The balanced budget multiplier and labour intensity in home production

Transcription

1 Inenaonal Jounal of Economc Behavo and Oganzaon 205; 3(2-): Publshed onlne Febuay 26, 205 (hp:// do: 0.648/j.jebo.s ISSN: (Pn); ISSN: (Onlne) The balanced budge mulple and labou nensy n home poducon Masaosh Yoshda, *, Sephen J. Tunbull 2 Faculy of Economcs, Ryukoku Unvesy, 67, Fukakusa, Tsukamoo-cho, Fushm-ku, Kyoo, Japan 2 aduae School of Sysems and Infomaon Engneeng, Unvesy of Tsukuba, --, Tennoda, Tsukuba, Ibaak, Japan Emal addess: yoshda@econ.yukoku.ac.jp (M. Yoshda) To ce hs acle: Masaosh Yoshda, Sephen J. Tunbull. The Balanced Budge Mulple and Labou Inensy n Home Poducon. Inenaonal Jounal of Economc Behavo and Oganzaon. Specal Issue: Recen Developmens of Economc Theoy and Is Applcaons. Vol. 3, No. 2-, 205, pp do: 0.648/j.jebo.s Absac: Ths pape shows ha he labou nensy of home poducon of a fnal consumpon good affecs naonal ncome and ncome mulple effecs of publc expendue fnanced by axaon. A educon n labou nensy nceases he level of naonal ncome bu deceases he magnude of he balanced budge mulple effec. Ths esul holds whehe he ax nsumen s dsoonay o non-dsoonay. I follows ha he ecen dffuson of labou-savng nnovaons such as washng machnes and vacuum cleanes may have he effec of deceasng he effecveness of fscal polcy. Keywods: Mulple Effecs, Publc Expendue, Taxaon, Labou Inensy, and Home Poducon. Inoducon In an mpefecly compeve economy, Dxon (987), Mankw (988) and ohes showed ha an expanson of publc expendue fnanced by lump-sum axaon gves se o a posve ncome mulple effec. Howeve, Molana and Mouos (99) poned ou ha hs effec depends on he ype of axaon whch he govenmen uses o fnance s expendue and showed ha () he mulple effec s zeo when axes ae popoonal o oal ncome (wage and pof ncome) and () can be negave when axes ae leved on wage ncome alone. Afe ha, Hejda, Lgha, and van de Ploeg (998) showed ha esul () depends on he assumpon of he Cobb-Douglas uly funcon wh unay elascy of subsuon beween lesue and consumpon and demonsaed ha when hs elascy s smalle (geae) han uny, he mulple effec s posve (negave). All of hese ncome mulple effecs ely ccally on how he household s labou supply o he make (make labou), whch s he esdual of lesue, esponds o vaous ypes of axaon. Howeve, followng he heoy of me allocaon ognaed by Becke (965), wokng me n home poducon (home labou) s anohe mpoan faco affecng make labou. Fo example, no only npus of nemedae goods bu also asssance of home labou s necessay o poduce eldely and chld cae a home; boh gasolne and p me as npus ae ndspensable o avel by ca. Theefoe, s mpoan o exploe how home poducon of a fnal consumpon good needng labou as an npu affecs ncome mulple effecs of publc expendue. Ths pape fomulaes a smple mpefecly compeve model wh home poducon based on he followng assumpons: () a Cobb-Douglas uly funcon conssng of lesue and a fnal consumpon good; (2) a Leonef poducon funcon conssng of home labou and he compose nemedae good; (3) consan euns o scale echnology unde whch a monopolsc fm poduces s oupu wh labou as he sole poducon faco. In hs model, he magnal popensy o consume he compose good ou of household ncome depends on labou nensy of home poducon, ha s, he home labou-compose good ao. A educon n labou nensy sgnfcanly affecs ncome mulple effecs of publc expendue, because nceases he household s demand fo he compose good. When publc expendue s fnanced by lump-sum axaon, a educon n labou nensy nceases he equlbum level of naonal ncome. Howeve, deceases he magnude of he mulple effec. In he lump-sum ax sysem, as hee s only he ncome effec, an ncease n he lump-sum ax leads o a decease n lesue whch s a nomal good. Snce he fnal consumpon good s also a nomal good, home labou also deceases f s equed o poduce hs good. Thus, make labou and hence naonal ncome fuhe ncease.

2 24 Masaosh Yoshda and Sephen J. Tunbull: The Balanced Budge Mulple and Labou Inensy n Home Poducon Wh dsoonay ncome axaon, he ncome ax ae affecs he magnal popensy o consume he compose good hough he effec on he cos shae of hs good n home poducon. Theefoe, ogehe wh labou nensy, hs ax ae plays a ccal ole n deemnng he magnude of he mulple effec. The labou nensy effecs on naonal ncome and he balanced budge mulple also hold n he ncome ax sysem. Ths suggess ha he dffuson of labou-savng nnovaons such as washng machnes and vacuum cleanes may have he effec of deceasng he effecveness of fscal polcy. In he compehensve ncome ax sysem, whee ax aes on wage and pof ncome ae he same, he mulple effec s posve n he pesence of home labou. Wh he Cobb-Douglas uly funcon, he ncome ax ae does no affec lesue snce ncome and subsuon effecs cancel. Hence, whou home labou, an ncease n hs ax ae fo fnancng publc expendue does no change make labou and naonal ncome. Howeve, a decease n he fnal consumpon good due o ncome axaon leads o a educon n home labou. Ths denfes he channel fo he posve mulple effec n he household poducon economy. Ths esul may no hold when hee s a dffeenal ncome ax,.e., he wage and pof ncome ax aes ae dffeen. Howeve, even when govenmen can no use a pof ncome ax a all as a polcy nsumen, he mulple effec s posve f labou nensy s suffcenly hgh when he economy s opeang on he upwad slopng secon of he Laffe cuve. In hs ncome ax sysem, lesue nceases because he subsuon effec domnaes he ncome effec on lesue. Howeve, snce households subsue lesue fo he fnal consumpon good, home labou deceases. Naonal ncome nceases, as he decease n home labou domnaes he ncease n lesue, mplyng an ncease n make labou. Ths pape s oganzed as follows. Secon 2 pesens an mpefecly compeve model wh he home poducon. Secon 3 sudes how a change n labou nensy of home poducon affecs naonal ncome and he balanced budge ncome mulple effecs of publc expendue. Fnally, secon 4 povdes a bef concluson. 2. The Model Fs, le us descbe he behavou of he dencal households. Fo smplcy, we nomalze he numbe of households o uny. A epesenave household deves uly u fom pue lesue X and a fnal consumpon good Z. We assume he followng Cobb-Douglas uly funcon: u U( X, Z) X Z α α. () Followng Becke (965), he fnal good s poduced by usng home labou H, and I vaees of nemedae goods, (,..., I d d d,..., d ). We assume ha echnology of consumpon s gven by he followng Leonef household poducon funcon: C H Z Γ ( d, H) mn( C/ a, H/ a ), (2) whee C s a CES-aggegaon of d: I ( )/ /( ) C Θ ( d ) I[( I) ( d ) θ θ ] θ θ. (3) The compose nemedae good C and home labou H ae no subsuable. Howeve, he dffeen vaees ae subsuable and he elascy of subsuon beween hem s gven by he paamee θ ( > ). Snce he household effcenly poduces he fnal consumpon good, follows C H fom (2) ha C a Z and H a Z. Theefoe, holds ha H C, whee s he non-negave labou nensy n home poducon,.e., / H C H C a / a 0. The C H coeffcens, a and a, denoe he npu of he compose good and home labou, especvely, pe un of he fnal good. The epesenave household has a me endowmen of uny avalable fo wokng, excludng pue lesue. Ths s allocaed o home labou and make labou. Denong labou supply o he make by L, he me consan of he household s epesened as X + H + L. We now choose he pce of make labou,.e., he wage, as he numeae. Then, he household budge s gven by I pd ( ) L + ( τ) Π T, whee p ( p,..., p,..., p ) s he pce veco of he nemedae goods, Π s pof ncome dsbued o he household, and τ ae axes on wage and pof ncome, especvely, and T s a lump-sum ax. The uly maxmzaon poblem fo he epesenave household can be solved as follows. ven levels of C and p, he household mnmzes s expendue pd. The opmal soluons fo d C: d (,..., I ) ae gven by ( p P) θ C, whee P s he consume pce ndex fo θ I θ /( θ) P I [ I ( p) ], (4) and holds ha mnpd PC. Usng hs and he me consan, he household budge becomes PC + ( )( H + X) F, whee F s full-employmen dsposable ncome,.e., F + ( τ) Π T. Now, usng C C a Z and H H a Z, hs budge can be ewen as ( ) X + QZ F, (5) whee Q s he shadow pce of he fnal consumpon good C H and s compued as Q Pa + ( ) a. The household maxmzes he Cobb-Douglas uly funcon gven by () wh espec o X and Z subjec o he household budge The govenmen can ax consumpon of households as well as wage and pof ncome. Howeve, any one of hese ax nsumens s edundan. Theefoe, whou loss of genealy, we se he consumpon ax ae o be zeo n hs pape.

3 Inenaonal Jounal of Economc Behavo and Oganzaon 205; 3(2-): (5). We oban he opmal soluons fo pue lesue and he fnal consumpon good as follows: X ( α) F/( ) and Z αf/ Q. The opmal level of he compose nemedae good s gven by cf, (6) P C C a Z whee c s he magnal popensy o consume he compose good ou of full-employmen dsposable ncome. The magnal popensy o consume depends on he labou nensy, snce we can ewe c as c sα, whee s s he cos shae of he compose good n household poducon,.e., s PC/ QZ P/[ P + ( ) ]. Dffeenang C n (6) wh espec o, we oban C cf ( ) αp C < 0, whee c < 0 2. (7) P [ P + ( ) ] Theefoe, a educon n he labou nensy nceases he household s demand fo he compose nemedae good. 2 Second, le us fomulae he govenmen seco. The govenmen mposes lump-sum and ncome axes on households o puchase I vaees of he nemedae goods, (,..., I g g g,..., g ). The govenmen s budge s gven by pg L + τ Π + T. Fo smplcy, we assume ha he CES-aggegaon of g s he same as ha of d. 3 Then, follows fom (3) ha Θ( g ), whee s he compose nemedae good. ven levels of and p, he govenmen mnmzes s expendue pg wh espec o g subjec o hs consan. The opmal soluons fo (,..., I ) ae gven by g ( p P) θ. Usng mnpg P, he govenmen s budge consan can be ewen as g P L + τπ + T. (8) ven he level of, he govenmen mus deemne each of hee ax vaables ( T,, τ ) so as o sasfy hs budge consan. Thd, he poducon seco of he model s fomulaed as follows. Evey nemedae good s poduced by a sngle fm, so ha hee ae I fms. We assume ha he numbe of fms s so lage ha he behavou of an ndvdual fm can no nfluence macoeconomc vaables,.e., P, C, and. 2 A educon n he labou nensy nceases he household s make labou, 2 because follows fom X 0, H αfp/[ P + ( ) ] > 0, and X + H + L 0 ha L H < 0. 3 Unde hs assumpon, because he pvae and publc demand funcons fo oupu of a monopolsc fm have he same pce elascy θ, he aggegae pce elascy of demand s no affeced by he composon of aggegae demand. Unde consan euns o scale echnology, fm poduces s oupu y wh labou l as he sole poducon faco. The poducon funcons of all fms ae assumed o be he same. They ae gven by y l / ϕ, whee ϕ ( > 0) s he consan magnal cos n ems of uns of labou. The common wage ae s pad by fms because labou s moble acoss fms. Unde he Couno assumpon ha he ohe fms do no change he oupu levels, fm maxmzes s pof, π ( p ϕ) y, wh espec o oupu y subjec o / he nvese demand funcon, p [ y /( C )] + θ P. 4 As a esul, magnal evenue should equal magnal cos. The pof maxmzaon condon s gven by p p µϕ, whee µ θ/( θ ) >, ha s, µ s pce mak-up on vaable labo cos. I follows fom (4) and p p fo all ha P p µϕ. Thus, he pce ndex P s consan. Fnally, an mpefecly compeve equlbum s descbed. We esc ou aenon o a symmecal equlbum, whee he followng condons ae sasfed: d d, g g, and y y. In hs equlbum, holds ha C Id and Ig. Defnng naonal ncome (aggegae oupu) by Y p y / P. Aggegae pof, we oban Y Iy Π π can be epesened as a lnea funcon of naonal ncome,.e., Π θ PY. The symmecal equlbum condons ae shown by he followng smulaneous equaons whch have naonal ncome Y and any one of govenmen s polcy nsumens ( T,, τ, ) as unknown vaables: 5 + τ θ +, (9) Y c[( ) P ( ) Y P T] [ ( τ ) θ + ] Y + P T. (0) Eqs. (9) and (0) ae he goods-make equlbum condon n aggegae fom and he govenmen s budge consan n ems of naonal ncome, especvely Labou Inensy and he Balanced Budge Mulple In hs secon, we sudy how a change n he labou nensy of home poducon of he fnal consumpon good affecs an equlbum level of naonal ncome and he balanced budge ncome mulple effecs of publc expendue fnanced by vaous ypes of axaon. The wo ways fo fnancng publc expendue ae consdeed: lump-sum axaon and ncome axaon. Iespecve of hese 4 The nvese demand funcon of fm can be obaned by elmnang and g fom d ( p P) θ C, g ( p P) θ, and d + g y. 5 We need no consde he labou-make equlbum condon n he followng analyses due o Walas s law. 6 We can deve (0) by usng he govenmen s budge consan (8) and he deny n naonal ncome accoun,.e., PY L + Π. d

4 26 Masaosh Yoshda and Sephen J. Tunbull: The Balanced Budge Mulple and Labou Inensy n Home Poducon fnancng ways, wll be shown ha a educon n labou nensy nceases he level of naonal ncome bu deceases he magnude of he balanced budge mulple effec. 3.. Lump-Sum Taxaon Unde hs ax sysem, he goods-make equlbum condon (9) and he govenmen s budge consan (0) become Y c( P + θ Y P T) +, () P T, (2) especvely, whee c αp/( P + ). Elmnang T fom () and (2), we oban he equlbum level Yˆ of naonal ncome: ˆ c( P ) + Y > 0, (3) θ c whee 0 θ < c < and P P ( T) > 0. Thus, we assume ha T <, ha s, he lump-sum ax does no consume all of full ncome. Dffeenang Yˆ n (3) wh espec o, we have ˆ c( P + θ ) Y < 0 2. ( θ c) Nong ha c < 0 n (7), we fnd ha Yˆ s negave. Theefoe, fo a gven level of publc expendue, a educon n he labou nensy nceases he equlbum level of naonal ncome. Ths s because he household s demand fo he compose nemedae good s smulaed. Fom (3), we also have ˆ c Y > 0. c θ Ths s he well known esul n an mpefecly compeve economy ha he ncome mulple effec of publc expendue due o he ncease n pof s posve. c Now, dffeenang Yˆ wh espec o and usng <0, we oban ˆ c( θ ) 2 Y > 0. ( θ c) Thus, a educon n he labou nensy deceases he magnude of he mulple effec. 7 We can nuvely explan hs esul as follows. Snce hee s now only he ncome effec, an ncease n he lump-sum ax fo fnancng publc expendue leads o a decease n lesue whch s a nomal 7 Noe ha hs mples ha he effec n he model wh home labou (.e., > 0) s geae han ha n he adonal model whou (.e., 0). good. The fnal consumpon good s also a nomal good. Theefoe, f home labou s equed o poduce hs good, make labou and naonal ncome fuhe ncease snce home labou as well as lesue deceases Income Taxaon Unde he ncome ax sysem, he goods-make equlbum condon (9) and he govenmen s budge consan (0) become + τ θ +, (4) Y c[( ) P ( ) Y] [ ( τ ) θ ] Y +, (5) especvely. Noe ha he magnal popensy of consumpon c depends on he wage ax ae as well as he labou nensy. ven levels of Y and, he govenmen mus deemne wo ax aes, and τ, so as o sasfy (5). Elmnang fom (4) and (5), we oban c( ) P Y. (6) + ( τ) θ ( τ) θ Fo a gven level of publc expendue, ogehe wh (5), (6) deemnes naonal ncome Y and he wage ax ae n he symmecal equlbum. In hs pape, we ea he wage ax ae as an endogenous vaable and analyze he wo pola cases wh espec o he pof ax ae τ. In he one case, he govenmen equalzes he pof ax ae o he wage ax. We call hs he compehensve ncome ax sysem. In he ohe, he govenmen ses he pof ax ae o zeo. We call hs he dffeenal ncome ax sysem. () The Compehensve Income Tax Sysem Snce τ n hs ax sysem, (5) and (6) become Y, (7) cp Y, (8) θ c especvely. The se of he ncome ax ae and naonal ncome whch sasfy (7) s shown by he hypebola BC n Fg.. On he ohe hand, follows fom (8) ha cp Y ( θ c) 0 2 αp, whee c 0 2. [ P + ( ) ] Thus, f he labou nensy s posve,.e., > 0, a se of he ncome ax ae and naonal ncome whch sasfy (8) s shown by he upwad slopng cuve ME. Ths cuve nesecs he hozonal lne,.e., Y Y, a he pon (, Y ), whee Y α/ P( αθ ) > 0. Noe ha hs hozonal lne s he ME n he case of 0.

5 Inenaonal Jounal of Economc Behavo and Oganzaon 205; 3(2-): ˆ Y > 0 and J ( θ α) P + ˆ α[( θ α) P + ] > 0 2, JY ( + α) whee J + ( Y/ Y ) > 0, we can confm an ncease n naonal ncome. Dffeenang Yˆ wh espec o, we oban ˆ ( θ α) P 2 Y > 0. [( θ α) P + ] Fg.. The mulple effec unde he compehensve ncome ax sysem. The nesecon pon E of he hypebola BC and he cuve ME s he unque equlbum pon. The ax ae and naonal ncome n he equlbum ae gven by ˆ [( αθ ) + ] P + α and ˆ +α Y ( αθ ) P +, especvely. Dffeenang Yˆ wh espec o, we oban whee ˆ ( Y) P( αθ ) Y < 0 2, [( αθ ) P + ] ˆ / ( P ) < Y Y α αθ. Thus, a educon n he labou nensy nceases he equlbum level of naonal ncome. 8 Ths mples ha he equlbum naonal ncome wh home labou s smalle han ha whou. A se n publc expendue shfs he hypebola BC upwad. Howeve, he cuve ME does no shf. The equlbum pon moves fom E o E (see Fg.). Snce Yˆ Y n he case of 0, naonal ncome s no affeced by publc expendue. Howeve, naonal ncome nceases n he case of > 0. Toally dffeenang (7) and (8) a a neghbohood of he equlbum pon o vefy mahemacally hs esul, we oban dy + ( Y/ ) d (/ ) d, ( / Y) dy + d 0, whee Y > 0. Snce holds ha Thus, he magnude of he mulple effec deceases wh a educon n he labou nensy. 9 Noe ha he mulple effec s posve wh home labou, bu hs effec s zeo whou. We can explan he nuon behnd hese esuls. As was poned ou by Hejda, Lghha and van de Ploeg (998), wh he Cobb-Douglas uly funcon he ncome ax ae does no affec lesue, snce ncome and subsuon effecs n lesue cancel due o he unay elascy beween lesue and he fnal consumpon good. Hence, whou home labou, an ncease n hs ax ae fo fnancng publc expendue does no change make labou and naonal ncome. Howeve, a decease n he fnal good due o ncome axaon leads o a educon n home labou. Ths denfes he channel fo he posve mulple effec n he household poducon economy. (2) The Dffeenal Income Tax Sysem Snce he pof ax ae s zeo n hs sysem, he govenmen s budge consan (5) and he goods-make equlbum condon (6) become ( θ ) Y, (9) ( ) cp Y, (20) θ c ( θ ) especvely. The se of he wage ax ae and naonal ncome whch sasfy (9) s shown by he downwad slopng cuve. Dffeenang (20) wh espec o, we have c( )[ ( θ )] c( c) θ Y 2. (2) P[ θ c ( θ )] Alhough he second em n he numeao of he gh-hand sde on (2) s negave, he fs em s no so. Theefoe, snce he sgn of Y s ndeemnae, he confguaon of he cuve ME s ambguous n geneal. 8 Ths esul can be geomecally confmed n Fg.. I follows fom (9)and c < 0 ha Y < 0. Theefoe, fo a gven level of publc expendue, snce a decease n shfs he cuve ME upwad, he equlbum pon moves fom E o E, so ha naonal ncome nceases. 9 eomecally, hs esul can be explaned as follows. In Fg., snce he angen of he ME cuve s seep when he labou nensy s hgh, he upwad shf of he BC cuve due o an ncease n publc expendue poduces he gea expanson effec on he equlbum naonal ncome.

6 28 Masaosh Yoshda and Sephen J. Tunbull: The Balanced Budge Mulple and Labou Inensy n Home Poducon In he case of 0, follows fom (2) and c 0 ha Y < 0. Thus, whou home labou, as s llusaed n Fg.2, he cuve ME s downwad slopng. Fo a gven level of, should be now noed ha hee ae wo equlbum pons. 0 As nceases, he one pon moves on he lne ME, nceasng bu deceasng Y. See he movemen of he equlbum pon fom E o E n Fg.2. Ths movemen ases n he upwad secon of he Laffe cuve. Thus, a se n publc expendue deceases naonal ncome. Fom (20) and c < 0, we also have gea,.e., > P( α)/( θ ), he fs em n he numeao of he gh-hand sde on (22) s domnan. Thus, holds ha Y > 0 fo low ax aes. If he economy s opeang on he upwad slopng secon of he Laffe cuve (see Fg.3), hen a se n publc expendue nceases naonal ncome. Y c( )[ ( θ )] < 0 2. P[ θ c ( θ )] In Fg.2, hs mples ha a se n shfs he cuve ME downwad. Theefoe, fo a gven level of publc expendue, an ncease n he labou nensy deceases he equlbum level of naonal ncome. The same esul holds n he case of > 0, oo. Fg. 2. The mulple effec unde he dffeenal ncome ax sysem whou home labou (.e., 0 ). On he ohe hand, f > 0, he fs em n he numeao of he gh-hand sde on (2) s posve. Snce holds ha Y <0 a a neghbohood of, he cuve ME s downwad slopng. Howeve, nong ha a 0, (2) can be ewen as ( θ ) θ P( α) Y 2, (22) Pc ( P + )( θ c) he cuve ME may be upwad slopng a a neghbohood of 0. If a posve value of he labou nensy s suffcenly 0 In he dffeenal ncome ax sysem, he ncome ax ae and naonal ncome n he equlbum canno be explcly solved as funcons of publc expendue. Noe ha he ohe equlbum pon moves n he oppose decon on he lne ME n Fg. 2. Ths movemen ases n he downwad secon of he Laffe cuve. Fg. 3. The mulple effec unde he dffeenal ncome ax sysem wh home labou (.e., > 0 ) and he Laffe cuve. In ode o vefy he above geomecal esuls, oally dffeenang (9) and (20) a a neghbohood of he equlbum pon, we oban ( / ) [/( θ )] dy + Y d d, Fom hese equaons, we have ˆ Y ( θ ) ( / Y) dy + d 0. K and ˆ, ( ) KY whee ( / ) K Y Y +. If he economy s opeang on he upwad slopng secon of he Laffe cuve, follows fom θ

7 Inenaonal Jounal of Economc Behavo and Oganzaon 205; 3(2-): ˆ > 0 ha KY > 0. I holds ha Y < 0 n he case of 0. Snce K < 0, we can deve Y ˆ < 0. Bu, as has been aleady menoned, f he sgn of s posve and s value s suffcenly gea, s possble ha Y > 0 a a neghbohood of 0. In hs case, follows fom K > 0 ha Y ˆ > 0. In he dffeenal ncome ax sysem, wh home labou s possble ha he mulple effec s posve, whle whou hs effec s negave. The nuon behnd hese esuls can be explaned as follows. Because axes ae mposed on only pa of household ncome, he ax ae n hs ax sysem mus be nceased by moe han n he compehensve ax sysem, n ode o manan a balanced budge. Snce he posve subsuon effec domnaes he negave ncome effec n lesue, he wage ax ae nceases lesue. Thus, n he Molana and Mouos (99) model whou home labou, an ncease n hs ax ae deceases make labou and naonal ncome. Howeve, as a se n he wage ax ae nduces households o subsue lesue fo he fnal consumpon good, hs good and hus home labou decease n he household poducon economy wh home labou. When he labou nensy s suffcenly gea, a decease n home labou may domnae an ncease n lesue, so ha make labou and naonal ncome wll ncease. 4. Concluson The objecve of hs pape has been o sudy how home poducon of a fnal consumpon good needng npus of labou as well as nemedae goods affecs ncome mulple effecs of publc expendue fnanced by of axaon n an mpefecly compeve model. In hs model, labou nensy of home poducon sgnfcanly nfluences he magnal popensy o consume he compose good ou of household ncome. Theefoe, labou nensy plays an mpoan ole n deemnng he magnude and he sgn of he ncome mulple effec. We have shown ha () a educon n labou nensy nceases he level of naonal ncome bu deceases he magnude of he balanced budge mulple effec; () hs esul holds whehe he ax nsumen s dsoonay o non-dsoonay; () n he lump-sum ax sysem, he mulple effec n he adonal model whou home labou s smalle han ha wh ; (v) n he compehensve ncome ax sysem, he effec s posve n he pesence of home labou; (v) n he dffeenal ncome ax sysem, f labou nensy s suffcenly hgh, he effec s posve when he economy s opeang on he upwad slopng secon of he Laffe cuve. Hee may be helpful o commen on he assumpons whch wee used n devng hese esuls. Fs, he home poducon funcon has been assumed o be of he Leonef ype. Ths s he sandad appoach o applyng he Becke (965) famewok, snce s flexble enough o nclude as a specal case he pue make labo-lesue adeoff, whle beng acable when used as a componen of a lage model. Ths funcon s fequenly used, fo example by Kleven (2004) n a sudy of he opmal commody ax ule wh home poducon. Second, we have assumed a Cobb-Douglas uly funcon. The Cobb-Douglas funcon s mpoan snce solaes he channel fo he ncome mulple effec va cos educon n home poducon fom he effecs of non-unay elascy of subsuon denfed by Hejda, Lghha and van de Ploeg (998). Dxon (987) assumed a Cobb-Douglas funcon whch depends on money balances as well as lesue and consumpon. Ths would add lle o ou model so we follow Mankw (988) n excludng money fom he uly funcon. Thd, we have assumed ha publc expendue s no useful. Ths s a sandad appoach whch allows us o focus solely on he ansmsson mechansm fo fscal polcy. Howeve, s mpoan o noe ha f he publc good povded conbues o educon of he cos of home poducon, hee wll be effecs on he channel dscussed n hs pape. In a companon pape, Yoshda and Tunbull (2009), we chaaceze he opmal povson of such a publc good. Inegang he fscal and publc good povson aspecs of publc expendue s beyond he scope of hs pape, and we leave as a ask fo fuue eseach. Fnally, we have no consdeed he possble effecs on savng, snce ha would eque a dynamc model. In ha case, an addonal ndependen nsumen (he consumpon ax) would be avalable. We consde exenson o a dynamc model o be an mpoan ask fo fuue eseach n hs aea. Acknowledgemen The auhos would lke o hank Pofessos A. Yaka and S. Kaku fo consucve commens. The fs auho acknowledges he fnancal suppo fom he Mnsy of Educaon, Culue, Spos, Scence and Technology of Japan unde ans-n-ad fo Scenfc Reseach C (No ). The pape s dedcaed o Pofesso Toshkazu Io on he occason of hs eemen a Ryukoku Unvesy. Refeences [] Becke,. S. (965). A Theoy of he Allocaon of Tme, Economc Jounal, 75, [2] Dxon, H. D. (987). A Smple Model of Impefec Compeon wh Walasan Feaues, Oxfod Economc Papes, 39, [3] Hejda, B. J., Lghha, J. E. and van de Ploeg, F. (998). Fscal Polcy, Dsoonay Taxaon, and Dec Cowdng Ou unde Monopolsc Compeon, Oxfod Economc Papes, 50, pp [4] Kleven, H. J. (2004). Opmal Taxaon and he Allocaon of Tme, Jounal of Publc Economcs, 88, pp [5] Mankw, N.. (988). Impefec Compeon and he Keynesan Coss, Economcs Lees, 26, pp. 7-3.

8 30 Masaosh Yoshda and Sephen J. Tunbull: The Balanced Budge Mulple and Labou Inensy n Home Poducon [6] Molona, H. and Mouos, T. (99). A Noe on Taxaon, Impefec Compeon and he Balanced Budge Mulple, Oxfod Economc Papes, 43, pp [7] Yoshda, M. and Tunbull, S. (2009). Publc oods and he Technology of Consumpon unde Impefec Compeon, mmeo.