The Economic Consequences of Mandating Accrual Accounting for Pensions in Governments

Transcription

1 The Economc Consequences of Mandang Accrual Accounng for Pensons n Governmens Shuen-Zen Lu* Yuhchang Hwang+ James M. Paon** * Naonal Tawan Unversy +Arzona Sae Unversy **Unversy of Psburgh Aprl 2000 Please communcae wh he frs auhor a: Deparmen of Accounng College of Managemen, Naonal Tawan Unversy, (02) , E-mal: slu@mba.nu.edu.w We acknowledge helpful commens from parcpans n he Unversy of Psburgh Kaz Graduae School of Busness Accounng-Fnance workshop. Specal hanks go o San Baman (Unversy of Pennsylvana) and Harry Evans (Unversy of Psburgh). Any remanng flaws are our responsbly. The frs auhor acknowledges fnancal suppor of a research gran from he Naonal Scence Councl.(#NSC-2416-H )

2 The Economc Consequences of Mandang Accrual Accounng for Pensons n Governmens 2 ABSTRACT Ths paper analyzes he economc effecs on czens of mandang accrual penson accounng sandards n governmens. The model consders he poenal conflcs among he young and old generaon of czens n governmen spendng ncludng penson fundng. We frs demonsrae ha young generaon czens have ncenves o fund pensons n order o smooh her consumpon of prvae goods and publc servces over me; old generaon czens have no ncenves o fund pensons. Our model predcs ha he preferred penson fundng of young generaon czens wll ncrease as her emphass on he fuure ncreases and as he reurn on penson asses ncreases. The equlbrum penson fundng as well as he correspondng ax rae and publc servce levels are characerzed va an elecoral compeon game among polcal pares. Penson fundng and accounng polcy are lnked va balanced-budge requremens whch apply o many governmenal uns worldwde. We demonsrae ha he equlbrum ax rae wll ncrease and he level of publc servces wll decrease f an accrual-bass of penson accounng s mandaed n a growng economy. As a resul, everyone n a growng economy wll be made worse off f accrual penson accounng n governmens s mandaed. Alhough accrual accounng may be more conssen wh measurng nerperod equy, produces an economcally neffcen oucome n a growng economy. We also fnd ha dfferenal welfare effecs for dfferen groups of czens may arse as a resul of mandang accrual penson accounng n a declnng economy. As a resul, some czens are made beer off whle oher are made worse off f accrual penson accounng n governmens s mandaed n a declnng economy. These resuls sugges ha here are some poenally negave economc consequences whch governmenal accounng sandard seers should consder before mandang accrual accounng for pensons. Keywords:penson accounng, nerperod equy, overlappng generaon model

3 3 1. Inroducon The purpose of hs paper s o develop a model whch examnes he economc effecs on czens of mandang accrual accounng for pensons n governmens. Whle accounng research has exensvely suded he economc consequences of fnancal accounng rules on shareholders and bondholders n he prvae secor (e.g., Was and Zmmerman [1978] [1990], Holhausen and Lefwch [1983]), lle work has been done on he economc mplcaons of governmenal accounng sandards. Due o he exsence of balanced-budge requremens whch apply o many governmenal uns, 1 he economc consequences of dfferen governmenal accounng sandards can be drec and could have mporan mplcaons for czens. Research n hs area should help he Governmenal Accounng Sandards Board (GASB) beer undersand he possble economc mplcaons of her choces of governmenal fnancal reporng sandards. An overlappng generaons model s employed n our analyss. 2 We assume ha czens lve for wo perods, wh lfespans overlappng so ha he young generaon's frs perod of lfe corresponds o he older generaon's second perod of lfe. A czen derves uly hrough consumng boh publc goods and prvae goods. We frs characerze ndvdual czens' preferences concernng penson fundng polces. Accounng polcy and penson fundng are lnked va balanced budge requremens whch apply o mos sae and local governmens. We show ha older czens prefer no o fund pensons a all -- so ha more resources can be allocaed o curren publc servces for a gven level of ax revenue. In conras, younger czens may have ncenves o prefer fundng some penson amouns -- so ha he fscal burden lef o he nex generaon s no so excessve as o lm spendng on publc goods when he (currenly) young czen s older. As a resul, a young generaon czen may prefer o fund some of he penson (by foregong some curren prvae consumpon) when she s young n order o smooh he consumpon of publc servces over her lfeme. To nvesgae he possble equlbrum oucomes concernng penson fundng, we show ha he equlbrum choce of fscal polces n sae and local governmens can be characerzed by a vong game n whch ax raes, levels of publc servces, and penson fundng are deermned by a smple majory voe on ax raes alone. In hs vong game, voers are assumed o be raonal, and polcal pares are

4 4 assumed o have an nfne horzon. Alhough czens do no voe explcly on penson fundng n our model, we show ha an eleced pary's choce of penson fundng wll converge o he medan voer's preference n a repeaed game f voers use a pary's choce of fundng level (afer beng eleced) o form her belef abou he pary's lkely fuure fundng choces. We fnd ha he equlbrum oucome of he vong game and, hus he level of penson fundng, depends on several characerscs, e.g., he rae of reurn on penson asses and czens' emphass on he fuure. Based upon he equlbrum oucome concernng penson fundng, we demonsrae ha, f he economy s growng, mandang an accrual accounng mehod (a mehod whch s frequenly advocaed n debaes concernng reforms n governmenal accounng) reduces he level of publc servce provded and ncreases he ax rae. Thus, alhough mandang an accrual penson accounng mehod may be more conssen wh he noon of "Inerperod Equy" (GASB [1987]), hs accounng polcy change may cause a welfare loss for every czen n a growng economy. We also fnd ha dfferenal welfare effecs for dfferen groups of czens may arse as a resul of mandang accrual penson accounng n a declnng economy. As a resul, some czens are made beer off whle oher are made worse off f accrual penson accounng n governmens s mandaed n a declnng economy. We conclude ha he governmenal accounng sandard seers should consder he economc envronmens n whch her accounng sandards wll be appled. Specfcally, n growng economes he hey wll face a rade-off beween economc effcency and nerperod equy concerns. In declnng economes, ner-czen equy 3 should also be a concern for he accounng sandard polcy maker. The res of he paper s organzed as follows. The res of Secon 1 revews pror leraure relaed o governmenal penson fundng. Secon 2 dscusses assumpons and he underlyng concep of polcal compeon used n our model. Secon 3 presens a model of czens' preferences regardng penson fundng and ax raes and deermnes a correspondng vong equlbrum n a growng economy. Secon 4 provdes defnons for wo dfferen ypes of governmenal penson accounng regmes -- lassez-fare vs. mandaed accrual. Secon 5 examnes he equlbrum choces of penson fundng level and ax raes f an accrual-bass accounng s mandaed for governmens. Secon 6 dscusses he economc consequences of mandang accrual penson accounng n a growng economy. Secon 7

5 5 brefly presens and dscusses he effecs of mandang accrual penson accounng n a declnng economy. Fnally, Secon 8 summarzes he paper and dscusses lmaons/fuure research drecons. 1.1 Leraure Revew Prevous research has offered a varey of possble explanaons concernng governmenal penson fundng. For example, Mumy [1978] vews underfunded pensons as a loan from curren workers o czens. In hs model, underfundng occurs when a governmen's cos of borrowng from penson funds s less han he cos of borrowng from he capal marke. In Epple and Schpper [1981], penson underfundng arses for he purpose of ax smoohng. They argue ha he dead-wegh coss (e.g., he dsoron of effcen resource allocaon resulng from ax collecon) would be very hgh f an exraordnarly hgh ax s leved n any one perod. Thus a governmen, amng o mnmze czens' dsuly from ax burdens, has ncenves o desgn ax polces whch ensure a more even ax collecon across perods. As sae and local governmens are generally no allowed o ssue bonds o fnance her operang expendures, Epple and Schpper conclude ha one ool avalable o help smooh axes s penson underfundng. In conras, Inman [1982] suggess ha penson underfundng may resul from mperfecons n local housng and labor markes. For example, resdens have ncenves o 1) over-consume publc servces hrough penson underfundng and hen 2) leave he jursdcon whou bearng full coss of penson underfundng (e.g., dscouns on he houses hey sell or a wage ncrease of publc employees). Whle Inman's approach mplcly recognzes poenal conflcs beween he curren and fuure homeowners, conflcs of neres beween dfferen groups of czens (e.g., he young vs. he old) have no ye been explcly modelled o explan he dfferences n penson fundng pracces. Conflcs of neress among czens can be explcly capured by overlappng generaons (O-G hereafer) models. Convenonal O-G models have exensvely suded he ncenves of czens o leave bequess o fuure generaons (e.g., Barro [1974], Drazen [1978], Wel [1987] and Cukerman and Melzer [1989]). If he amoun of money pu no penson fund accouns s vewed as a beques from curren czens o fuure generaons, our model s a specal case of he convenonal O-G models.

6 6 However, our model dffers from hose convenonal O-G models n one mporan aspec. Prevous O-G models assume ha czens are concerned abou he welfare of her offsprng. As a resul, fuure generaons' ules ener no curren czens' uly funcons. Convenonal O-G models show ha curren generaons leave bequess o fuure generaons only f her concern over he welfare of her offsprng s srong enough. In conras, we do no assume hs ype of alrusc exernaly on he par of curren czens. The czens n our model are self-neresed, wh no concern abou anyone excep hemselves. However, her concern does exend o boh perods of her lves. The analyss presened n hs paper also relaes o neoclasscal models whch suded he effec of governmenal deb on he growh of he economy; e.g., Damond, These neoclasscal models examned he long-erm effecs of naonal deb on capal accumulaon, neres raes, and he wage level n an economy. Such deb s equvalen o a pay-as-you-go penson fundng approach n our seng. Our model dffers from hose sudes n wo mporan ways. Frs, whle hey were slen on he role of polcal compeon n deermnng he level of deb, we explcly model he polcal compeon process n deermnng he governmenal fundng for pensons. Second, whle we assume ha he neres rae and wage are gven, n her models such varables are deermned endogenously. Our model of polcal compeon s descrbed n Secon 2. The lmaons of our model, ncludng he presence of exogenous varables, are dscussed n Secon Assumpons and a Model of Polcal Compeon 2.1 Assumpons We assume ha here s an nfne bu counable number of generaons of czens. Generaon s denfed wh he me perod ; {se of all negers}. Czens' uly funcons are assumed o be addve and o have dencal funconal form. However, czens dffer n her neremporal dscoun facors, ncome levels and me horzons. Czens lve for wo perods. In he frs perod (when hey are young) hey are employed eher by he governmen or by prvae enerprses, and earn ncomes correspondng o her skll levels. Alhough he sources of penson fundng are dfferen, we assume

7 7 ha penson sysems exs n boh he prvae and he publc secor. Thus, n he second perod (when hey are old) czens rere and lve on he penson earned (eher from he prvae or publc secor) n he prevous perod. Several oher specfc assumpons are made as follows. Assumpon 1: Uly Funcons In perod, a young generaon czen s assumed o have an addve Cobb-Douglas (C-D) uly funcon denoed as: V =C á S 1-á + ö C á S 1-á ; 0 á 1, where C denoes he prvae consumpon a ; S denoes he amoun of publc servces receved, whch s measured by he number of publc employees; and ö s he neremporal dscoun facor (0 < ö < 1). Ths neremporal dscoun facor s assumed o ncrease wh an ndvdual's ncome level -- dö / di > 0;.e., ndvduals wh more curren ncome wegh fuure consumpon more heavly han hose wh less ncome (Lawrence [1990]). An old generaon czen j has a uly funcon U j = C á S 1-á, snce he has only one perod o lve. Fnally, noe ha he publc servces n our model refer o pure publc goods,.e., hey canno be used as subsues for prvae consumpon (e.g., he publc good s no welfare). C-D uly funcons are used here because hey are wdely used n he publc fnance leraure (e.g., Romer [1975]) and because hey enable us o unambguously denfy he medan voer n a wo-pary vong game. 4 Assumpon 2: Income Dsrbuon Czens are endowed wh dfferen skll levels and can eher work for he prvae secor or for he governmen when hey are young. Assumng ha he labor marke s perfec, a young generaon czen wll command an ncome of I (correspondng o her skll level) when she s young regardless of wheher she works n he publc or he prvae secor. When czens become old, hey receve a penson whch s proporonal o her earned ncome when young (.e., ä I, where 0 < ä < 1). We also assume ha czens' ncomes n a gven perod are unformly dsrbued over a fxed nerval;.e., I [ I, ˆ I ]. An old generaon czen reles upon he penson receved as he sole source of hs ncome. Assumpon 3: Demographc Srucure The economy n our basc model s assumed o be growng. In a growng economy, he populaon s ncreasng and he per capa ncome s also growng. We assume a growng economy o develop he

8 8 man pons n he paper because he economes n almos all saes and a majory of local governmens have exhbed growh over me. In Secon 7 we brefly presen and dscuss he effecs of assumng a declnng economy. In a growng economy he number of young generaon czens mus (by defnon) be greaer han he number of old generaon czens. We also assume ha he dsrbuon of per capa ncome expands on s upper bound a a rae of k where 0 < k < 1. 5 The assumpon mples ha I -1 [ I, ˆ I -1 ] n perod -1, and I [ I, ˆ I ] where ˆ I = (1+ k) Iˆ- 1 n perod. 6 Assumpon 4: Penson Fund Operaon A governmen's penson fund s assumed o be separae from s general operang fund. Denoe B -1 as he balance of he penson fund a he end of perod -1 and ì -1 as he average ncome of czens who worked for he governmen n -1. The gross rae of reurn on he penson fund's nvesmen durng perod s assumed o be r. We assume ha no borrowng from he penson fund accoun s allowed and ha he penson plan s desgned as a defned benef plan. The balance of he penson fund accoun a he end of perod of s: B = B -1 r + P - S -1 ì -1 ä Ths means ha he endng balance ncreases wh he gross reurn on penson fund nvesmens (r ) and wh he amoun of curren penson fundng (P ), bu decreases wh paymens o curren rerees (S -1 ì -1 ä). For smplcy, he balance of penson funds s assumed o be posve each perod (.e., B > 0). In addon, here s no prvae savng by czens n any perod. Czens consume all her afer-ax wage or penson ncome. Assumpon 5: Tax Rae and Balanced-Budges Czens are oblgaed o pay a ceran percenage of her salary ncome (young generaon) or penson ncome (old generaon) as axes. Conssen wh many sae and provncal laws worldwde, we assume ha governmens are requred o operae under he consran of a balanced-budge. Ths means ha oal recorded ax revenue has o be greaer han or equal o oal recorded publc expendures durng he fscal year, and ha such expendures are funded by he governmen n he same perod. 7 In addon, governmens are no allowed o ssue new deb o fnance curren publc servces.

9 9 In perod, we assume ha he average wage level of he publc employees equals ì, he oal number of workers hred by he publc secor equals S, and he amoun of penson fundng equals P. Thus, he oal amoun of publc expendures (e ) from he governmen's general accoun durng perod becomes: e = µ S + P In hs equaon ì S s he oal wage pad o he publc employees and P s he oal amoun njeced no he penson fund n perod. We assume ha he average wage pad o publc employees (ì ) s a consan n a gven perod regardless of he publc servce level seleced by he governmen; however, ì could be dfferen across perods. Denong ô as he ax rae and T as he oal axable ncome avalable n a communy for perod, a balanced-budge consran mples ha he oal ax revenue (ô T ) equals oal ouflows for publc servce (ì S ) and penson fundng (P ): 8 τ T = µ S + P In order o sudy he economc consequences of mandang accrual penson accounng n governmens, s mporan o frs undersand he underlyng governmenal decson process concernng penson fundng, publc servce provson, and ax raes. Therefore, we nex examne how he penson fundng, he publc servce level, and he ax rae are deermned n a governmen va a model of polcal compeon. 2.2 Polcal compeon In he publc choce leraure, he medan voer heorem (Black [1958]) s wdely used o deermne he equlbrum vong oucome. Tha s, f a decson problem s un-dmensonal and voers' preferences sasfy some regulary condons, a canddae wll wn an elecon f hs plaform s conssen wh he medan voer's preferred oucome. However, he decson problem analyzed n our model s mul-dmensonal,.e., czens are concerned abou he ax rae, publc servces, and penson fundng. I s well known ha when a decson problem s mul-dmensonal a sable equlbrum rarely exss under he smple majory vong rule -- unless some resrcve condons are sasfed (Romer and

10 10 Rosenhal [1979], Mueller [1989]). To overcome hs dffculy, he elecoral compeon model used here explcly assumes ha vong occurs only on he ssue of he ax rae -- a un-dmensonal vong process. However, o capure he mul-dmensonal aspec of he problem, we allow czens (as well as he opposon pary) o use he eleced pary's acual choce of penson fundng level n ancpang he pary's lkely fuure acons. By so dong, we can show ha alhough voers do no acually voe explcly on he penson fundng level, n equlbrum, he wnnng pary's choce of penson fundng level wll conform o he medan voer's preference. Gven an equlbrum ax rae and penson fundng level, he correspondng publc servce level s hen auomacally deermned due o he balanced-budge consran. The advanage of hs elecoral compeon model s ha we can collapse a mul-dmensonal vong problem no a mul-sage, un-dmensonal program n a manner such ha he equlbrum oucome of he game s racable analycally. Imporan assumpons concernng he elecoral compeon model are as follows: 1) A smple majory vong rule s used o decde elecons. 2) Czens voe only on he ax rae o be leved n each perod. The eleced pary selecs an appropraon plan whch specfes he acual amoun o be allocaed o provdng publc servces versus fundng pensons;.e., we assume hese are admnsrave decsons, gven a ax rae. 3) There are wo polcal pares n he economy. Each pary has s own preferred oucomes concernng he ax rae, he level of publc servce and penson fundng. A pary's objecve funcon s o mnmze s long-erm expeced loss, whch s measured as he squared amoun of he dfferences beween he acual polcy mplemened (concernng he ax rae and penson fundng level) and he pary's own preferred oucomes. 9 4) Czens are raonal and nformed. By observng he eleced pary's choce of penson fundng, czens form a belef abou he ype of sraegy he same pary wll ake n he fuure. 5) To make he analyss racable and non-rval, he preferred ax rae of he boh pares as well as he preferred penson fundng level of one of he pares are assumed o be known, whle he second pary's preferred fundng level s assumed o be random. 10 (See Appendx A for a dealed descrpon.) Based upon he above assumpons and followng procedures smlar o hose n Alesna [1988], we show ha one of he equlbra n our model 11 s equvalen o a program ha allows voers o voe

11 11 sequenally on he ndvdual ssues of a mul-dmensonal problem. Thus, our model converges o a mul-sage, un-dmensonal problem, f boh czens and pares are raonal when selecng her penson fundng, ax rae and publc servce levels. Proposon 1 summarzes an equlbrum resul for our elecoral compeon game. A dealed descrpon of he elecoral compeon model s presened n Appendx A. Proposon 1. Gven he assumpons n Secons 2.1 and 2.2, n a wo-pary elecoral compeon seng here exss an equlbrum such ha he equlbrum ax rae, level of publc servces, and penson fundng from vong on he ax rae only s equvalen o he one obaned va a sequenal vong process n whch voers frs voe on he ax rae and hen voe on he penson-fundng and publc servce levels. Proof. (See Appendx A). Proposon 1 provdes an mporan foundaon for characerzng he equlbrum oucome n he polcal compeon whch deermnes he ax rae, penson fundng and publc servce level of a governmen n our model. Alhough acual vong occurs only on a sngle dmenson (ax rae) n our model, he assumpon of raonal voers n he model gves polcal pares a srong ncenve o ake care of he oher dmensons (.e. penson fundng and publc servce levels) ha are also of concern o czens. Ths s because f he amoun of penson fundng appropraed afer he elecon does no sasfy a majory of he czens, we assume ha raonal czens and he opposon pary would form a belef ha he eleced pary would behave n a smlar manner n he fuure (Alesna [1988]). As a resul, a equlbrum, he seleced penson fundng level afer elecon wll conform o he preferences of a majory of he voers. Hence he equlbrum oucomes n our model concernng he ax rae and penson fundng level are equvalen o hose derved va a sequenal vong process (Shepsle [1979]). Proposon 1 enables us o rea our problem as f a sequenal vong process akes place. In hs way, he medan voer heorem can legmaely be nvoked sequenally n deermnng he penson fundng, publc servce level, and he ax rae leved. Secon 3 frs characerzes he medan voer's preferred penson fundng level and ax rae. Some basc properes of he vong equlbrum are hen dscussed.

12 12 3. Equlbrum Penson Fundng and Tax Rae n a Growng Economy Based upon Proposon 1 and applyng he sandard approach of sequenal vong models, he equlbrum oucome of he elecoral game s analyzed backwards. Tha s, we frs examne czens' choces concernng penson fundng for a gven ax rae level. Ths enables us o characerze he medan voer's preferred penson fundng level. Followng a smlar procedure, we hen characerze he medan voer's preferred ax rae. 3.1 Medan Voer's Preferences Concernng Penson Fundng To characerze he medan voer's preferred penson fundng level, we frs examne he dsrbuon of czens' (young and old) preferred fundng levels. A. Dsrbuon of Young Czens' Preferred Penson Fundng Levels For a young generaon czen (wheher she works n he publc or prvae secor) 12, he preferred penson fundng and publc servce levels for a gven ax rae are deermned hrough he followng program. Program 1: Max V = C P s.. (1) P 0, (2) C = ( 1 - τ ) I, (3) C + 1 = ( 1 - τ + 1 ) δ I, 1 (4) S = [ T τ - P ], µ (5) S + 1 α 1 = µ S α + Φ C [ T + 1 τ + 1 α + 1 S - P 1-α ]. Consran (1) represens he condon of no borrowng from he penson fund. Consrans (2) and (3) are ndvdual budge consrans, whch mply no-savng or beques for each czen. Consrans (4) and (5) reflec he governmen's balanced-budge requremens n and.

13 13 In hs program, a young czen's concern abou publc penson fundng s drven by he fac ha fundng could affec he governmen's fuure fnancal condon. Ths, n urn, could also affec he publc servce level and ax rae n he fuure. These effecs become apparen f one rewres consran (5) n he above opmzaon program and expresses he nex perod's publc servce level as a funcon of curren penson fundng level P. Based upon he defnon of penson fund balance a he end of perod (B ), (see Assumpon 4 n Secon 2.1.) we have: B = B -1 r + P - δ S -1 µ -1 P = B - B r + δ S µ Then, based upon he above expressons for B, P and consran (4), consran (5) of Program 1 (he nex perod's publc servce level S ) can now be expressed as: = = µ 1 µ 1 [ - ( - + δ µ ) ] [ ( + δ µ ) - δ - ) ] [ - + ( δ ) - δ ( - δ µ ) ] T S T τ = τ µ 1 B B T + r τ + r B B1 r P T τ + r Thus, he nex perod's publc servce level (S ) s shown o be a funcon of curren fundng level P. I s ncreasng n he amoun of curren penson fundng (P ), snce an ncrease n fundng reduces he fuure generaon's burden o pay he rerees. Subsung consrans (2)-(4) and he above expresson for S no he objecve funcon, he Kuhn-Tucker condon for a young generaon czen's opmzaon program yelds: B r P 1 s S 1 B (T τ -1 r P -1 s -1 α C -α S -φ µ µ ( δ + r ) C α S -α + 1 = 0 f P > 0 0 f P = 0

14 Several observaons follow mmedaely from he above condon. Frs, one can characerze he economes n whch a young czen would have ncenves o fund he penson;.e., P > Proposon 2: Denoe P * (I ô ) as he opmal penson fundng level of young czen. For a gven ö ( or r ), I, ä, k and r ( or ö ); P * (I ô ) > 0 f, and only f r (or ö ) exceeds a parcular cuoff pon r * (or ö * ). Proof: (See Appendx B). Proposon 2 assers ha a young generaon czen s lkely o prefer a polcy of fundng pensons a some posve level f: 1) he reurn on nvesmen s relavely hgh, or 2) she s very concerned abou her second perod's welfare (ö s hgh). The nuon of Proposon 2 concernng he rae of reurn (r ) s as follows. A young generaon czen has o sacrfce some of her curren consumpon of publc or/and prvae goods n order o fund he penson. The young generaon czen hopes ha fundng he penson n he curren perod wll lessen he fnancal burden on czens n he nex generaon. In ha way he amoun of publc servces provded n he nex perod wll be greaer. A young generaon czen may prefer o fund he penson currenly f he reurn on he penson nvesmen s large enough because a hgh reurn mples ha a lesser amoun of fundng would be needed n o fulfll ha perod's penson oblgaons. Conversely, o acheve he same fuure fundng resul f he gross reurn s very low, a young generaon czen would have o pu asde a large amoun for penson fundng. Because hs would sgnfcanly reduce he amoun avalable for curren perod publc servce consumpon, a young czen would have less ncenve o fund he penson n hs suaon. The nuon concernng me preference (ö ) s as follows. A young czen would no sacrfce curren consumpon of socal servces f she dd no value he mporance of he uly generaed from he consumpon of fuure socal servces when she becomes old. In he exreme case ha ö = 0, a young czen would compleely gnore he oucome of wha s expeced o happen when she becomes old. Consequenly, here would be no ncenve for such a czen o sacrfce her curren consumpon and o fund he penson. Assumng ha he condons for posve penson fundng (.e., Proposon 2) hold for all I, 13 we nex characerze facors whch mgh nfluence he dsrbuon of he preferred penson fundng among

15 15 young generaon czens. Based upon he above frs order condon, a young generaon czen's preferred penson fundng level, for a gven ax rae, can be derved as: T - ( I ) A P * τ ( )= Ω I > 0 τ 1+ Ω( I )( δ + r ) Where A and Ù are defned as follows: Ω( I ) [ φ A T τ - B u u ( δ + r ) ] 1 - α - δ T τ + ( B -1 µ (1-τ ) µ δ (1-τ r - δ µ -1 S -1 ) ) r Ths mples ha a young generaon czen's preferred penson fundng level s a funcon of her ncome level. Lemma 1: For a gven ax rae (ô ), he opmal level of penson fundng of a young generaon czen (P * (I ô )) s srcly ncreasng n I. Proof. (See Appendx C). The nuon for Lemma 1 s as follows. Snce a young czen wh hgher ncome level derves more uly from consumng fuure publc servces (dö /di > 0 from Assumpon 1 n Secon 2.1), she cares more abou he fuure, and s more lkely o prefer o exchange her curren consumpon and publc servce for he fuure publc servce (hrough ncreased curren penson fundng). Thus, he preferred penson fundng level of a young generaon czen ncreases monooncally n a young czen's ncome level. Lemma 1 wll provde a useful nsgh for characerzng he medan voer's preferred fundng level. Nex we sudy he dsrbuon of old generaon czens' preferred penson fundng level for a gven ax rae. B. Dsrbuon of Old Czens' Preferred Penson Fundng Levels For a gven ax rae, an old generaon czen chooses hs preferred penson fundng by solvng he followng program: j α 1- Max U = C S p α

16 subjec o all consrans lsed n Program 1. I can be shown easly ha he opmal fundng level for an old generaon czen s as follows: Lemma 2: The opmal penson fundng level desred by he old czen s zero, regardless of hs ndvdual ncome level (I j ). Proof. (See Appendx D). 16 The man dfference beween he old czen's program and he young czen's s he me horzon of decsons. The old czen, havng only one perod of lfe o lve, does no care abou he level of publc servce n he subsequen perod (.e., afer hs deah). M C. Medan Voer's Preferred Penson Fundng Level--P Lemmas 1 and 2 ogeher characerze he dsrbuon of he preferred penson fundng levels of all czens. Specfcally, Lemma 1 ensures ha all young generaon czens would fund some posve amoun of pensons and ha he amoun s ncreasng n her ncome levels. Lemma 2 says ha all old generaon czens would prefer zero fundng. Ths means ha he preferred fundng level of he old generaon does no overlap wh he preferred levels of he young generaon. In a growng economy he number of voers n he young generaon s greaer han ha n he old generaon. Ths fac plus he resuls obaned n Lemmas 1 and 2 mply ha he medan voer on he penson fundng ssue mus be a member of he young generaon. 14 Denoe he medan voer's preferred fundng level as P M (I ô ). Because, for a gven ax rae, he preferred penson fundng P M s a funcon of czen's ncome level, he medan voer's preferred fundng can be obaned by subsung he medan voer's ncome level no expresson (2). Thus, P M (I M ô ) = [T ô -Ù M A]/[1 + Ù M (ä+r )]. Noe ha n hs expresson P M ( ô ) s condonal on a gven ax rae, ô, whch s o be deermned va he vong process a he begnnng of perod. To characerze he equlbrum level of P M, we nex nvesgae how he equlbrum ax rae s deermned n a growng economy.

17 Preferences Concernng Tax Rae A. Dsrbuon of he Young Czens' Preferred Tax Rae As dscussed earler, when czens voe on he ax rae hey ancpae ha he eleced polcan wll mplemen a penson fundng level o please he majory of voers. Thus, o examne how a raonal czen chooses her (hs) preferred ax rae, we frs subsue he equlbrum level of penson fundng (P M ) no each ndvdual czen's uly funcon. For a gven P M, when a young czen s asked o voe on he ax rae, she s maxmzng he followng program: Program 2: α 1 Max C S p -α + φ C α s.. M P = P,and Consran s (2) - (5)n Program 1. S 1-α + 1 The preferred ax rae for a young generaon czen mus sasfy he followng frs-order condon: M Y ( P,I ) φ (1 -α ) C µ S α - δ T + ( δ + r d P ) d τ M + α C S S (1 -α ) dp - α I + T - C µ d τ M = 0 To assure ha he ndvdual czen's opmzaon program sasfes he condon of sngle-peakedness, he second order dervave mus also sasfy he followng condon: M G ( P M Y ( P, I ),I ) < 0 τ To see how each young czen wll voe on a proposed ax rae, we frs examne how a young czen's ax preference changes wh respec o her ncome level. Comparave sacs yeld:

18 18 C α φ (1-α )( ) µ d τ = - S M d I G( P, I ) d S d τ Snce G (P M,I ) < 0 (condon for sngle-peakedness), from expresson (4) we conclude: Lemma 3: A young generaon czen's preferred ax rae monooncally ncreases (decreases) n ndvdual ncome level f he nex perod's publc servce level ncreases (decreases) wh respec o an ncrease n curren ax raes (.e., dependng on he sgn of ds /dô ). Lemma 3 ndcaes ha, dependng on he sgn of ds /dô, he preferred ax rae for a young generaon czen s eher monooncally ncreasng or decreasng n her ncome level. The nuon of Lemma 3 s as follows. Snce a wealher young czen derves hgher uly from fuure consumpon, she wll voe for a hgher curren ax rae f ha ncreases he fuure publc servce level; conversely, she wll voe for a lower curren ax rae f fuure publc servce level decreases as a resul of hgher ax raes. Unforunaely, n general, he sgn of ds /dô canno be unambguously deermned. Ths s because he amoun of fuure publc servce provded s affeced by wo offseng forces as he ax rae ncreases. Frs, from expresson (2), can be shown ha for a young czen he preferred penson fundng level s ncreasng n ax rae -- dp /dô > 0. An ncrease n penson fundng, n urn, could resul n an ncrease of fuure publc servces. However, an ncrease n ax rae could also be used o ncrease he level of curren publc servce level, whch causes an ncrease n he fuure penson lables (because more employees are hred). Ths reduces he level of fuure publc goods. Wheher ds /dô s greaer han or less han zero would depend on he relave srengh of hese wo offseng effecs. Alhough he sgn of ds /dô canno be unambguously deermned, he preferred ax rae for he young czen s eher monooncally ncreasng or decreasng n he ndvdual's ncome level. Ths propery of monooncy wll enable us o nvoke he medan voer heorem o unambguously deermne he equlbrum ax rae as long as he dsrbuon of he old generaon's preferred ax rae does no overlap wh ha of he young generaon. We nex examne he dsrbuon of he preferred ax rae of he old generaon.

19 19 B. Dsrbuon of Old Czens' Preferred Tax Rae By followng a procedure smlar o ha n Program 2, one can derve he frs order condon for old czens concernng her preferred ax rae: O j( P M M j S j (1 -α ) dp,i ) α I + - T + = 0 C µ dτ The assumpon of sngle-peakedness requres ha: α M dp M (T - P ) d + τ 2 (1 -τ ) 1-τ 2 d - (1 -α ) P d τ - 2 M < 0 Takng he oal dervave of he above frs order condon wh respec o he ncome I j, we have: d τ j di M dp M T - P d α - + τ 2 (1 -τ ) 1-τ 2 d - (1 - ) P α 2 d τ M = 0 Expressons (5) and (6) ogeher mply ha dô /di j = 0 for he old generaon czens. Thus: Lemma 4: The preferred ax rae of an old czen s a consan, regardless of he ncome level. By comparng he relaonshp beween he dsrbuon of he preferred ax raes of he young versus ha of he old generaon, we have: Lemma 5: Regardless of ncome levels, f ds /dô > 0, he preferred ax raes of all young czens are hgher han ha of all old czens. Conversely, f ds /dô < 0, he preferred ax raes of all he young czens are less han ha of all old czens. Proof. (See Appendx E). Lemma 5 mples ha he dsrbuons of he preferred ax raes of he young generaon and he old

20 20 generaon are separaed regardless of he sgn of ds /dô. Togeher, Lemmas 3, 4 and 5 provde a bass for us o esablsh he medan voer's preferred ax rae. M C. Medan Voer's Preferred Tax Rae -- ô Noe ha Lemma 5 ndcaes ha wo dfferen dsrbuon paerns of he preferred ax rae among czens may exs, dependng on he sgn of ds /dô. We eher have every young czen's preferred ax rae hgher han he preferred rae of he old czens, or he old czens' preferred ax rae s hgher han he preferred ax rae of every young czen. I s mporan o noe ha Lemmas 3, 4 and 5 ogeher mply ha he preferred ax raes among young and old czens do no overlap. Ths separang propery makes sgnfcanly easer for us o denfy he medan voer whch, n urn, wll smplfy he analyss concernng he mpac of mandang accrual penson accounng sandards. Gven ha he economy s growng, he monooncy propery of he preferred ax raes among he young generaon czens (Lemma 3) and he separang propery concernng he preferred ax raes beween he young and he old (Lemmas 4 and 5) ensure ha he medan voer on he equlbrum ax rae ssue s n he young generaon, and s dencal o he medan voer of he penson fundng/publc servce ssue regardless of he specfc ype of he dsrbuon of he preferred ax rae. Proposon 3: Gven ha he economy s growng, he medan voer on he ax ssue s dencal o he medan voer n he penson fundng/publc servce provson ssue, and s a member of he young generaon czens. Proof. Noe ha old czens prefer zero penson fundng, whle a young generaon czen's desred penson fundng level s ncreasng n he ndvdual's ncome. From Lemma 5, f ds /dô > 0, he rankng of a young generaon czen's preferred ax rae s also monooncally ncreasng n he ndvdual's ncome level. As a resul, he medan voer s he same on boh ssues. If ds /dô < 0, he rankng of he desred ax rae among czens s compleely reversed when compared wh he rankng of he penson fundng ssue. However, he medan voer of he wo ssues s sll exacly he same snce he preferred ax raes beween he young and old never overlap n eher case. Q.E.D. In summary, Secons 3.1 and 3.2 characerze he equlbrum relaonshp beween he level of

21 21 penson fundng and he level of ax rae of a governmen n an elecoral compeon game. The model focuses on he smoohng of across generaons publc servces and prvae consumpon as he man ncenve for he medan voer o suppor a fundng of some of he penson accoun. Our nex sep s o examne he effecs of dfferen penson accounng regmes on he choce of penson fundng, ax raes, and publc servce provson. To do so we frs defne wo dfferen accounng regmes n Secon Dfferen Penson Accounng Regmes n Governmens For he purpose of comparson, wo sylzed regmes of penson accounng for governmens are analyzed n hs paper -- a lassez-fare accounng regme and an accrual accounng regme. A bref dscusson of each regme s gven n he nex wo subsecons. 4.1 The Lassez-Fare Accounng Regme In he lassez-fare accounng regme, a governmen s free o choose any penson accounng mehod ha prefers. 15 However, governmens mus operae under he resrcon of a balanced-budge (see Assumpon 5 n Secon 2.1). Our assumpon of balanced-budges requres ha he repored revenue mus be greaer han or equal o he recorded expendures, and ha such expendures mus be funded n he same perod. As a resul, n he lassez-fare regme he recorded penson expendure would equal he preferred fundng level chosen by he governmen. Because a governmen (he wnnng pary) has dscreonary power n choosng s desred accounng mehod o record he penson expendure n he lassez-fare regme, he choce of he penson accounng mehod would be drven by he choce of he desred fundng level. Thus, n a lassez-fare accounng regme s he choce of penson fundng level ha deermnes he selecon of a correspondng accounng mehod wh whch o record he penson expendure. The economy analyzed n Secon 3 s conssen wh he lassez-fare accounng regme, because n Secon 3 he focus of he governmen s he fundng level self. Hence he economc consequences of a lassez-fare penson accounng regme are deermned by he equlbrum choce of ax rae and penson fundng of he governmen saed n Secon 3.

22 The Accrual Accounng Regme In an accrual accounng regme, he oal accrued cos of publc servce s defned as he sum of he salares pad plus he presen value of fuure penson benefs promsed by he governmen. Recall ha he amoun of promsed penson s equal o a fxed proporon (ä) of a worker's curren salary (Assumpon 2 n Secon 2.1). Denong P A as a governmen's oal accrued penson expendure n perod where he correspondng publc servce level s S A. We defne he amoun of penson fundng n an accrual accounng regme as: A A µ S δ P = r Thus he amoun of penson fundng (P A ) n an accrual accounng regme s deermned by he oal wage paymens for publc servces provded n perod (ì S A ). Subsung P A no he balanced-budge consran of Program 1 (consran (4)), he servce level under accrual accounng mehod can be solved as: A A 1 A 1 µ S δ S = [ Tτ - P ] = [ Tτ - ] _ µ µ r A S = µ A T τ δ 1+ r Thus, n he accrual accounng regme, he penson fundng s deermned drecly by he equlbrum publc servce level provded by he governmen. As wll be dscussed n nex secon, due o he balanced-budge requremen, he equlbrum publc servce level s deermned by he choce of he ax rae of a governmen. Hence, unlke he lassez-fare regme, where boh he penson fundng level and ax raes affec he level of fuure publc servce, n he accrual accounng regme he publc servce level s deermned by he equlbrum choce of curren ax rae alone.

23 23 5. Equlbrum Penson Fundng Level and Tax Rae -- Accrual Penson Accounng Regme Secon 3 provdes an analyss of he equlbrum penson fundng and ax rae under a lassez-fare accounng regme. To sudy he effec of mandang accrual penson accounng n governmens, we nex analyze he equlbrum choce of ax rae by a governmen n a mandaed accrual accounng regme. No analyss concernng he choce of penson fundng level wll be provded. Ths s because, under he assumpon of a balanced-budge, n an accrual penson accounng regme he choce of a ax rae deermnes he correspondng servce level, and he servce level deermnes he requred penson fundng auomacally due o he defnon of an accrual-bass penson accounng. Expressons (7) and (8) show ha n an accrual penson accounng regme he prevous perod's penson fundng level (P A -1 ) has no effec on he choce of he curren penson fundng (P A ), on he curren publc servce level (S ), or on he fuure publc servce level (S ). As a resul, he cross-perod consumpon-smoohng hrough curren penson fundng ha exss n a lassez-fare regme s no feasble n an accrual penson regme. Thus, czens' choces of ax rae and penson fundng level under he accrual accounng regme would dffer sgnfcanly from hose n a lassez-fare regme. In shor, he amoun of penson fundng n he accrual accounng regme s purely a funcon of he level of curren socal servces, whch s deermned by he choce of he equlbrum ax rae of a governmen. To characerze he equlbrum ax rae, we nex sudy he dsrbuon of czens' preferred ax raes n he accrual accounng regme. Subsung he fundng level P A (defned n Expresson (7)) for P n Program 2 and solvng for he frs-order condon for he choce of he preferred ax rae of a young generaon czen yelds: S + (1 - ) T r -α I α = 0 C ( δ + r ) µ By nserng he defnon of C and S from consran (2) and (4) n Program 2 no he above expresson, we have: S T + (1- ) r -α I α C µ [ δ + r = - τ α + (1-α )= 0 ] 1 -τ

24 24 Ths mples ha he preferred ax rae (ô A ) of a young czen s: A τ = 1 -α Followng a smlar procedure, we also oban he mos desred ax rae for he old generaon a perod as ô A = 1 - á. Snce all czens have he same preferred ax rae, he equlbrum medan voer's preferred ax rae can be defned as : ô A = 1 - á. Thus we have he followng proposon: Proposon 4: In a mandaed accrual penson accounng regme, czens' (young and old) preferred ax rae as well as he equlbrum medan voer's preferred ax rae equals (1 - á). Based on he derved equlbrum ax rae and on expresson (8), we oban he equlbrum penson fundng as: A A µ S δ P = r The correspondng publc servce levels for perod and are: A S = µ T (1 -α ) r ; S A 1 = (1-α ) ( ) + 1+ δ / µ ( 1+ δ / ) T r +2 From Proposon 4 s clear ha, gven he regme of accrual penson accounng, all czens wll agree upon a consan ax rae a equlbrum. Ths means ha hs preference s ndependen of czens' ncome levels. Ths dramac dfference n preferred ax raes among czens n he accrual vs. he lassez-fare regmes s manly due o he fac ha he curren penson fundng P A has no effec on he fuure publc servce level S A (see expresson (9a)). Therefore, n an accrual regme he curren ax decson, alhough affecs he curren publc servce level and he amoun of penson fundng, no longer affecs he level of fuure publc servces. In conras, n a lassez-fare regme he ax rae decson can affec he level of fuure publc servces va he choce of penson fundng level seleced by he governmen f he medan voer belongs o he young generaon (see expresson (1)). Ths s because

25 25 penson fundng s a choce varable for he governmen. In an accrual regme, he curren level of penson fundng s enrely deermned by he level of curren publc servces chosen. The level of fuure publc servces s a decson o be made solely by czens n he nex perod. Curren czens canno affec he level of fuure publc servces hrough curren ax rae or penson fundng decsons. As a resul, when czens (boh he young and he old) consder he ax rae ssue, hey only ake no accoun rade-offs beween prvae consumpon and publc servces n he curren perod. Based upon he resuls from Secon 3 (lassez-fare) and Secon 5 (accrual), we nex compare he effecs of he dfferen penson accounng regmes on he equlbrum ax rae and publc servce level. 6 Economc Consequences -- Lassez-Fare vs. Accrual Accounng Regmes n a Growng Economy Noe ha n a lassez-fare accounng regme, he equlbrum penson fundng could be greaer, less, or equal o penson amouns under he accrual regme. In he case where a penson s already fully funded n he lassez-fare envronmen, here are no economc consequences of mandang accrual penson accounng. We hus have wo poenally neresng cases lef: over-funded or under-funded penson accouns. Emprcal evdence (e.g., Wlshre Assocaes Inc [1990], Zorn [1992]) suggess ha penson underfundng (.e., acual penson fundng s smaller han P A ) s common n U.S. sae and local governmens. As a resul, n hs subsecon we wll focus on he case of under-funded pensons n a lassez-fare accounng regme. The frs sep of our analyss s o esablsh he suffcen condon under whch penson underfundng would occur n a lassez-fare accounng regme. Lemma 6: In a lassez-fare economy, he acual penson fundng wll be smaller han he accrual amoun f [äô M - (ä+r ) P M /T ] > 0, gven ha he economy s growng. Proof: (See Appendx F).

26 26 Recall ha T s he oal axable ncome n he communy. Hence, he rao of penson fundng o he oal ax base (P M /T ) n Lemma 6 s lkely o be very small compared o ä (he rao of he penson amoun o he earned ncome), r ( he gross rae of reurn), and ô M (he ax rae) (Zorn, [1992]). Hence, we beleve s reasonable o assume ha he nequaly n Lemma 6 holds, and herefore ha pensons wll be under-funded n a lassez-fare economy. As a resul, we assume ha [äô M - (ä+r ) P M /T ] > 0 n our analyss hereafer, and ha he penson s under-funded n a lassez-fare accounng regme. Based upon hs assumpon, we nex examne he economc effecs of mandang an accrual accounng sysem for pensons. By comparng he equlbrum penson fundng and ax rae n Secon 3.1 and 3.2 (ô M and P M ) and he equlbrum penson fundng and ax rae n a mandaed accrual regme, (ô A and P A ) n Secon 5, we oban: Proposon 5: In a growng economy: a) The equlbrum ax rae of a governmen n an accrual penson accounng regme s srcly hgher han ha n a lassez-fare regme, and b) he equlbrum publc servce level n an accrual accounng regme s srcly lower han ha n a lassez-fare penson accounng regme. Proof: (See Appendx G). The nuon concernng he equlbrum ax rae s as follows. Under he assumpon of balanced-budges and penson underfundng, mandang he accrual accounng for pensons would force he czens o pay he full cos (wage plus presen value of penson) of publc servces n he curren perod. In conras, f full fundng s no requred, a czen has an opon o defer par of he cos of publc servces o he fuure. Thus, he preferred ax rae under lassez-fare would be smaller han under he case of mandaed accrual accounng. The nuon concernng he equlbrum publc servce level s as follows. Based on Proposon 5(a), he equlbrum ax rae s hgher n he regme wh accrual penson accounng regulaon. A frs glance, gven ha he "cos" (wages plus dscouned penson lably accrued as a curren expense) for hrng a publc employee s fxed, may appear ha governmens should be able o provde a hgher level of curren publc servces snce he oal curren ax revenue s hgher. However, a src accrual

27 27 accounng regulaon plus he balanced-budge fundng requremen also rases he amoun of requred penson fundng level. As a resul, he "cos" of hrng a publc employee also ncreases. Proposon 5 ndcaes ha accrual penson accounng and a full fundng assumpon resul n a hgher ax rae and a lower publc servce level. In oher words, an accrual penson accounng requremen prevens he young generaon czens from akng advanage of he poenal growh opporuny n he economy by deferrng he fundng for fuure pensons and herefore consumng more of he publc servces currenly. 6.1 Welfare Implcaons of Mandang Accrual Penson Accounng n a Growng Economy If he accrual penson accounng s mandaed a perod and s held n all fuure perods, Proposon 5 says ha he lkely oucomes n a growng economy are: 1) an ncrease n ax rae (.e., an decrease n he level of prvae consumpon n a gven perod); and 2) a decrease n he level of publc servces provded. As a resul, he level of uly for boh young and old czens wll decrease. Ths means ha here would be a negave mpac on he overall socal welfare f an accrual-bass accounng were mandaed, gven ha he economy s growng. In conras, n a lassez-fare accounng regme, he level of penson fundng can be used as a mechansm of smoohng he consumpon of publc servces across perods when he economy s growng. Gven he assumpon ha he economy s growng, he ax base of he localy s expandng over me. As a resul, czens n each generaon may be beer off by deferrng par of he fscal burden o he nex generaon, f he burden shfed o he nex generaon s bearable o he czens n he followng perod. Alhough requrng czens o pay full coss of publc servces by mandang an accrual-bass accounng may be more conssen wh he noon of "Inerperod Equy" (GASB [1987]), he same regulaon may also lm he effcency wh whch czens can arrange (va deferrals of penson fundng) o smooh her consumpon paern of prvae goods and publc servces across perods. Thus, n growng economes here may be a rade-off beween economc effcency and nerperod equy concerns when mandang an accrual penson accounng sandard n governmens.

28 28 7. Effecs of Mandang Accrual Penson Accounng n a Declnng Economy The resuls repored above are based on he assumpon of a growng economy. In hs secon we brefly presen and dscuss he effecs of mandang accrual penson accounng on czens' welfare n a declnng economy. Alhough no dealed proofs are provded here (hey are avalable from he auhors upon reques), we are able o show ha f accrual penson accounng s mandaed n a declnng economy: 1) he equlbrum ax rae wll decrease; and 2) he publc servces provded by he governmen wll also decrease. As a resul, mandang accrual penson accounng reduces he uly of old generaon czens. Ths s because n a declnng economy an old generaon czen wll be he medan voer and n a lassez-fare seng old czens could choose her mos preferred fscal polcy -- whch s dfferen from he one n he accrual accounng regme. In conras, for young czens he effec of mandang accrual penson accounng n a declnng economy s ambguous. A young generaon czen's uly level mgh mprove by mandang accrual penson accounng f she prefers fundng a subsanal amoun of penson n he lassez-fare accounng regme (.e. closer o he full-fundng amoun); or, her uly mgh decrease f she prefers fundng a mnmum amoun of penson (.e., sgnfcanly less han he full-fundng amoun). The fac ha some young generaon czens could mprove her uly levels whle all old generaon czens would be hur by mandang accrual penson accounng suggess ha he governmenal accounng sandard seers should consder he fac ha accounng regulaon can have a dfferenal effec on dfferen groups of czens n a declnng economy. Our model, havng shown he poenal conflc of neress beween young generaon czens and old generaon czens concernng penson accounng sandards n a declnng economy, suggess ha ner-czen equy as well as nerperod equy ough o be consdered when assessng he equy effecs of accounng sandards. 8. Summary, Lmaons, and Fuure Drecons Ths paper analyzes he economc effecs on czens of mandang accrual penson accounng sandards n governmens. Usng an overlappng generaons model, we frs demonsrae ha young generaon czens have ncenves o fund pensons n order o smooh her consumpon of prvae