Environmental Policy, Allocation of Resources, Sector Structure and Comparative Price Advantage

Siebe , Ho s A icle En i onmen al Policy, Alloca ion o Resou ces, Sec o S uc u e and Compa a i e P ice Ad an age Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik P o ided in Coope a ion wi h: Duncke & Humblo , Be lin Sugges ed Ci a ion: Siebe , Ho s (1978) : En i onmen al Policy, Alloca ion o Resou ces, Sec o S uc u e and Compa a i e P ice Ad an age, Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik, ISSN 0342-1783, Duncke & Humblo , Be lin, Vol. 98, Iss. 3, pp. 281-293, h ps://doi.o g/10.3790/schm.98.3.281 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/291410 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. 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I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by/4.0/ En i onmen al Policy, Alloca ion o Resou ces, Sec o S uc u e and Compa a i e P ice Ad an age Von Ho s Siebe * The pape analyzes how en i onmen al policy a ec s sec o s uc u e, he alloca ion o esou ces and compa a i e p ice ad an age in a wo-sec o equilib ium model. En i onmen al quali y can be conside ed as a public good being in- luenced by emissions om consump ion and p oduc ion p ocesses. Since he assimila i e capaci y o he en i onmen has been used so a as a ee p oduc ion inpu , he common-p ope y- esou ce has been hea ily o e used. En i onmen al policy a emp s o decide which o he compe ing uses o he en i onmen should ha e p io i y and by which policy ins umen s en i onmen al sca ci y can be in e nalized in o he decisions o he subsys ems o he economy. In his pape we analyze o wha ex en en i onmen al policy will a ec sec o s uc u e, he alloca ion o esou ces and ela i e p ice. Since ela i e p ice in a closed economy de e mines compa a i e ad- an age ( ela i e o he o eign coun y), he pape also answe s he ques ion o wha ex en en i onmen al policy will a ec he com- pa a i e p ice ad an age o a coun y. In o me models (Siebe 1974, 1976) only pa ial equilib ium models we e de eloped neglec ing he demand side o no closing he model wi h espec o eceip s om he emission ax. In his pape , he model is closed wi h espec o he demand side, and demand condi ions a e explici ly aken in o con- side a ion. The ame o e e ence is a wo-sec o -model in which p oduc ion gene a es pollu an s as a join p oduc . The go e nmen le ies an emission ax pe uni o pollu an emi ed o he en i onmen . We ea he en i onmen as a na ional public good and igno e in e - na ional, ansna ional and egional en i onmen al sys ems1. Sec ion I p esen s he assump ions, Sec ion II de elops he model, and in Sec ion III he implica ions o he model a e discussed. Sec ion IV poin s ou possible ex ensions. * Uni e si ä Mannheim (WH), D-6800 Mannheim A 5. 1 On hese p oblems compa e Wal e (1975). OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.98.3.281 | Gene a ed on 2023-04-04 11:54:31 282 Ho s Siebe I. Assump ions A 1. In o de o keep he model as simple as possible we assume only one ype o esou ce, R, and a p oduc ion unc ion A 2. The p oduc ion o commodi ies i — 1,2 gene a es pollu an s as a join p oduc . Fo simpli ying pu poses he e is only one ype o pollu an s. I is assumed ha pollu an s emi ed ise p opo ionally o p og essi ely wi h esou ces used, i. e. (2) S i = Hi (Q;) = H{ [F{ (Ri)] = Zi (Ri) wi h Z; >0, Z'/ ^ 0; H; > 0 The con ex emission unc ion Zi is sugges ed in ui i ely by enginee - ing p oduc ion unc ions2. Wi h he ac i i y le el o an engine eaching o exceeding capaci y, i is ealis ic o assume ha inpu s ha e o be inc eased p og essi ely o an addi ional uni o ou pu . This sugges s ha emissions ise p og essi ely. A mo e p ecise explana ion o he con exi y o he emission unc ion ollows om he applica ion o he mass balance concep o p oduc ion unc ions. In e ms o weigh a mass balance exis s be ween inpu and ou pu . Since mass canno be los in a p oduc ion p ocess, egula ou pu and emissions mus be iden ical o inpu s, in weigh e ms. De ine he p oduc ion unc ion in weigh e ms. Fo a gi en echnology his unc ion mus be conca e, i he egula p oduc ion unc ion is conca e. Then i ol- lows ha he emission unc ion Zi mus be con ex.3 A3. Resou ces may also be used o aba emen pu poses. Le S? indica e he quan i y o pollu an s educed in Sec o i. The aba emen unc ion is gi en by The aba emen unc ion desc ibes a echnology ha p e en s pol- lu an s om en e ing he en i onmen . Addi ionally i could be as- sumed ha a echnology exis s o educe pollu an s ambien in he en i onmen (wa e ea men ). A4. Ne emissions o pollu an s ambien in he en i onmen a e de ined as emissions p oduced minus emissions aba ed. A di usion unc ion is no explici ly in oduced. (1) Qi = F (Ri) wi h F'i > 0, F'l < 0 (3) s . = Fj: ( î) wi h F1.' > 0, F i < 0 (4) Si = S -Sl 2 Gu enbe g (1972), S. 326. 3 Compa e Son heime (1975). OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.98.3.281 | Gene a ed on 2023-04-04 11:54:31 En i onmen al Policy, Alloca ion o Resou ces 283 A 5. Fi ms maximize p o i s and ega d commodi y p ices, ac o p ices and he emission ax as gi en. A 6. The esou ce can be used o p oduc ion and aba emen and is gi en (5) + H2 + R[ + R 2 = R A 7. Commodi y demand is gi en by (6) Q? =Di(p, Y) wi h p = pi/p2 whe e pi indica e nominal p ices and p is he ela i e p ice. A 8. Income Y is de ined om he p oduc ion side. The e a e no sa ings. In o de o close he model, we assume ha he go e nmen spends he ax income ecei ed in o m o ans e s o he households. Consequen ly disposable income o he households is iden ical o ne na ional income a ma ke p ices and is de ined as (7) Y = pQi + Q2 Obse e ha Y includes ans e s no explici ly shown and ha p is consume s p ice and no p oduce s p ice. I Y would be de ined wi h espec o p oduce s p ice p*, emissions axes (and ans e s) would appea explici ly on he igh side o (7). A 9. Commodi y ma ke s mus be in equilib ium so ha (8) Qi = Q A 10. The go e nmen le ies an emission ax z (in nominal e ms) on ne emissions Si, wi h z being changed pa ame ically4. II. The model 1. Fac o demand by he p o i maximizing i m is gi en by maxi- mizing U = Pi Qi - (Ri + R]) — zSi s. . Qi-FilRj)^ 0 4 Addi ionally, a damage unc ion may be in oduced indica ing ha en i- onmen al quali y is a ec ed by ne emissions U = G (S) wi h G' < 0, G" < 0. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.98.3.281 | Gene a ed on 2023-04-04 11:54:31 284 Ho s Siebe H{ (Qi)-S?< 0 ^ - F (R ) < 0 - Si + SV - sj < 0 whe e deno es he esou ce p ice in nominal e ms. Assuming ha p oduc ion akes place in bo h sec o s, i. e. ha we ha e a meaning ul p oblem, and de ining = ?/p2 and z = z/p2 he condi ions o p o i maximizing ac o demand a e gi en as R = (P- ZHJ F[ (Rx) (9) = (1 - ZH2) F2 (Rg) = zFl' (Rj) 2. The sys em o equa ions (1) - (9) has he 17 a iables S?, Si, S {, Qi, Ri, R i Q , p, Y and and 18 equa ions. The de ini ion o Y in equa- ion 7 s a es ha o al demand is equal o income, so ha in a wo- sec o model he equilib ium condi ion o one o he p oduc ma ke s is edundan (Wal as Law) and should be omi ed. By subs i u ion he sys em can be simpli ied o F1 (Ri) = D1 (p, pFi (Ri) + F2 (R2)) (i) = zF l (Rj) (ii-iii) = (p-zH1) F[ (R{) (i ) = (1 -ZH2) F2 (Rg) (V) R = Rj -j- Rg Rj R*2 (Vi) To al di e en ia ion and subs i u ion o (10 i) in o (i) - ( ) yields al 0 0 1 dR1 — H j Fj dz 0 a2 0 1 0 dR2 -H2F'2dz (11) U 0 1 0 dR[ = F i dz zF 2 zF 2 zF 2 1 0 d F 2dz ~D1YF2 0 0 -b2 dp 0 OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.98.3.281 | Gene a ed on 2023-04-04 11:54:31 En i onmen al Policy, Alloca ion o Resou ces 285 The coe icien s a e de ined as ollows5 (12) o< = zH'l F? - (Pi - zH ) F'l > 0 (i) b1 = l-DlY == D2Y (ii) b2 = Dlp + D1Y Fx< 0 (iii) In (12 i) we ha e Pi = p o i = 1 and p* = 1 o i = 2. III. Implica ions The p oblem is o de e mine how he alloca ion o esou ces is a - ec ed by en i onmen al policy. We i s s udy how ac o demand o i ms changes wi h an emission ax o a gi en ela i e p ice p. We hen analyze how ela i e p ice changes, and how he alloca ion o esou ces and na ional income a e a ec ed in his case. 1. Assuming a gi en commodi y p ice and conside ing only he ac o ma ke condi ions and he esou ce cons ain , i. e. (10 ii - i), he change in ac o use in esponse o an inc ease in he emission ax is gi en by he subsys em o equa ion 11 no con aining he i h ow o he sys em and no con aining he i h column o he ma ix o de i a i es. F om appendix I we ha e he ollowing esul s dRi (13 i) —-i > 0 dz (13 ii) <0: H^F'^H'zF, ZdR; (13 iii) -^<0 H- F- indica es he ma ginal endency o pollu e (pe uni o e- sou ce). Hx Fx > H2 F'2 speci ies ha Sec o 1 is pollu ion in ensi e6. Fo 5 b2 < 0 ollows om Slu sky's ule. Le D^ deno e he pu e subs i- u ion e ec . We ha e comp, Di*> = Di*W ^ o Di*w = Di*> + (Rl) = b2 < 0 , since he pu e subs i u ion e ec is always nega i e. S Sp « I Z1 (Rx) > Z2 (R2) o Rx = Rg, H^ F^ > H'2 F'2 can be speci ied as~ > ^ o R{ > R2. This ans o ma ion also holds o R < R2 i ei he Sec o 1 is no " e y" small compa ed o Sec o 2 o i Z2 has a su icien ly weake cu - a u e han Zx. Obse e ha H'x F^ > H'2 F'2 demands ha he Z unc ion should no c oss, i. e. emission in ensi ies should no be e e sed. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.98.3.281 | Gene a ed on 2023-04-04 11:54:31 286 Ho s Siebe gi en commodi y p ices, an emission ax will educe he ou pu o he pollu ion-in ensi ely p oduced commodi y. Resou ce use in he pollu- ion aba emen ac i i y o he pollu ion-in ensi ely p oducing sec o will inc ease. Also we know ha esou ces will be wi hd awn om p oduc ion and will be used in aba emen ac i i ies. This e ec does no depend on di e ences in he p oduc ion in ensi y o he wo sec o s. 2. Allowing he commodi y p ice o a y we ha e he ollowing esul s om appendix II (as su icien condi ions): d' y > 0 (14i) A>0: { ?F T , , I D^ + D^F^O dR (14 ii) --1 > 0: D1YF2 + D^yFj > 0 Assuming (14 i) is gi en we ha e 2 dR{ ^ (14 iii) ——1 < 0 (14 i ) dz dRL<0. J D1Y> 0 dz ' H; F[ > H2 F2 dp ^ ( h > H' F' (14 ) - ->0: > >22 < ' dz y a2 D2Y FJ p > ax DlY F2 dY ^ (14 i) - -<0: a z H1F1> H2F2 F2 1 - —2- — )lp > <x > 1 wi h a = - 1 - PFi In (14 i) jip deno es he di ec p ice elas ici y o demand. Diag am 1 summe izes he su icien condi ions o equa ion 14. We ha e he ollowing esul s: 3. Assume bo h commodi ies a e no in e io , so ha hei ma ginal p opensi ies o consume (DiY>0) a e nonnega i e. Then he de e - minan A > 0. Assume Sec o 1 is he pollu ion-in ensi ely p oducing sec o . Then we ha e: Resou ce use in he pollu ion-in ensi ely p oducing sec o will de- cline. Resou ce use in each aba emen ac i i y will inc ease; esou ce in p oduc ion (2 Ri) will be educed. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.98.3.281 | Gene a ed on 2023-04-04 11:54:31 En i onmen al Policy, Alloca ion o Resou ces 287 Diag am 1 : Su icien condi ions En i onmen al policy will shi he sec o s uc u e o he economy in a o o he aba emen ac i i ies wi h p oduc ion being a ec ed nega i ely. We can es ablish ha p oduc ion in he pollu ion-in en- si ely p oducing sec o will decline7. In he less pollu ion-in ensi ely p oducing Sec o 2, esou ce use may inc ease o dec ease. The model allows bo h cases. Thus, in one case Sec o 1 and Sec o 2 lose esou ces o he aba emen ac i i y, whe eas in he o he case, Sec o 1 loses esou ces o Sec o 2 and he aba emen ac i i y. Unde he assump ions made, emissions will be educed and en i onmen al quali y will im- p o e. This ollows om 2 dRi/dz < 0 and 2 dR {/dz > 0. 4. Condi ion (14 ) o a ise in he ela i e p ice can be spli in o wo su icien condi ions8. i) D'2Y > pDlY. Unde he condi ions speci ied below, na ional income will decline as a consequence o en i onmen al policy. Then D2Y> pD'lY gua an ies ha demand o he pollu ion-in ensi ely p oduced com- modi y 1 is educed less han demand o he commodi y 2. This di - e ence in he income e ec o he wo commodi ies makes su e ha 7 This also holds i Sec o 2 we e he pollu ion-in ensi ely p oducing sec o . 8 No e ha F1P>F2 ollows om H[ FX > H'2F2. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.98.3.281 | Gene a ed on 2023-04-04 11:54:31 288 Ho s Siebe he ela i e p ice o he pollu ion-in ensi ely p oduced commodi y mus ise. dR* . dR2 ii) a2 > ai: |—— | > | | speci ies9 ha ( o gi en p and z), Sec o 1 is mo e sensi i e o changes in esou ce p ice han Sec o 2; we may also say ha Sec o 1 is mo e dependen on he esou ce R. This con- di ion can be in e p e ed as a udimen a y o m o a ac o -in ensi y condi ion in a one- ac o model. We can expec ha his condi ion un olds in o a se o ac o in ensi y condi ions in a mul i- ac o model. As a esul we ha e: The ela i e p ice o he pollu ion-in ensi ely p oduced commodi y will ise i he ma ginal p opensi y o consume o his commodi y is lowe han he less pollu ion-in ensi ely p oduced commodi y and i he pollu ion-in ensi ely p oducing sec o depends hea ily on he esou ce R. Su icien condi ions o a ise in he ela i e p ice can pa ly sub- s i u e each o he . Assume Sec o 1 is " e y" pollu ion-in ensi e10. Then he ela i e p ice o commodi y 1 may ise e en i i has a high income elas ici y o demand and loses demand quan i ies wi h a decline in income. O o iden ical pollu ion-in ensi ies o bo h sec o s, he ela- i e p ice will ise, i Sec o 1 has a su icien ly smalle p opensi y o consume and hus loses a smalle quan i y in demand equi ing a highe adjus men in ela i e p ice. Finally, assume Sec o 2 hea ily depends on esou ce R. Then p can ise ne e heless, i Sec o 1 is su - icien ly mo e pollu ion-in ensi e o i Sec o 1 has a su icien ly lowe income elas ici y. dp/dz > 0 indica es ha en i onmen al policy will unde he con- di ions indica ed a ec he compa a i e p ice ad an age o a coun y. Assume a coun y expo s he pollu ion-in ensi ely p oduced commo- di y 1. Then en i onmen al policy will educe he compa a i e p ice ad an age o ha coun y11. Conside wo coun ies wi h a di e en abundance o en i onmen al se ices and assume ha z > z* e lec s he di e ence in endowmen wi h z* indica ing he emission ax o he » Di e en ia e he ac o demand condi ions (9) o gi en p and z wi h espec o 10 Assume o ins ance Sec o 2 does no pollu e a all wi h H2 = 0. 11 I a coun y expo s he less pollu ion-in ensi e commodi y and i i unde akes en i onmen al policy, i s compa a i e p ice ad an age will be imp o ed. dR 1 OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.98.3.281 | Gene a ed on 2023-04-04 11:54:31