Privatization and government preference in an international Cournot triopoly

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1 Fernanda A Ferrera Flávo Ferrera Prvatzaton and government preference n an nternatonal Cournot tropoly FERNANDA A FERREIRA and FLÁVIO FERREIRA Appled Management Research Unt (UNIAG School of Hosptalty and Toursm Polytechnc Insttute of Porto Rua D Sancho I Vla do Conde PORTUGAL faf@eshtpppt; fff@eshtpppt Abstract: - Ths paper presents an analyss of the relatonshp between the prvatzaton of a state-controlled frm and government preferences for tax revenue by usng a mxed Cournot model wth domestc and foregn frms We assume that the government fxes a tax rate on the domestc producton and a tarff for mported goods The state-controlled frm ams to maxmze the sum of consumer and producer surplus; the government s objectve functon s a weghted sum between socal welfare and tax revenue Key-Words: - Prvatzaton mport tarff government preference Cournot tropoly Introducton Studes on prvatzaton polces have been developed usng mxed olgopoly theores Competton between publc and prvate frms exsts n a range of ndustres lke telecommuncatons electrcty natural gas arlnes ndustres as well as servces ncludng hosptals bankng and educaton Some authors studed mxed duopoly markets and some others consdered markets wth more than two frms DeFraja and Delbono [] s one of the poneerng papers on mxed olgopoly where a welfaremaxmzng state-controlled frm (SCF competes wth several proft-maxmzng prvate frms Fjell and Pal [] consdered an nternatonal Cournot model n whch a domestc SCF competes wth both domestc and foregn prvate frms to study the effects of an open door polcy and foregn acqustons Fjell and Heywood [] studed these felds under a Stackelberg model n whch a statecontrolled leader frm competes wth both domestc and foregn prvate follower frms Pal and Whte [4] adopt Fjell and Pal s model to study the effects of prvatzaton and strategc polcy takng the form of domestc producton subsdes and mport tarffs Ferrera and Ferrera [5] studed n both mxed and prvatzed markets the effects of envronmental and trade polces n an nternatonal duopoly servng two countres wth polluton abatement Ferrera and Ferrera [] analysed domestc and nternatonal compettons wth one publc leader frm and one follower prvate frm producng complementary goods and competng on prces Ferrera and Ferrera [7] studed the relatonshp between the prvatzaton of a publc frm and government preferences for envronmental tax revenue n a market wth two frms competng à la Cournot Kato [8] used a mxed Cournot model to study the relatonshp between prvatzaton and government preferences for tax revenue He assumes that the government prefers tax revenue to the socal welfare whereas the publc frm only cares about the socal welfare Ferrera and Ferrera [9] dd a smlar analyss n a Stackelberg duopoly model wth the publc frm as the leader Ferrera and Ferrera [] also studed the relatonshp between prvatzaton and government preferences for tax revenue but by consderng a Cournot tropoly nstead of a Cournot duopoly Furthermore the authors consdered that frms produce dfferentated goods nstead of homogenous goods They showed that prvatzaton polces depend on the government preference for the tax revenue and on the dfferentaton of the goods Tomaru [] nvestgated how decson-makng upon cost-reducng R&D nvestment by a domestc publc frm s affected by prvatzaton and entry of a foregn frm The author showed that prvatzaton deterorates domestc socal welfare In ths paper we analyse the relatonshp between the prvatzaton of a state-controlled frm and government preferences for tax revenue by usng a mxed Cournot model wth domestc and foregn frms The paper s organzed as follows In Secton we ntroduce and descrbe the model Then we study the mxed market n Secton and the E-ISSN: Volume 7 8

2 Fernanda A Ferrera Flávo Ferrera prvatzed market n Secton 4 In Secton 5 we analyse the effects of prvatzaton Secton presents the results for the domestc competton and n Secton 7 we compare some results n the domestc model wth the ones n the nternatonal model Secton 8 concludes the paper In the frst stage the government fxes the tax rate t and the mport tarff µ ; In the second stage all frms smultaneously decde ther outputs To obtan a subgame perfect equlbrum the game wll be solved by backward nducton Descrpton of the model We consder a tropoly model wth one statecontrolled frm (SCF F one domestc prvate frm F and one foregn prvate frm F Assume that frms produce a homogenous good and the market nverse demand s gven by p Q where p s the prce of the good and Q q where q s the quantty produced by frm F s the total producton of all frms All frms have the same cost functon C( q q / We also assume that the government fxes a tax rate t on the domestc producton and a tarff µ on the mported goods Thus the frms F proft functons are gven by q ( p t q q ( p µ q As usual socal welfare W s defned as the sum of consumer surplus CS and producer surplus W CS + + where CS ( q + q The government s payoff s gven by U W + ( + α R where R t( q + q + µ q s the total tax revenue and α s the parameter that represents the weght of the government preference for the tax revenue We consder α whch means that the government puts a larger weght on R than on W Assumpton To assure that all the frms are actve n the market we assume that α > / The game runs as follows: Ths demand functon results from maxmzaton of a sem-lnear utlty functon of a representatve consumer The mxed nternatonal tropoly Startng from the last stage the SCF solves the optmzaton problem maxw and the prvate frms q solve the optmzaton problems max wth By solvng the system W q q q t q q q q t q q q q µ q we fnd the optmal quanttes q and q produced respectvely by the SCF and each prvate frm as functon of t and µ : t +µ t +µ + t 5µ q q and q Therefore the prce of the good also as functon of the tax rate and the mport tarff s gven by + t +µ p Furthermore frms profts are as follows: ( t + µ 7 ( t + µ 9 and ( + t 5µ 9 and socal welfare s gven by ( t +µ W 8 Next proposton presents the comparatve statc analyss PROPOSITION Producton of stated-controlled frm and of prvate domestc frm decreases n tax rate and ncreases n mport tarff; producton of the prvate foregn frm ncreases n tax rate and q E-ISSN: Volume 7 8

3 Fernanda A Ferrera Flávo Ferrera decreases n mport tarff Prce ncreases n both tax rate and mport tarff PROOF The results follow from the followng: q q q < < and > ; t t 4 t 4 q q q 5 > > and < ; µ µ µ p p > > t µ Now solvng gves IM 9α t U t U µ IM and µ REMARK Snce we are assumng α > / the optmal tax rate s postve By the above results we can easly get the subgame perfect equlbrum as stated n the next proposton PROPOSITION The subgame perfect equlbrum for the nternatonal mxed tropoly s as follows: IM α + IM α + q q ( α 4 ( α IM α IM α + q Q ( α ( α The prce clearng the market at equlbrum s: IM α + p ( α SCF s proft s gven by IM ( α ; 8 ( α domestc prvate frm s proft s IM ( α ; ( α and foregn prvate frm s proft s IM ( α 9 α + Socal welfare and government s payoff are respectvely as follows: IM ( α IM α + 5α + W U α + α + Next proposton states a statc analyss PROPOSITION In the mxed market and wth respect to government preference for the tax revenue we have the followng: ( Producton of stated-controlled frm and of domestc prvate frm decreases; ( producton of the foregn prvate frm ncreases; ( aggregate quantty n the market decreases; (v Prce ncreases; (v The profts of both domestc publc frm and domestc prvate frm decrease; (v foregn prvate frm s proft ncreases (resp decreases for hgh (resp low values of government preference for the tax revenue; (v (v Socal welfare decreases; Government s payoff ncreases (resp decreases for hgh (resp low values of government preference for the tax revenue PROOF The results follow from the followng: q q < < α ( α α ( α q Q > < α ( α α ( α p > α ( α α + ( α + < < α ( α α 8 ( α < se α < α α 8 ( α + se α W ( α < α ( α se α U 9α α < < + α ( α se α E-ISSN: Volume 7 8

4 Fernanda A Ferrera Flávo Ferrera 4 The prvatzed nternatonal tropoly Now suppose that the publc frm s prvatzed So all frms am to maxmze ther own profts Frst order condtons gve q t +µ q wth and + t µ q 5 Thus we get + t +µ p 5 ( t + µ wth ( + t µ 5 and ( t +µ W Now solvng U t U µ gves IP 4α IP t and µ 4α + REMARK Snce we are assumng α > / the optmal tax rate s postve By the above results we can easly get the subgame perfect equlbrum as stated n the next proposton PROPOSITION 4 The subgame perfect equlbrum for the nternatonal prvatzed tropoly s as follows: IP IP ( α IP 4α q q q 54 ( α ( 4α IP α + 7 Q ( 4α The prce clearng the market at equlbrum s: IP 8α + p ( 4α Domestc prvate frms profts are gven by IP IP ( α ; 5( 4α and foregn prvate frm s proft s IP 4 ( α ( 4α Socal welfare and government s payoff are respectvely as follows: IP 4( α IP ( α ( α + 7 W U 54α+ ( 4α Next proposton states a statc analyss PROPOSITION 5 In the prvatzed market and wth respect to government preference for the tax revenue we have the followng: ( Producton of domestc prvate frms decreases; ( producton of the foregn prvate frm ncreases; ( aggregate quantty n the market decreases; (v Prce ncreases; (v The profts of both domestc publc frm and domestc prvate frm decrease; (v foregn prvate frm s proft ncreases; (v Socal welfare decreases; (v Government s payoff ncreases PROOF The results follow from the followng: IP IP q q < α α 54 ( α IP IP q 4 Q 8 > < α 54 ( α α 54 ( α IP p 8 > α 54 ( α IP IP ( α < α α 5( 4α IP 4 ( α > α 5( 4α IP W 4( α < α 54α+ E-ISSN: Volume 7 8

5 Fernanda A Ferrera Flávo Ferrera ( + IP U α 8α > α 4 + ( α 5 Effects of prvatzaton Frst we compare the optmal tax and mport tarff before and after prvatzaton n order to nvestgate the effect of prvatzaton on these strategc polces From the results above we conclude that IM IP prvatzaton decreases taxes ( t > t and does IM IP not affect the mport tarff ( µ µ Furthermore under optmal producton tax and mport tarff prvatzaton of a SCF worsens (resp rases socal welfare for low (resp hgh values of the government preference for the tax revenue: W + ( α ( 8α 8α f < α < W 4 ( α ( 4α + f α 4 IM IP Snce IM IP α + α + α U U > 4 we conclude that the government has an ncentve to prvatze the SCF Domestc competton Here we suppose that all the frms F F and F are domestc In ths case the tax rate t s appled to the producton of the three frms Socal welfare s gven by W CS where CS ( q + q + q and the government s payoff s gven by U W + ( + α R R t q + q + q where From the results presented by Ferrera and Ferrera [] we get the followng propostons and 7 PROPOSITION In the domestc competton wth mxed competton the subgame perfect equlbrum s gven by: DM α t 4α + q DM W 4 DM α + q 4α + 4α + DM 8( α DM α + Q p 4α + 4α + DM 8( α 4α + DM DM ( α ( 4α + 5( α DM U ( 4α + wth wth 4 4α + PROPOSITION 7 In the domestc competton wth prvatzed competton the subgame perfect equlbrum s gven by: DP 5α t 5α+ DP α + q 5 ( α 85 DP Q 5 W DP DP 9 45 wth DP 7α + p 5 wth U 45 DP Snce n the domestc competton DM DP ( α ( 8α U U 4( 5α + ( 4α + the government wll prvatze the SCF f α < /8 7 Comparsons: domestc versus nternatonal competton Now let us compare some results n the domestc model wth the ones n the nternatonal model Here we have to assume α > / As we saw above n the nternatonal competton the government always has an ncentve to prvatze the SCF The same does not occur n the domestc competton: the government only prvatze the SCF f t has low preferences for the tax revenue We note that n the domestc competton we do not mpose any restrcton n the values of α E-ISSN: Volume 7 8

6 Fernanda A Ferrera Flávo Ferrera In both mxed and prvatzed models the tax revenue n the domestc competton s hgher (resp lower than n the nternatonal competton f the government has low (resp hgh preferences for the tax revenue: DM IM α 9α R R ( α ( 4α + + < f < α < + f α ( 7 + 8α 44α f < < α < DP IP R R ( 4α ( 5α + f α Socal welfare s always hgher n the domestc competton than n the nternatonal competton: ( α ( α + 9α 7 DM IM W W > ( α ( 4α + ( α ( α + 4α 9 DP IP W W > ( 4α ( 5α + 8 Concluson In ths paper we analysed the relatonshp between the prvatzaton of a state-controlled frm and government preferences for tax revenue by usng a mxed Cournot model wth domestc and foregn frms We concluded that prvatzaton decreases taxes and does not affect the mport tarff Furthermore under optmal producton tax and mport tarff prvatzaton of a SCF worsens (resp rases socal welfare for low (resp hgh values of the government preference for the tax revenue Furthermore we showed that n the nternatonal competton the government always has an ncentve to prvatze the SCF The same does not occur n the domestc competton: the government only prvatze the SCF f t has low preferences for the tax revenue We also proved that the tax revenue n the domestc competton s hgher (resp lower than n the nternatonal competton f the government has low (resp hgh preferences for the tax revenue Socal welfare s always hgher n the domestc competton than n the nternatonal competton Acknowledgements UNIAG R&D unt funded by the FCT Portuguese Foundaton for the Development of Scence and Technology Mnstry of Scence Technology and Hgher Educaton under the Project UID/GES/475/ References: [] G DeFraja and F Delbono Alternatve Strateges of a Publc Enterprse n Olgopoly Oxford Economc Papers Vol pp - [] K Fjell and D Pal A mxed olgopoly n the presence of foregn prvate frms Canadan Journal of Economcs Vol 9 99 pp [] K Fjell and J S Heywood Publc Stackelberg leadershp n a mxed olgopoly wth foregn frms Australan Economc Papers Vol 4 pp 7-8 [4] D Pal and MD Whte Mxed olgopoly prvatzaton and strategc trade polcy Southern Economc Journal Vol pp 4-8 [5] F A Ferrera and F Ferrera Envronmental taxaton: Prvatzaton n an nternatonal duopoly wth tarffs Appled Mathematcs and Informaton Scences Vol 7 pp -8 [] F A Ferrera and F Ferrera Prvatzaton n a publc leadershp mxed duopoly Proceedngs of the Internatonal Conference of Numercal Analyss and Appled Mathematcs Rhodes Greece Amercan Insttute of Physcs Vol 78 pp - -4 [7] F A Ferrera and F Ferrera Government preference envronmental taxes and prvatzaton Proceedngs of the Internatonal Conference on Industral Engneerng and Operatons Management Duba Unted Arab Emrates 5 [8] H Kato Prvatzaton and government preference Economcs Bulletn Vol 8 pp -7 [9] F A Ferrera and F Ferrera Prvatzaton and government preferences n a mxed duopoly: Stackelberg versus Cournot n Dscontnuty and Complexty n Nonlnear Physcal Systems edted by Tenrero Machado et al Sprnger Internatonal Publshng Swtzerland 4 pp 4-4 [] F A Ferrera and F Ferrera Prvatzaton and government preference n a dfferentated Cournot tropoly Proceedngs of the Internatonal Conference on Mathematcal E-ISSN: Volume 7 8

7 Fernanda A Ferrera Flávo Ferrera Methods & Computatonal Technques n Scence & Engneerng Cambrdge UK 8 [] Y Tomaru Prvatzaton productve effcency and socal welfare wth a foregn compettor Research n Economcs Vol 7 pp 4- E-ISSN: Volume 7 8