4>0.Takingboth periodsintoaccount,itfollowsthat

T^S2−T^S1=−2[1−3c+c²+c

c(2−c)]

2−2c+c² . (A5)

Finally, considering (A3)---(A5)renders the resultof the proposition.

ProofofProposition5.

(a) Ifthegovernmentbehavesinsuchawaythatthefirm’s private informationis fullytransmitted throughsepa- rating equilibrium S2 (see Proposition 1 and Fig. 3), expected consumer surplus in period 2 amounts to CS^∗2=[1−2(1−)c+(1−)c²]/8, which, taking tax revenueintoaccount,leadsto

W2^∗=CS^∗2+T2^∗= 3

8[1−2(1−)c+(1−)c²] (A6) asperiod-2welfare.Ontheother hand,period-1wel- fareamountsto

W1^S2=CS^S21 +T1^S2+IR^S21H

= 1 2

⎡

⎣_¹

4+(1−)

1− c(2−c) 2

2⎤

⎦

+1

4{1−c[4−c−2

c(2−c)]}

+c[4−c−2

c(2−c)]

4 , (A7)

whereIRstands forinformationalrent.From(A6)and (A7),welfareleveloverbothperiodsamountsto W^S2=W1^S2+W2^∗= 1

4{[3−

c(2−c)][1−2(1−)c]

+2(1−)c²+

c(2−c)}. (A8)

TakingintoaccountthatW2^S2=W2^∗,welfarecompar- isonunderseparatingequilibriumS2andequilibriumof symmetricinformationis reduced towelfarecompar- isonin period 1. Hence, comparison of (A6) and(A7) renderstheresultstatedinpart(a)oftheproposition.

(b) When the government leads the taxed firm not to disclose its private informationthrough period-1out- put that forms part of the pooling equilibrium (see Proposition2andFigure3),expectedwelfareinperiod 1is

W1^P=CS^P1+T1^P+IR^P1H= 1 2

1−c 2

2

+ 1−c

2

2

+1

2c(1−c)= 3

8(1−c)²+1

2c(1−c) (A9) andinperiod2is

W2^P=CS^P2+T2^P+IR^P2H= 1 2



1

4+(1−)(1−c)² 4



+(1−c)²

4 +c(2−c)

4 = 3

8[1−(1−)c(2−c)].

(A10)

Asaresult,welfareoverbothperiodsamountsto W^P= 1

8[6(1−c)²+c(10−7c)]. (A11) Likewise, in S1 equilibrium, expected welfare in each period t,t=1,2, amounts to W_t^S1=CS^S1_t +T_t^S1=

1 2₁

2

2

+₁

2

2

= ³₂₁

2

2

,wherebywelfareoverboth periodsisgivenby

W^S1= 3

4. (A12)

Finally,comparing(A6),(A11)and(A12)allowsusto obtaintheresultstatedinpart(b)oftheproposition. ProofofProposition6. Taking(A8),(A11)and(A12)into accountprovestheresultoftheproposition.

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