Leonard F.S. Wang Department of Applied Economics, National University of Kaohsiung. Abstract

Transcription

1 Trade lberalzato ad evrometal tax deretated olgopoly wth cosumpto exteraltes Leoard F.S. Wag Departmet o Appled Ecoomcs, Natoal Uversty o Kaohsug Ya-Ch Wag Departmet o Face ad Bakg, Ku Sha Uversty Ta-Lag Che Isttute o Ecoomcs ad Maagemet, Natoal Uversty o Kaohsug Abstract Ths paper vestgates the evromet tax ad trade lberalzato wth deret market structures (pure olgopoly or mxed olgopoly) juxtaposg the substtutablty o the goods (homogeous goods ad deretated goods), where evrometal damage s assocated wth cosumpto. It shows that the evrometal tax mxed olgopoly s hgher tha pure olgopoly rrespectve o the propertes o goods. I addto, t demostrates that whe the domestc market creases ts opegs, the tar reducto does ot always brg postve eects o the evromet mxed olgopoly; but, pure olgopoly wth homogeeous goods, the tar reducto s bad or the evromet. Ctato: Wag, Leoard F.S., Ya-Ch Wag, ad Ta-Lag Che, (27) "Trade lberalzato ad evrometal tax deretated olgopoly wth cosumpto exteraltes." Ecoomcs Bullet, Vol. 7, No. 8 pp. -9 Submtted: August 27, 27. Accepted: October 3, 27. URL:

2 . Itroducto Cotrollg polluto emsso has become the most mportat ad pressg ssue or most govermets to deal wth. I partcular, may developg coutres ace the alteratves betwee poor evrometal-qualty mprovemet ad developmet o the ecoomy. Wth market opeg, the mpact o trade lberalzato o the evromet has become the ocus o much atteto ad debate. May exstg studes are cocered about teralzg polluto exteraltes by usg evrometal tax lke Krutlla (99) who has ocused atteto o the determato o evrometal regulatos, ad dsregard the eect o trade lberalzato o polluto cotrol. Few studes have cosdered egatve exteraltes assocated wth cosumpto o the good such as gum-chewg, cgarette smokg ad gasole cosumpto that cause evrometal damage. Aderso (992) showed that lberalzg trade a good whose cosumpto gves rse to polluto wll cause a coutry s evromet to deterorate the good s mported. Metcale ad Begh (998) argued that whe polluto testes emtted cosumpto edogeously respod to evrometal polcy, ad whe ths polcy ders betwee tradg parters, a addtoal polcy strumet s requred to cap polluto testes, such as a stadard or a prohbtve tax o ay crease the testy o cosumpto polluto. La (24) examed trade ad evrometal polces a pure duopoly market, whle Ohor (26) exteded La s work a mxed duopoly model ad showed that the optmal evrometal tax a mxed duopoly s hgher tha the Pgouva level ad the optmal tax a pure duopoly. Furthermore, La ad Hu (25) demostrated that trade lberalzato wll ehace global welare trasboudary polluto-assocated cosumpto s sucetly strog as well as blateral reducto tars s beecal to the global evromet. I ths paper, we vestgate the optmal evrometal tax ad the evrometal eect o trade lberalzato a mxed olgopoly ad pure olgopoly, where rms produce the deretated goods ad the evrometal damage s assocated wth cosumpto. As a bechmark, we used the study coducted by La (24), who demostrates that trade lberalzato o drty goods leads to evrometal mprovemet ad Ohor (26), who demostrates that trade lberalzato o such drty goods has o luece o evrometal mprovemet. We the compared the evrometal tax beore prvatzato wth that ater prvatzato, ad that o producg deretated goods wth homogeeous goods. We oud that whe the domestc market creases ts opegs, the tar reducto does ot always brg postve eects o the evromet mxed olgopoly; but, pure olgopoly wth homogeeous goods, the tar reducto s bad or the evromet. Mxed olgopoly models wth oreg competto, see Fjell ad Pal (996), Pal ad Whte (998), ad Fjell ad Heywood (22)

3 Ths paper s orgazed as ollows. Secto 2 provdes the basc model. Secto 3 cludes the results o the aalyss olgopoly wth deretated goods ad does a comparso. Secto 4 aalyzes the eects o trade lberalzato. Secto 5 presets cocludg remarks. 2. The Model The model ollows Ohor s (26) basc set-up but cludes product deretato. Cosder a sgle teratoal market whch there exsts oe domestc rm (rm ) ad several prvate oreg rms (rm, =,..., ) competg a domestc coutry. Uder the Courot-Nash assumpto, the domestc rm s publc, t selects ts output order to maxmze the sum o cosumer surplus ad ts ow prot U ; the domestc rm s prvate, t chooses ts output order to maxmze ts ow prot π. The domestc ad oreg rms produce a deretated good, gve by q ( =, ), ad ths leads to polluto. The domestc govermet sets the evrometal tax t to cotrol the polluto that results rom evrometally harmul cosumpto. We assume that all cosumers the domestc coutry are the same, ad ormalze the sze o the populato the domestc coutry to oe. The represetatve cosumer derves utlty rom cosumg the good uder cosderato, ad suers rom cosumpto-type polluto. The utlty ucto o the represetatve cosumer the domestc coutry s as ollows Häcker (2) geeralzg the utlty ucto to allow or oreg rms ad oe domestc rm producg deretated goods, 2 2 V = a( q+ q) ( q + q + 2 γ qq j) + I θq () = 2 = j Where I s the composte goods, ad θ s the coecet o the margal polluto damage. By solvg the optmzato problem o the domestc cosumer, we ca derve the domestc verse demad ucto or the good, p pq ( ), where Q= q + γ q. Q deotes the aggregate output. We assume p <. I order to sharpe the study, t s also assumed that the verse demad ucto s lear (.e. p( Q) = a Q). The prot ucto o rm, π = ( p c t) q, where c s the costat margal producto cost. The publc rm s objectve ucto s deed as the sum o cosumer surplus ad the rm s prot, Q ( η) η π. (2) U = p d pq+ The evrometal damage ucto s gve by D= θq, where θ deotes the margal evrometal damage adθ. Socal welare the domestc coutry s = 2

4 Q ( η) η π τ. (3) = W = p d pq+ + tq+ q D The oreg prvate rm selects ts ow output order to maxmze ts prot, π = ( p c t τ ) q, =,2,...,, (4) where c s the costat margal producto cost ad τ s the tar rate, τ.whe we exame the duopoly case, equato (2) (3) ad (4) assumg = to represet oe oreg rm. For smplcty, each rm does ot have xed cost. It also assumes that the margal producto cost o the domestc rm s hgher tha that o the oreg rm ( c > c > ). 2 Moreover, as La ad Ohor, we cosder trade lberalzato to be a orm o tar reducto. 3. Evrometal Tax Olgopoly We exted the basc model cocerg the umber o oreg rms whch there s oe domestc rm ad oreg prvate rms producg deretated goods. 3. Pure Olgopoly We rst derve the optmal evrometal tax the pure olgopoly wth deretated goods. Uder the Courot-Nash assumpto, the domestc prvate rm selects ts output order to maxmze ts ow protπ, whle the oreg prvate rm chooses ts output order to maxmze ts ow protπ. We obta the ollowg rst-order codtos: p c t+ pq =, ad (5) p c t τ + p γ q =, =,2,...,. (6) The output eects o the taxes are obtaed by deretatg (5) ad (6) wth respect to t ad q, δ q δ t = ( + 2) p ad = ( δq δt) = γ( + 2) p. Ths demostrates that a crease the evrometal tax reduces the market share o all rms. Havg obtaed these results, we deretate socal welare equato wth respect to t ad set dw / dt = to obta optmal evrometal tax, DP * + 2γ + t = [2 ( c 2 c ) ( ) pq ] [ ] τ + θ, (7) ( + ) + γ ( + ) * where Q deotes optmal aggregate output 3. 2 See Cremer et al (989) or a justcato o ths assumpto. 3 (a) We use the superscrpts M P DM ad DP or the mxed Courot-Nash wth homogeeous goods, 3

5 3.2 Mxed Olgopoly We derve the optmal evrometal tax the mxed olgopoly wth deretated goods. Uder the Courot-Nash assumpto, the domestc rm selects ts output order to maxmze the sum o cosumer surplus ad ts ow protsu, whle the oreg prvate rm chooses ts output order to maxmze ts ow protπ. We obta the ollowg rst-order codtos, p c t p γ q =, ad (8) = p c t τ + p γ q =, =,2,...,. (9) The output eects o the taxes are obtaed by deretatg (8) ad (9) wth respect to t ad q, δq / δ t / ' ad = ( δq / δt) =. These demostrate that a crease the evrometal tax reduces the market share o the less ecet publc rm. Havg obtaed these results, we deretate socal welare equato wth respect to t ad set dw / dt = to obta optmal evrometal tax, c ( c ) DM t τ = + θ. () + From equato (7) () (A..4) ad (A.2.4) 4, we d that the optmal evrometal tax deret market wth deret propertes o goods s, M DM P DP t = t > t > t. We have the ollowg proposto. Proposto : I a teratoal olgopoly market where the evrometal damage s assocated wth cosumpto, the order o optmal evrometal tax parallels the results o the duopoly model. 4. The Eects o Trade Lberalzato We ow cosder the mpact o a chage the tar rate o the outputs o oe domestc rm ad oreg prvate rms the domestc market. We derve the total mpact o trade lberalzato o the evromet by deretatg the evrometal damage ucto wth respect toτ, dd δ D δd δt = + =. dτ δτ δt δτ pure Courot-Nash homogeeous goods, mxed Courot-Nash wth deretated goods, ad pure Courot-Nash wth deretated goods olgopoly respectvely. (b) Because the orm o optmal evrometal tax pure duopoly s ot as usual, there exsts a Thereore, we supply a specal case to smply ths equato appedx B. 4 See appedx A. or dervg optmal tax rate pure ad mxed olgopoly homogeeous goods. 4 ' * p Q term.

6 We obtaed the ollowg our results or deret market structures ad commodtes propertes: Case (): pure olgopoly wth homogeeous goods P dd = dτ ( + 2) ( + ) p ( ) 2 2 P 3 2 δt ( ) = < 2 δτ ( + ) ( + 2) P dd dτ > 2 P dd dτ < 3 Case (): mxed olgopoly wth homogeeous goods M dd = ; dτ M δt = < δτ + Case (): pure olgopoly wth deretated goods dd = > ; DP [( γ ) + ( 4γ + 4γ 3) + ( 8γ + 4γ 2) + ( 5γ + 2 γ) ] dτ ( + 2) ( + ) γ p DP δt + γ + + γ + = < δτ 3 2 [ 3( ) (3 2) ] 2 γ ( + ) ( + 2) Case (v): mxed olgopoly wth deretated goods DM dd ( γ) θ = < ; dτ ( + ) γ p DM δt = < δτ + Accordg to the above results, we kow o matter what types o market structures, there s a egatve relatoshp betwee tar rate τ ad evrometal taxes t ; that s, the govermet opes the market wholly to make the umbers o oreg rms crease rom to, t may cause more polluto; hece, the govermet should rase the evrometal tax. I pure olgopoly wth homogeeous goods, the umbers o rms are equal ad less tha two (.e. 2 ), a tar reducto wll mprove the evromet;however, the umbers o rms are equal ad greater tha three (.e. 3 ), a tar reducto has harmul eect o the evromet. I mxed olgopoly wth homogeeous goods, a tar reducto has o 5

7 eect o the evrometal damage assocated wth cosumpto, whch s the same as Ohor s (26) result. However, the pure olgopoly wth deretated goods, a tar reducto has a postve mpact o the evromet; but, mxed olgopoly wth deretated goods, a tar reducto has harmul eect o the evromet. Whe exogeous varables or γ equal, we obta the same results as the duopoly market (La ad Ohor s work). We have the ollowg proposto. Proposto 2: The eects o trade lberalzato olgopoly cocde wth that duopoly; except or the oe pure olgopoly wth homogeeous goods. Whe the domestc market creases ts opegs, the tar reducto does ot always brg postve eects o the evromet mxed olgopoly; but, pure olgopoly wth homogeeous goods, the tar reducto s bad or the evromet. 5. Cocludg Remarks Usg the smple lear demad model, part o our dgs are cosstet wth what has bee show La (24) ad Ohor (26), eve though they cosdered all rms producg homogeeous goods. I a teratoal olgopoly market where the evrometal damage s assocated wth cosumpto, the order o optmal evrometal tax parallels the results o the duopoly model rrespectve o the propertes o the goods. I addto, we have show that whe the domestc market creases ts opegs, the tar reducto does ot always brg postve eects o the evromet mxed olgopoly; but, pure olgopoly wth homogeeous goods, the tar reducto s bad or the evromet. 6

8 Appedx A A. Pure Olgopoly wth Homogeeous Goods Uder the Courot-Nash assumpto, we obta the ollowg rst-order codtos, p c t+ pq =, ad (A..) p c t τ + pq =, =,2,...,. (A..2) tot, Havg obtaed the results, we the deretate socal welare equato wth respect δ q q dt δt δq δt δq δt dw δw δw δw = + + = = = q + [ p c + t+ τ ( + ) θ] = p (A..3) The optmal evrometal tax, P * ( + 3) t = [2 ( c 2 c ) ( ) pq ] τ + θ. 2 (A..4) ( + ) ( + ) A.2 Mxed Olgopoly wth Homogeeous Goods Uder the Courot-Nash assumpto, we obta the ollowg rst-order codtos, p c t p q =, ad (A.2.) = p c t τ + pq =, =,2,...,. (A.2.2) The deretatg socal welare equato wth respect to t, t yelds δ q q dt δt δq δt δq δt dw δw δw δw = + + = = ( p c θ ) = p The optmal evrometal tax, t c M c r = θ + (A.2.3) ( ). (A.2.4) + Appedx B We ollow La s (24) basc set-up but assume the lear verse demad ucto s p = a q γ q. Deretatg domestc ad oreg rms total prots wth respect to = ther ow output, we obta the ollowg rst-order codtos, a 2q γ q c t =,ad (B) = 7

9 a q 2γq γ qj c t τ =,, j =,2,...,. j The, the outputs are gve by (B2) DP q = [ a ( + ) c + c + τ t ] ; (B3) + 2 DP q = ( a+ c 2c 2 τ t). (B4) γ ( + 2) The optmal evrometal tax s [(2+ ) c 3 c + ( ) a] DP (3γ 2) t = [ + ] τ + ( ) θ γ + 4+ (B5) I all rms produce homogeeous goods, letτ =, the optmal output ad evrometal tax are P q = [ a ( + ) c + c + τ t ] ; (B6) + 2 P q = ( a+ c 2c 2 τ t) ; (B7) ( + 2) [(2+ ) c 3 c + ( ) a] P t = [ + ] τ + ( ) θ. (B8)

10 Reereces Aderso, K. (992) The Stadard Welare Ecoomcs o Polces Aectg Trade ad the Evromet The Greeg o World Trade Issue by K. Aderso ad R. Blackhurst, Eds., Harvester Wheatshea: New York, Cremer, H., Marchad, M., ad J. F. Thsse (989) The Publc Frm as a Istrumet or Regulatg a Olgopolstc Market Oxord Ecoomc Papers 4, Fjell, K., ad J. Heywood (22) Publc Stackelberg Leadershp a Mxed Olgopoly wth Foreg Frm Australa Ecoomc Papers 4, Fjell, K., ad D. Pal (996) A Mxed Olgopoly the Presece o Foreg Prvate Frms Caada Joural o ecoomcs 29, Krutlla, K. (99) Evrometal Regulato a Ope Ecoomy Joural o Evrometal Ecoomcs ad Maagemet 2, La, Y. B. (24) Trade Lberalzato, Cosumpto Exteraltes ad the Evromet Ecoomcs Bullet 7(5), -9. La, Y. B., ad C. H. Hu (25) Trade Lberalzato ad Trasboudary Polluto Evrometal Ecoomcs ad Polcy Studes 7, -4. Metcale, M. R., ad J. C. Begh (997) Pecemeal Reorm o Trade ad Evrometal Polcy Whe Cosumpto Also Pollutes Workg paper, North Carola State Uversty. Häcker, J. (2) A Note o Prce ad Quatty Competto Deretated Olgopoles Joural o Ecoomc Theory 93, Ohor, S. (26) Trade Lberalzato, Cosumpto Exteraltes ad the Evromet: A Mxed Duopoly Approach Ecoomcs Bullet 7(5), -9. Pal, D., ad M. D. Whte (998) Mxed Olgopoly, Prvatzato, ad Strategc Trade Polcy Souther Ecoomc Joural 65, Sgh, N., ad X. Vves (984) Prce ad Quatty Competto a Deretated Duopoly RAND Joural o Ecoomcs 5, Walz, U., ad D. Wellsch (997) Is Free Trade the Iterest o Exportg Coutres whe There s Ecologcal Dumpg? Joural o Publc Ecoomcs 66,