A Correction to: The Structure of General Equilibrium Shadow Pricing Rules for a Tax-Distorted Economy

Transcription

1 A Correcton to: Te Structure of General Equlbrum Sadow Prcng Rules for a Tax-Dstorted Economy Crs Jones Department of Economcs Faculty of Economcs and Commerce Te Australan Natonal Unversty Worng Paper No 386 July 2000 JEL Classfcaton: D6; H2 Key Words: sadow prces; sadow value of government revenue; margnal socal cost of publc funds Natonal Lbrary of Australa Card Number and ISBN Number

2 Abstract Ts paper maes a correcton to te way te margnal socal cost of publc funds (MCF s used n Seper (98 to obtan uncompensated sadow prces wen transfers are made wt dstortng taxes We derve a sadow value of government revenue to measure te cange n utlty from endowng an extra dollar of revenue on te government wo transfers t to consumers Ts rater tan te conventonal Harberger measure of te MCF converts te compensated sadow prce of any good nto ts uncompensated sadow prce We use t to prove tat Ramsey optmal taxes wc mnmze te compensated taneffcency for a gven revenue requrement ave equal uncompensated margnal excess burdens per dollar cange n government revenue

3 Introducton Wen a conventonal cost-beneft analyss s used to evaluate publc sector projects te welfare effects of ter separate components are solated by lump-sum transfers Harberger (968 exploted ts property to compute te sadow prces of te ndvdual nputs and outputs for eac project Tese prces provde a way of measurng ow projects mpact on socal welfare In practce owever transfers are rarely made as a lump-sum but rater wt dstortng taxes and ts ntroduces taneffcency tat canges te sadow prces In an mportant contrbuton to appled welfare analyss Seper (98 derves mplementaton-problem corrected (ereafter corrected sadow prces as conventonal Harberger sadow prces plus te cange n tax neffcency on any notonal lump-sum transfers As a part of te analyss Seper examnes te relatonsp between te compensated and uncompensated sadow prces of goods and argues tat wt dstortng taxes tey are lned togeter by te conventonally measured margnal socal cost of publc funds (MCF In partcular t s clamed te uncompensated sadow prce of any good s equal to ts compensated sadow prce multpled by te MCF We prove owever tat ts s ncorrect Instead te sadow prces are lned togeter by te sadow value of government revenue wc s te cange n utlty wen a dollar of revenue s endowed on te government After all te compensated sadow prce s te extra revenue tat a good wll endow on te government at uncanged prvate utlty We cannot use te MCF to convert tese dollars nto utlty because t doesn t capture te value of addtonal government revenue 2 To see wy ts correcton s necessary we begn by consderng te way conventonal sadow prces are computed wen lump-sum transfers are possble Te conventonal uncompensated sadow prce of any good s equal to: 3 S p were p s te producer prce of te good and / te nduced cange n government revenue e te tax-revenue effect Seper proves tat ts s equal to te compensated sadow prce Ŝ multpled by te conventonal sadow value of government revenue 4 S Z Te compensated prce solates te potental welfare gan Wen ts gan s transferred lump-sum to consumers eac dollar rases utlty by so te fnal cange n S Z Te conventonal measure of te MCF s attrbuted to Harberger and s te welfare cange solated by lump-sum transfers 2 We sow below tat te MCF s a component of te sadow value of government revenue Wen a dollar of revenue s endowed on te government t uses dstortng taxes to balance ts budget Eac resultng dollar transferred to te prvate economy wc wll n general be dfferent from one dollar due to endogenous canges n government revenue rases utlty by te MCF 3 All te partal dervatves are tose solated by lump-sum transfers Wen actual lump-sum transfers are ruled out we use notonal lump-sum transfers 4 Seper refers to ts sadow value of government revenue as te MCF It wll be argued below tat ts s not consstent wt te conventonal Harberger measure of te MCF wc s unty for lump-sum transfers A at over a varable denotes a compensated cange All oter canges are uncompensated

4 utlty s te uncompensated sadow prce: S S Z were te terms nsde te bracets are Ŝ p Bot sadow prces cange wen transfers are made wt dstortng taxes and te corrected uncompensated sadow prce becomes: (S MH p MH 0 were s te conventonal MCF Te frst term ( / s te cange n profts on publc producton (e te proft effect and t represents te excess of te fall n 5 consumer surplus over te ncrease n producer surplus wen ome goods prces rse Te second term s te cange n utlty wen te budget surplus s transferred to consumers wt dstortng taxes; ts surplus arses from te sales revenue p plus te tax-revenue and proft effects Clearly wen taxes are non-dstortng te MCF wll be unty (wt and ts corrected sadow prce collapses to te conventonal sadow prce above Seper rearranges (S as: (S p MH M 0 0 H and clams te terms nsde te square bracets represent te corrected compensated sadow prce (Ŝ We prove below tat ts s ncorrect and clam nstead tat: H M p MH (S 0 D were s te corrected sadow value of government revenue Now te terms 6 nsde te square bracets are (Ŝ wt (S (Ŝ Te dfference between te conventonal MCF and te sadow value of government revenue s captured by te reduced form expresson: H 0Z 0Z H 0Z Te frst term s te drect mpact on utlty of endowng an extra dollar of revenue on te government and te second te cange n utlty at rate on dollars transferred to consumers to balance te government budget It s clear tat te fnal transfers to consumers (n bracets wll dffer from te ntal dollar endowed on te economy wen tere are endogenous canges n government revenue Tus wen tere are no 5 Ts follows from te fact tat all te taxes are specfc so te nduced prce canges n ome goods marets do not affect te sze of any tax wedges In te absence of publc producton canges n consumer surplus would be exactly offset by te canges n producer surplus All traded goods prces are uncanged because te economy s small n world marets and te offcal excange rate s fxed 6 Seper obtans te corrected compensated sadow prce by drectly solvng te welfare cange for dx n te compensated equlbrum Wen ts s multpled by and not as clamed by Seper we obtan te corrected uncompensated sadow prce It s argued ere tat t s ncorrect to clam 2

5 endogenous canges n government revenue but not n general oterwse 7 Addtonal nsgt s obtaned by notng te MCF s equal to d were d s te margnal excess burden of taxaton (MEB per dollar cange n government e te normalsed MEB Ts allows us to wrte te sadow value of government revenue above as: 0Z d 0Z H 0Z Te frst two terms are te conventonal sadow value of government revenue; tey measure te cange n utlty wen a dollar s endowed on te government wo balances ts budget wt lump-sum transfers Te last term s te cange n taneffcency wen te notonal lump-sum transfers are made wt dstortng taxes Havng derved we ten use t to demonstrate te somewat surprsng proposton tat Ramsey optmal taxes wc mnmze te compensated taneffcency for a gven revenue requrement ave te same uncompensated taneffcency per dollar cange n government revenue Ts follows from te relatonsp between te uncompensated normalsed MEB for any ta d and ts compensated measure ˆd were: d ˆd 8 Ts s anoter example of te way te sadow value of government revenue solates te ncome effects tat ln togeter compensated and uncompensated welfare canges; n ts case te margnal excess burdens If we tae te rato of te normalsed MEB s for any two taxes and m we ave: d ˆd d m m ˆd m Wen d d m te sadow value of government revenue s ndependent of te tax used because eac tax converts dollars of surplus nto te same cange n utlty Under tese crcumstances we ave ˆd ˆd m Ts result togeter wt te observaton by Seper tat te rato of te uncompensated sadow prces for any two goods s equal to te rato of ter compensated sadow prces means tat project evaluaton can proceed usng welfare canges computed n full equlbrum models All te ncome effects tat ln togeter te compensated and uncompensated welfare canges are ndependent of te goods and taxes beng evaluated so tey dsappear wen we tae te rato of te uncompensated welfare canges Te paper commences n te next secton by dervng reduced form expressons for te conventonal MCF and te corrected sadow value of government revenue In secton 3 we prove te structural form expresson for te MCF n Seper on page 62 s n fact te corrected sadow value of government revenue and not te conventonal 7 Seper conjectures but obtans a reduced form expresson for on page 50 wc s not consstent wt te structural form expresson obtaned n Proposton 7 on pages 6-62 (We prove below tat te reduced form expresson s for wle te structural form expresson s for In fact te excellent dscusson on pages 60-6 for te dervaton of te structural form expresson s entrely consstent wt te reduced form expresson for above 8 Seper (994 refers to ˆd as te normalsed MEB of taxaton; t s te compensated cange n te government budget surplus per dollar cange n te compensatng transfers for a margnal ncrease n ta 3

6 MCF as conjectured on page 50 Ten n secton 4 we prove tat Ramsey optmal taxes ave te same uncompensated MEB per dollar cange n government revenue Te paper concludes n secton 5 wt a bref summary of te man fndngs 2 Reduced Form Sadow Prcng Rules We use te general equlbrum model and notaton n Seper for a small open economy From te prvate sector budget constrant togeter wt te frst order condtons n compettve marets we obtan a dollar measure of te cange n utlty of: 9 dw ( dl MH dp MT (c dt y ds MH ds In essence te terms n ( are canges n consumer surplus Usng te government budget constrant any cange n te budget surplus s determned by: (2 dz dr M p d MH dp MT ds dl and te tax-revenue effects by: (3 dr MT (t dc c dt M s (dy d M ds To proceed wt a conventonal Harberger analyss we use lump-sum transfers to balance te government budget n equaton (2 (wt dz = 0 and ten obtan te conventonal welfare equaton by substtutng tese transfers drectly nto ( were: 0 dw (4 M p d MT t dc M s (dy d (dz 2 Conventonal Uncompensated Sadow Prces Usng (4 te conventonal uncompensated sadow prce of any good s: S dw (5 p dx It s te sales revenue collected by te government wen t sells te unt of good plus te tax-revenue effect 22 Corrected Uncompensated Sadow Prces Wen te government balances ts budget wt dstortng taxes we can proceed wt a Harberger analyss by usng notonal lump-sum transfers and ten offsettng tem wt adjustments to dstortng taxes By dong ts we obtan corrected sadow prces for 9 See Appendx A for a summary of te model n Seper and te dervaton of equatons ( (2 and (3 0 In a compensated equlbrum te lump-sum transfers old utlty constant n equaton ( (wt dw/ 0 and te conventonal welfare equaton s obtaned by substtutng tese transfers nto equaton (2 Now te welfare effects are equal to canges n te government budget surplus 4

7 goods tat are ter conventonal sadow prces plus any taneffcency on transfers to balance te government budget In te followng dervatons te producton tax on ome good s used to mae tese offsettng transfers Tus we use te conventonal welfare equaton n (4 and solve te tax cange usng equaton (2 wt dz 0 were: (6 dl M p d MH dp MT ds dr 0 Proposton : Te corrected uncompensated sadow prce of any good s: (7 (S S d 0L were: d 0W 0L (8 s te normalsed MEB; t s te conventonal taneffcency per dollar cange n government revenue Followng Seper we assume te taxes are Ramsey optmal were ts maes te normalsed MEB te same for eac tax 2 Proof: Wen a unt of good s endowed on te economy te dollar cange n utlty s equal to: (S dw 0W 0W ds (9 dx D dx D were te tax cange solves: dl 0L 0L ds dx D dx D 0 wt: (0 ds 0L 0L dx D Notce ow te tax cange generates notonal lump-sum transfers to offset tose arsng from te extra unt of good After substtutng (0 nto (9 we ave: 0W (S 0W 0L ( 0L wc solves to equaton (7 usng te conventonal sadow prce n (5 and te normalsed MEB n (8 Te welfare canges n (7 are solated by notonal lump-sum transfers so tey are conventonal Harberger terms And te notonal transfers arsng from te mpact of good on government revenue determne te amount of taneffcency n te corrected transfers In te analyss tat follows all te partal dervatves are solated by notonal lump-sum 2 It s proved n Proposton 6 below tat wen taxes are Ramsey optmal tey ave te same uncompensated neffcency per dollar of transfer ( d 5

8 3 sadow prce because tey must be made wt dstortng rater tan lump-sum taxes From (6 tey are: 0L (2 p MH wc s te sales revenue plus te proft and tax-revenue effects Wen government revenue rses n (2 te dstortng tas lowered to reduce revenue by te 4 same amount In oter words te extra revenue s dstrbuted by adjustng te producton tax on good to balance te government budget A reducton n te tax neffcency adds to te gan n utlty captured by te conventonal sadow prce To see ts substtute (2 nto (7 were te corrected sadow prce becomes: (S p d p (3 MH 0 Ts s llustrated n Fgure for te ome goods and were for smplcty we gnore effects n related marets and assume tere are no cross-effects between te marets for te two goods Fgure : Te Corrected Sadow Prce of Good Wen te government sells te addtonal unt of good ts maret prce wll fall to ncrease prvate demand and crowd-out prvate supply Te conventonal sadow prce s equal to areas (a+(b+(c were (a+(b s te sales revenue and (c te taxrevenue effect It s te combnaton of te drect gan n utlty (d-(e = (f plus te 3 Seper solates any taneffcency n te corrected compensated sadow prce n te same way In ts settng owever te notonal lump-sum transfers old utlty constant so te tax neffcency s defned per dollar cange n compensatng transfers rater tan per dollar cange n government revenue 4 It s assumed tax revenue rses wen tax s s rased margnally 6

9 lump-sum transfers to consumers to balance te government budget (a+(b+(c-(f 5 Wen tese transfers are made by lowerng tax s eac dollar rases utlty by te normalsed MEB; t s te taneffcency (q dvded by te cange n government 6 revenue (u+(v-(q Under tese crcumstances te corrected sadow prce s te conventonal sadow prce (a+(b+(c plus te fall n taneffcency (q were: (S (a(b(c (q (u(v (q (a(b(c (f (a(b(c(q 23 Te Conventonal MCF We obtan te corrected sadow prce for good derved by Seper n Proposton 5 on page 50 by addng and subtractng te proft effect to te corrected sadow prce n (3 Ts yelds: (4 (S MH p MH 0 were: d 0W 0L 0L (5 s te conventonal MCF; t s te drect cost to utlty per dollar cange n government revenue wen tas rased margnally 7 Ts dervaton of (S n (4 can also be llustrated n Fgure above Te frst term s area (f; t s te amount by wc te rse n consumer surplus n (d exceeds te fall n 8 prvate producer surplus n (e were (d-(e=(f Te second term s te conventonal MCF multpled by te notonal lump-sum transfers (a+(b+(c-(f; te conventonal MCF s te drect cange n utlty n (u+(v per dollar cange n government revenue n 9 (u+(v-(q Ts maes te corrected sadow prce n (4 equal to: s (S (f (u(v (u(v (q (a(b(c (f (f(u(v It s clear tat tese two approaces must yeld te same cange n utlty Ts s confrmed by recallng te notonal lump-sum transfers for dx are offset by te notonal 5 Area (f s te fall n profts on publc producton of good It terefore reduces government revenue 6 Area (w s te rse n proft from publc producton of good but t s equal to te fall n tax revenue on tat same output so t as no net mpact on government revenue 7 Ts s te reduced form expresson for te conventonal MCF n Seper on page 50 0V 0L 0V 0W 0L were: wt Notce tat Seper defnes government revenue as A ( L 8 Ts follows from s beng a specfc tax 9 Area (w s te rse n proft on publc producton of good and t s equal to te reducton n tax revenue on te same output Consequently t as no mpact on government revenue 7

10 lump-sum transfers for ds were: By addng (f and (q to bot sdes we ave: (a(b(c (f (u(v (q (S (a(b(c(q (f(u(v 24 Te Corrected Sadow Value of Government Revenue Seper proves tat wt lump-sum transfers te uncompensated sadow prce of any good s equal to ts compensated sadow prce multpled by te conventonal sadow value 20 of government revenue S Z were S S Z Ŝ We now prove ts same relatonsp for te corrected sadow prces and by dong so confrm te dfference between te conventonal MCF and te corrected sadow value of government revenue Ts leads to: Proposton 2: Te corrected uncompensated sadow prce for any good s: (6 (S (Ŝ were: (7 S Z d S Z MH s te cange n utlty from endowng a dollar of 0Z government revenue on te economy n te full equlbrum Proof: Followng Seper wrte socal welfare condtonal on te publc producton vector x and te government budget surplus Z as W(xZ were te vector of taxes v are endogenous and replace te (actual lump-sum transfers Te cange n te government budget surplus requred to old utlty constant wen good s rased margnally s defned by: (8 dw (W dx (W Z dz 0 2 From ts te compensated sadow prce of good becomes: dẑ (Ŝ (W / (S (9 dx D (W Z / were: 20 2 Ts s Proposton 4 on page 2 of Seper Te partal dervatves n (8 are: (W dw dx D 0W 0W (W Z dw 0W dz D 0Z 0W ds and dz D 8 ds dx D

11 0W dw 0W 0s 0L (20 dz D 0Z 0L 0Z Ts solves to te corrected sadow prce n (7 usng (4 were: 0W 0Z 0Z S 0L Z 0Z S Z and (6 were: H M 22 0Z By addng and subtractng te proft effect H to (7 we ave: 0Z 0Z S (2 Z 0Z H It s clear from (2 ow te conventonal MCF value of government revenue 3 Structural Form Sadow Prcng Rules Seper expresses te reduced form sadow prcng rules derved above n terms of te structural form parameters Tese parameters determne ow te economy adjusts to exogenous canges n publc producton; a structural form expresson for te conventonal uncompensated sadow prce s obtaned n Proposton 9 and te corrected uncompensated sadow prce n Proposton (8 At no stage owever does Seper derve a structural form expresson for te MCF Instead one s derved for and te clam s made t s te MCF We now prove ts s ncorrect by dervng structural form expressons for te MCF and 3 Te Conventonal MCF H dffers from te corrected sadow Proposton 3: A structural form expresson for te conventonal MCF n (5 s: ˆd (22 H 23 were: ˆd H 22 We use te transfer equaton n (6 were: dl M p d MH dp dr dz 23 We use te notaton n Seper were MT t 0c 0E M T t M jh 0ĉ j M s M jh 0y j j measures te mpact on te budget 0c j 0ĉ MjH j 0E j 0y surplus of a unt rse n real prvate spendng and 0y j j MjH j 9

12 ˆd 0Ẑ 0 ˆL (23 s te taneffcency per dollar of notonal y MH lump-sum transfer n te compensated equlbrum wen tax s s rased margnally; t s te compensated normalsed MEB 24 Proof: Usng te welfare equaton n (4 and te transfer equaton n (6 we can rewrte te reduced form expresson n (5 as: (24 H H Structural form expressons are requred for te proft and tax-revenue effects n (24 For te tax-revenue effect we ave: (25 25 and for te proft effect : x MH (26 MH x MH 26 Once tese structural form expressons n (25 and (26 are substtuted nto (24 we obtan (22 27 Ts structural form expresson for n (22 s dfferent to te expresson obtaned by Seper n Proposton 7 on pages 6-62 We now prove tat te expresson obtaned by Seper s for 24 MT t M jh For notatonal smplcty we wrte: 0ĉ M j s M jh 0y j M s 0y See Appendx A2 for a detaled dervaton of ts tax-revenue effect See Appendx A3 for te dervaton of ts expresson It sould be noted tat: MH 0 ˆq MH 27 Te worngs are presented n Appendx A4 togeter wt te dervaton of te structural form expresson for ˆd 0

13 32 Te Corrected Sadow Value of Government Revenue Proposton 4: A structural form expresson for te corrected sadow value of government revenue n (7 s: (27 ˆd H Proof: Usng te welfare equaton n (4 and te transfer equaton n (6 we can wrte te reduced form expresson for n (7 as: S (28 Z S Z 28 H 0Z 0s H Two addtonal structural form expressons are requred for te effects of te extra dollar of government revenue n (28 From Seper te conventonal sadow value of government revenue s: (29 S Z wle te proft effect s: MH MH (30 0Z H M S Z 29 j 0Z wt: j ; 30 0Z Once te sadow prce n (29 te tax-revenue effect n (25 and te proft effects n (26 and (30 are substtuted nto (28 we obtan (27 3 Contrary to te clam made by Seper n Proposton 7 t s clear from (22 and (27 tat g Seper appears to derve te structural form expresson for n Proposton 7 MEB s: 28 Usng te welfare equaton n (4 and te transfer equaton n (6 te normalsed d 0s H 29 MH 0Z Ts comes from: H M MH x 0Z Z Snce no relatve prces cange n te compensated equlbrum we ave Z 0 MH 30 3 Ts s equaton (5 n Seper Te worngs are presented n Appendx A5

14 by explotng te decomposton provded n (6 wtout realsng g 33 Corrected Sadow Prces Proposton 5: A structural form expresson for te uncompensated sadow prce of any good s: (3 (S Ŝ ˆd H ˆd #(Ŝ H were: (Ŝ Ŝ ˆd wt for H and 0 for FT 32 H Proof: Usng equatons (4 (5 (6 and (8 we can rewrte te corrected sadow prce n (7 as: (S p p 0 H 0x (32 0s H Two addtonal structural form expressons are requred n (32 for te partal dervatves tat arse from Followng te approac used earler te tax-revenue effect s: p (33 33 and te proft effect s: x Ŝ MH (34 MH x MH 34 were: 0 p 0 wt for H and 0 for FT 35 Wen te tax-revenue effects n (25 and (33 and te proft effects n (26 and (34 32 Ts corrected compensated sadow prce s Proposton 6 on page 56 n Seper 33 0ĉ MT t M 0y For notatonal smplcty we wrte: jh M s j M jh s j wt for H and 0 for FT 34 (34 comes from: MH x MH 0 p MH usng (33 and Ŝ p 35 See Appendx A6 for detaled worngs 2

15 are substtuted nto (32 we obtan ( Ramsey Optmal Taxaton and te Margnal Excess Burden of Taxaton Seper obtans Ramsey optmal taxes (on pages by equatng te uncompensated margnal taneffcency per dollar cange n government revenue on eac tax for a gven revenue requrement e equates ter uncompensated normalsed MEB Ts s dffcult to ratonalse because we now tat dollar canges n utlty are under general 37 crcumstances unrelable measures a welfare cange For ts reason we wor wt compensated measures of te taneffcency to mnmse te socal cost of rasng te requred revenue It turns out owever tat wen te uncompensated normalsed MEB s equated across dstortng taxes tey ave te same compensated taneffcency per dollar cange n transfers e te same compensated normalsed MEB Ts follows from te fact tat te compensated and uncompensated measures of te normalsed MEB are lned togeter by te sadow value of government revenue We confrm ts as: Proposton 6: Te uncompensated normalsed MEB for any ta s equal to: (35 d ˆd Proof: A reduced form expresson for te normalsed MEB n (8 s obtaned usng te cange n utlty n (4 and te cange n government revenue n (6 were: 0W ( y 0s d (36 0L 0s H Once te structural form expressons for te tax-revenue effect n (25 and te proft effect n (26 are substtuted nto (36 we ave: (37 d ˆd ˆd H Ts solves to (35 usng te structural form expresson for n (27 38 It s clear from (35 tat te corrected sadow value of government revenue lns te uncompensated and compensated normalsed MEB s for eac tan just te same way t lns te sadow prces for any good n (6 If we now tae te rato of te normalsed MEB s for any two taxes and m we ave: 36 See Appendx A7 for detaled worngs 37 Te dollar canges n utlty are relable measures of a welfare cange wen te margnal utlty of ncome s constant and ts s te case for omotetc or quas-lnear preferences 38 See Appendx A8 for detaled worngs 3

16 5 Concluson d ˆd (38 d m m ˆd m Wen te uncompensated margnal taneffcency per dollar cange n government revenue s te same for eac tax (wt d d m te corrected sadow value of government revenue n (7 s ndependent of te tax cosen so Ts s because eac dstortng tax converts a dollar of government budget surplus nto te same addtonal utlty Consequently eac tax wll ave te same compensated tax neffcency per dollar cange n compensatng transfers (wt ˆd ˆd m and ts s confrmed by (38 Ts extends te result obtaned by Seper tat te rato of te uncompensated sadow prces for any two goods s equal to te rato of ter compensated sadow prces And t means tat we can wor wt welfare canges obtaned n full equlbrum models to correctly evaluate publc sector projects Any ncome effects tat ln togeter te compensated and uncompensated welfare canges are ndependent of te goods cosen wen taxes are Ramsey optmal A dstncton s made n ts paper between te conventonal MCF and corrected sadow value of government revenue Te latter of tese measures te rate tat dollars of compensated government budget surplus rase prvate utlty wen te budget s balanced wt dstortng taxes; t terefore converts te compensated sadow prce of any good nto ts uncompensated sadow prce In contrast te conventonal MCF s te cange n utlty on dollars transferred from te government to consumers; t does not measure te cange n utlty from an extra dollar of revenue By not dstngusng between and Seper obtans a reduced form expresson tat s nconsstent wt te structural form expresson derved later n te paper Te dfferences are summarsed n te followng table were te saded cells are te expressons obtaned by Seper Clearly we cannot ave g As s to be expected te conventonal MCF wll be unty wen tere s a non-dstortng tax (wt ˆd 0 so collapses to S Z /( and te corrected sadow prce of every good collapses to ts conventonal lump-sum sadow prce Reduced Form Structural Form H H ˆd H ˆd H D H 0Z S Z H 0Z ˆd H 4

17 Fnally we proved tat Ramsey optmal taxes ave te same uncompensated MEB per dollar cange n government revenue Ts terefore maes t possble for polcy maers to set Ramsey optmal taxes usng welfare measures obtaned n full equlbrum models 5

18 Appendx A: Te model and notaton tat follows s taen from Seper (98 wt slgt modfcatons A sngle consumer maxmses U(c were c s te vector of n goods Tere are H ome goods wose prces are determned by domestc demands and supples and T fully-traded goods wose prces are determned n world marets (as a small open economy 4 Te prvate (sector budget constrant s: qc E qe py L wt: E - expendture q - te vector of consumer prces; p - te vector of producer prces; y - te vector of prvate net-outputs; e - te vector of prmary factor endowments (wc are non-traded; and L - te lump-sum transfers receved from te government Te term py captures te profts wc consumers receve as owners of prvate frms were te outputs are produced subject to te followng tecnologcal constrant: F y n 0 Te dstortng taxes (and subsdes are set n specfc terms were: p r s q r t p q s T H s > 0 producton subsdy wen y >0 s > 0 producton tax wen y <0 s < 0 producton tax wen y >0 s < 0 producton subsdy wen y <0 t > 0 consumpton tax on T Ts allows us to wrte te tax revenue collected by te government as: 39 We omt quota-protected traded goods to smplfy te analyss Also we assume tere s a sngle consumer; ts s n essence wat Seper does by assumng a dollar as a dollar for eac consumer 40 Wen tere are consumers we ave te socal welfare functon W=W(U(c were U(c s te vector of te consumer utltes Tus: dw M 0W M 0U From prvate sector utlty maxmsaton we ave: n socal welfare above to be wrtten as: 0U (c dc 0c 0U (c 0c q were ts allows te cange 0W dw M q dc wen 0U for all (e a dollar s a dollar 4 Tus n = H + T We assume all ome goods are non-traded (NT wt H = NT; ter are no quota restrcted traded goods (QT so all traded goods are fully traded T = FT 6

19 R t c s ( y T By rearrangng te prvate sector budget constrant we ave: L E py qe After totally dfferentatng ts and addng and subtractng cdq we obtan: dl de pdy ydp edq cdq cdq From te frst order condtons for consumers we ave: dw/ qdc Were de cdq qdc we can wrte ts as: dw/ de cdq and from te frst order condtons for frms: pdy 0 Usng tese frst order condtons and te fact tat dq dp ds for ome goods and dq cdt and dp yds for traded goods te cange n transfers becomes: dl dw/ (c y e dp (c e ds c dt y ds H H T T Once te maret clearng condtons are appled we ave: wc s rearranged as ( dl dw/ dp ds (c dt y ds H H T Te publc sector budget constrant s: L R px were s te vector of publc sector net outputs and px te profts from publc producton After rearrangng ts we obtan te government budget surplus: Z R px L Wen ts s totally dfferentated we obtan equaton (2 Te cange n tax revenue n equaton (3 s obtaned by totally dfferentatng tax revenue R above A2: Te tax-revenue effect s obtaned from (3 by usng te functons for prvate consumpton demand c (qe and supply y (p were: 42 (39 MT t M jh 0c 0c MT t 0s 0E Te partal cange n expendture n (39 s: 0E M s M jh M s 0y 0y j 42 0q 0q We use te fact tat: and for all g 7

20 0E 0q (40 MH c 0s 43 and te equlbrum prce canges solve te followng system of equatons: (4 0c 0y 0c j 0E 0y 0E were: (42 0s j y j j 0c J J jg 0 j 0y wt: and MjH j and 0E j MjH j 44 After substtutng te expendture cange n (40 and te prce canges n (42 nto (39 and applyng te Slutsy decomposton te tax-revenue effect becomes: 45 (43 wc smplfes to (25 y MT t M jh 0ĉ j M M s 0y s M jh 0y j A3: Te structural form expresson for te proft effect n (26 s obtaned by usng te equlbrum prce canges n (42 togeter wt te tax-revenue effect n (25 A4: Wen te structural form expressons for te tax-revenue effect n (25 and te proft effect n (26 are substtuted nto (24 we ave: 43 Usng te publc sector budget constrant we can wrte prvate expendture as: E qc qe py R px Usng q p s for H and q p s t for T we can rewrte t as: E p(e y x se t e R ( Z T were te cange n prvate expendture becomes: de MH c dp M p d M e ds MT e dt dr ( dz From te maret clearng condtons we ave: c e y and from te compettve FOC s for frms: pdy = 0 Also snce te endowments are fxed: pde = 0 44 Followng Seper we ave: j 0ĉ 0y j 45 MT t 0c 0E M T t M jh of a unt rse n real prvate spendng 0ĉ j M s M jh 0y j j s te mpact on te budget surplus 8

21 H ( y H (44 H ( y H After dvdng te numerator and denomnator n (44 by H y y H ( y H (45 H y ( y H ts becomes: wc solves to (22 usng te structural form expresson for te compensated normalsed MEB n (23 Ts normalsed MEB s obtaned usng te compensated welfare equaton: (46 dzˆ M p d ˆ MT (t dĉ s dŷ MH s (dŷ d ˆ and te transfer equaton: (47 d ˆL MH d ˆp MT (c dˆt y dŝ MH dŝ were: 0Ẑ 0s ˆd (48 0 ˆL 0 ˆp 0s H Ts solves to te structural form expresson n (23 usng (26 were: 0 ˆp M MH x H 0s A5 Wen (25 (26 (29 and (30 are substtuted nto (28 we ave: H y H (49 ( y H After dvdng te numerator and denomnator n (49 by y H ts becomes: 9

22 (50 H ( y H wc solves to (27 usng te structural form expresson for te normalsed MEB n (23 A6: Te equlbrum prce canges solve te followng system of equatons: 0c 0y j 0c 0E (5 j 0E were te cange n expendture s equal to: 0E (52 MjH c 0x j p wt for H and 0 for FT Wen (52 s substtuted nto (5 we obtan (34 by usng (33 and te Slutsy decomposton A7: After substtutng te structural form expressons n (25 (26 (33 and (34 nto (32 we obtan: S y MH ( MH (53 (S H y MH Wen te numerator and denomnator n (53 are dvded by: y H we ave: S H MH y H (54 (S ( y H Equaton (3 s obtaned usng te structural form expressons for te compensated normalsed MEB n (23 and te corrected sadow prce n (27 A8: Wen we substtute te structural form expressons n (25 and (26 nto (36 te uncompensated normalsed MEB becomes: 20

23 y (55 d H H After manpulatng (55 we ave: y H (56 d y wc smplfes to: H y y H (57 d y ( y H We obtan te structural form expresson for ˆd n (37 by usng (23 H 2

24 References Harberger AC (968 Survey of Lterature on Cost-Beneft Analyss for Industral Project Evaluaton n Evaluaton of Industral Projects UNIDO 968; Seper E (98 Te Structure of General Equlbrum Sadow Prcng Rules for a Tax- Dstorted Economy Centre of Polcy Studes Monas January 98; Seper E (994 Sadow Prces and te Margnal Excess Burden of Taxaton: Reconclng Harberger and Damond and Mrrlees mmeo ANU February 994;