PRIVATIZATION IN CLOSED AND OPEN MIXED OLIGOPOLIES Najiba Benabess, Norwich University, Vermont, USA,

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1 Privatizatio i losed ad Ope Mixed Oligopolies PRIVATIZATION IN LOED AND OPEN MIXED OLIGOPOLIE Najiba Beabess, Norwich Uiversity, Verot, UA, beabes@orwich.edu Abstract This paper is the first to collect ad orgaize the ay past theoretical results o the predicted welfare effects of atizatio i ixed oligopolies. Our review of past odels deostrates that the ost critical eleets i predictig the ifluece of atizatio i ixed oligopoly are the tiig of the gae, ad whether or ot the aret is ope to foreig copetitio. I orgaizig these results it becoes apparet that several cases reai issig i the resultig atrix. I develop these cases ad coclude that a lic tacelberg leader should ever atize while a lic ourot fir should be atized whe a doestic aret is ore copetitive. Keywords: Privatizatio, Mixed Oligopoly, ourot odel, tacelberg odel. 1. Itroductio: A large literature has developed exaiig ixed oligopoly odels ofte with the object of ivestigatig the cosequeces of atizatio. While these odels have reached soewhat cotradictory predictios, the eed for usig theory to ae predictios reais great. As the ext sectio aes clear, the results of actual cases of atizatio appear to be ixed. The characteristics of the ay idividual cases differ draatically ad call for the drawig of geeral priciples based o differeces i uderlyig aret ad behavioral variables. Our review of past odels deostrates that the ost critical eleets i predictig the ifluece of atizatio i ixed oligopoly are the tiig of the gae, ad whether or ot the aret is ope to foreig copetitio. Apparetly, less relevat are assuptios o the exact ature of the dead ad cost structure. Thus, the stylized exaple frequetly used ivolves liear dead ad icreasig but liear argial costs. Allowig for a dowward slopig dead ad covex costs does ot, to date, alter the results (see for exaple Myles ad epahvad. This paper is orgaized as follows: ectio briefly reviews evidece o the ifluece of atizatio ad tries to give a flavor of its variety across the World. ectio presets the results associated with a closed ixed oligopoly i which there are ate firs ad oe lic fir. ectio presets the results associated with a ope ixed oligopoly i which there are ate doestic firs ad foreig ate firs ad oe lic doestic fir; ad fially, sectio 6 cocludes this paper.. Experiece with Privatizatio. Privatizatio has swept both developed ad developig coutries with Hodge ( idetifyig ore tha fifty ajor exaples fro the 198s ad 199s i the UK, Australia ad New Zealad aloe. Goverets ofte ae clear that the objectives i atizig iclude icreasig copetitio ad efficiecy with the ed result of lower prices ad better service for custoers (Hodge P Yet, despite these desires, Hodge s ( etaaalysis shows the estiated perforace effects of atizatio are alost as liely to be egative as positive. These results tae o particular iportace i ixed oligopolies where the very purpose of the lic fir has ofte bee thought to be reducig the chaces for collusio, icreasig the copetitiveess of the oligopoly ad expadig idustry output (Merrill ad cheider Fro Morocco to the Arabia Gulf, the goverets of the Arab world are turig to atizatio to raise reveues ad iprove the efficiecy of their eterprises ad services. Privatizatio ca brig with it a ijectio of foreig capital, techology ad expertise, oder busiess ethods, icreased profitability ad output ad icreased capital expeditures. May Middle East ad North Africa coutries are coitted to ehacig ate sector led growth toward atizatio easures ad perforace-based aageet cotracts. Jorda s atizatio progra is oe of the ost successful i the regio, with of its targeted copaies atized, icludig Jorda eet Factories ad Jorda Telecouicatios opay; the result is a icrease of $6 illio i foreig ivestet. Perforace-based aageet cotracts i water ad saitatio projects i Aa, the Gaza trip, ad the souther area of the West Ba have yielded alost iediate beefits. I Aa, results iclude better water quality ad aiteace, sewer cleaig, ad resposiveess to custoer coplaits. I the Gaza trip, a idepedet audit rated the aageet cotract as excellet i iprovig water quality ad quatity. I Morocco, ouicatios of the IBIMA Volue 11, 9 IN:

2 Najiba Beabess Ba support has targeted developet of soud istitutioal ad legal fraewor for the telecouicatios sector to facilitate ate sector developet ad expad cost-efficiet service to poor people, particularly i rural areas. Privatizatio cae later to the Uited tates tha to several other atios. ice the early 198s, however, atizatio i the Uited tates has oved fro a itellectual frige to becoe a ceterpiece i coteporary lic policy debates. The Reaga adiistratio bega to target progras ad assets for atizatio early i his first ter. I early 1987, the first ajor atizatio was carried out with the sale of the goveret s 85 % iterest i orail, a corporatio established by ogress i 1976 to provide freight rail service i the North-east. A presidet s oissio o Privatizatio established i epteber 1987 proposed further efforts to icrease ate participatio across a board rage of policy areas icludig low-icoe housig, air-traffic cotrol, the postal service, prisos, ad schools. Withi his first oth i office, Presidet George Bush sigaled a itet to carry o the atizatio iitiatives, speaig out i support of aret echaiss as the vehicle for school refor ad aig to his cabiet Jac Kep, a leadig advocate of eterprise zoes ad the sale of lic housig to existig teats.jeffrey R. Heig ( Depedig o its for, pace ad itesity, atizatio, o its ow, or as a itegral copoet of a wider policy of structural adjustet progras, is boud to have serious cosequeces o the society at large or o specific groups, regios, or sectors. Privatizatio etails redefiitio of the role of the state i ecooic ad social atters. This redefiitio ight brig about fudaetal chages or sigificat cotractio i the role of the state by givig way to the ate sector ad the roles of aret forces. Apart fro the ai acroecooic ad developetal issues, atizatio touches geeral ad specific social issues. These iclude atizatio effects o eployet ad eviroet; o icoe ad wealth distributio; o levels of poverty ad vulerable groups; o copesatory ad protective easures etc. All such effects for the "social balace sheet" of atizatio.. losed Ecooy This sectio aalyzes the effects of atizatio o welfare i a closed ecooy. There are three cases: ase 1 ourot to ourot deteries the effects of atizatio o welfare with ourot behavior aog all firs. ase tacelberg to ourot presets the effect of atizatio o welfare whe a lic tacelberg leader becoes a ate ourot copetitor, ad fially ase tacelberg to tacelberg presets the effect of atizatio o welfare whe a lic tacelberg leader becoes a ate tacelberg leader. I deterie the issig cases, ad fially, I copare ad aalyze the results. Table A1 suarizes these cases. ourot to ourot: De Fraja & Delboo (1989 copared the resultig welfare whe the lic fir axiizes welfare uder ourot oligopoly ad the welfare fuctio whe the lic fir axiizes its ow profit uder ourot oligopoly. They showed that the ipact of atizatio o welfare depeds o the uber of the doestic firs. If the doestic aret has a large uber of copetitors, it is socially better for the lic fir to atize ad axiize its ow profit istead of pursuig a social goal. With a large uber of firs, i the Nash case, the lic fir ust produce a very high level of output, drivig ate profits to a very low level, ad give that the lic fir s argial cost is equal to the aret price, the higher cosuers surplus uder the Nash Regie is ot high eough to copesate the lowest ate profits. De Fraja ad Delboo. (1989 P.7. tacelberg to ourot: De Fraja & Delboo (1989 copared the welfare fuctio whe the lic fir acts as a tacelberg leader ad axiizes the social welfare with the oe whe a lic fir is a ourot fir that axiizes its profit. They showed that welfare decreases with atizatio. tacelberg to tacelberg: Missig result. I copare welfare fuctios whe the goveret acts as a lic tacelberg leader ad whe it acts as a ate tacelberg leader. Previous literature has ot addressed this questio. The results of this case are preseted ext. ouicatios of the IBIMA Volue 11, 9 IN:

3 Privatizatio i losed ad Ope Mixed Oligopolies 5 Public tacelberg leader: There is a idustry coposed of ate firs ad oe doestic lic fir producig a hoogeous good i. The outputs of the ate firs are deoted q i, i 1,... ad that of the lic fir by q. The total output, the cost fuctio, the dead fuctio, the social welfare ad the ate ad lic firs profit are preseted: q q (1 Q i 1 i q c Where > ( ( (1/ q P D( q, qi a Q ; a >. ( W ( 1/ Q pr pr i ( pr qp c 1/ i i 1 ( q (5 i ( 1/ qi pr q P c (6 The lic tacelberg leader axiizes the social welfare. It deteries the best respose fuctio q i ( q for each follower the costructs the fuctio W ( q, qi ( q ad axiizes W with respect to q. Ad fially, I substitute the expressio of q ito the ate firs reactio fuctios to obtai the welfare fuctiow. The results are preseted below. The equilibriu outputs ad price are preseted below: q q i P a( 1 a( 1 a( 1 (7 (8 (9 The welfare fuctio is preseted i equatio (1: W Where: a ( 1 1 (1 Private tacelberg leader: I this sectio the lic tacelberg leader acts as a ate tacelberg leader ad axiizes its profit with respect to q ; q P Where: dpr ( q, qi ( q dq The results are preseted below: a(1 ( a(1 Β. Β ( ( 1 q i a(1 (11 Β (1 (1 ouicatios of the IBIMA Volue 11, 9 IN:

4 6 Najiba Beabess The Optial Welfare is preseted i equatio (1. a ( W Β (1 Propositio 1: I a closed ecooy, whe the lic tacelberg leader becoes a ate tacelberg leader, welfare ca ever icrease. Proof of the Propositio: W W a ( Β i.the axiizig differece i welfare yields ii. At * the differece i welfare equals zero. * As a illustratio, Figure B1 shows a represetative graph of the ad 1. ( 1. W W as a fuctio of whe a 1 The ituitio behid this propositio is that a ate tacelberg leader always produces ore tha ay followers. The atized leader produces where M>P ad the followers produce where P>M. Privatizig a lic tacelberg leader causes aret iefficiecy, therefore avoidig atizatio iproves welfare. Thus, i a closed ecooy, there is either a egative or o effect of atizatio o welfare except for the case of ourot to ourot where the atizatio could have positive effect whe there is a large. I other words, i tight oligopolies (sall, there is ever a welfare gai fro atizatio.. Ope ecooy I this sectio, I explicitly cosider a foreig copetitio. I assue a ecooy with oe lic doestic fir ad doestic ate firs ad foreig ate firs. I deterie the ipact of atizatio o welfare i three followig cases. There are two out of three cases issig i a ope ecooy. (Table A1. ourot to ourot: Missig result I copare the optial welfare whe the lic fir is a ourot player before atizatio ad whe it becoes a ate ourot player after atizatio. tacelberg to ourot: Missig result I copare the optial welfares resultig fro the case whe a lic tacelberg leader axiizes welfare with the oe it becoes a ate ourot copetitor. tacelberg to tacelberg: Fjell ad Heywood ( showed that atizatio of a lic tacelberg leader reduces leader output, icreases follower output, icreases prices, ad icreases followers profits. Regardless of ad, atizatio always icreases profit of the leader ad decreases welfare. Fjell & Heywood ( New results 1 There is a odest error i Fjell ad Heywood paper ( i the resultig social welfare of the lic tacelberg leader. But eve though the expressio of welfare they used was slightly wrog the result foud was correct. ouicatios of the IBIMA Volue 11, 9 IN:

5 Privatizatio i losed ad Ope Mixed Oligopolies 7 a. ourot to ourot i a ope ecooy. I this sectio, I copare the optial resultig welfares of a lic ourot ad the ate ourot. The Equilibriu of a Public ourot: The lic fir axiizes its welfare by choosig quatity siultaeously with the doestic firs ad foreig firs. The equilibriu yields the followig: The lic output, the doestic ad the foreig outputs ad the price are: a( 1 Λ a qf Λ a( 1 Λ Λ 1 q (15 q i (16 P (17 Where The social welfare is preseted i equatio (18: (18 a ( 1 W Λ The equilibriu of Private ourot I this case, the lic fir is atized ad axiizes its profit siultaeously with doestic firs ad foreig firs. The equilibriu lic output, ate ad foreig fir s output ad price are preseted respectively i equatio (19: q a (19 Ω a qi qf ( Ω a( 1 P (1 Ω Where Ω a ( W ( Ω Where: Ω. Propositio : I a ope ecooy, the effect of atizatio o welfare is ideteriate whe a lic ourot player becoes a ate ourot copetitor. The effect of atizatio o welfare depeds o the values of (the uber of doestic firs, (the uber of foreig firs ad (the argial cost slope. At ay give, the higher ad the positive is the effect of atizatio o welfare. Proof of the propositio: Let W W Φ ouicatios of the IBIMA Volue 11, 9 IN:

6 8 Najiba Beabess a ( Φ Φ at *: Ω Λ 1 ( ( ( * ( 1 Figure B shows * as a fuctio of whe 1, ad 6. It iplies that all the poits that are o the locus show that the differece of the welfares is equal to zero, ad the poits that are iside the locus show that Φ is egative ad the poits that are outside the locus show that the differece of the welfares is positive. Figure B also shows the effect of o Φ. The higher the the lower is Φ. This eas the higher the slope of the argial costs, the lower is welfare with atizatio. I observe that there is a iverse relatioship betwee ad. I other words, ad do substitute for each other i deteriig the value of Φ. I order to eep Φ the higher the lower is ad vice- versa. Thus, if the aret is copetitive (large ad, it is socially better for the lic fir to axiize its ow profit istead of pursuig a social goal. With the large uber of firs, the lic fir ust produce a very high level of output, drivig ate profits to a very low level; give that the lic fir s argial cost is equal to the aret price, the higher cosuers surplus is ot high eough to copesate the lower ate firs profits. q > q P < P Q > Q The lic fir produces ore ad the ate firs produce less tha the idividual output of a oligopolistic aret whe all firs are profit axiizers. As the cosuers surplus is a decreasig fuctio of the price, cosuers are better off with the atioalizatio ad worse off with the atizatio of the lic fir. b. tacelberg to ourot i a ope ecooy. I this sectio, I preset ad exaie the effect of atizatio o welfare whe a lic tacelberg leader becoes a ate ourot copetitor i a ope ecooy. First, I preset the outcoes resultig fro a lic tacelberg leader ad ext I preset the outcoes of a ate ourot ad fially I copare the resultig welfares. The Equilibriu of Public tacelberg Leader osider a idustry where oe state-owed lic fir is a tacelberg leader, with doestic ate ad foreig ate followers. The tacelberg leader oves first, aticipatig the reactio of the followers. The dead fuctio ad the cost fuctio are all idetical to the odels above. The equilibriu is preseted i the equatios below. a q [(1 (1 ] ( Ψ q i qf ( 1 a (5 Ψ ouicatios of the IBIMA Volue 11, 9 IN:

7 Privatizatio i losed ad Ope Mixed Oligopolies 9 P (1 ( 1 a Ψ (6 Where: Ψ 1 [ ( 1 ( ] [ ( ] The equilibriu welfare is preseted i equatio (7: W a ( Ψ 1 (7 Note that whe (i.e. i the absece of foreig firs, I get the result of the optial welfare of a lic tacelberg i a closed ecooy with o subsidy. The Private ourot Equilibriu The lic fir axiizes its profit siultaeously with doestic ate firs ad foreig ate firs. olvig the odel yields the equilibriu: a qi q f q (8 a(1 P (9 The resultig welfare is preseted below ( a ( W ( ( Propositio : I a ope ecooy, welfare decreases whe a lic tacelberg leader becoes a ate ourot copetitor. Proof of the propositio: Letδ. W W δ a ( 6 ( Ψ 1 < (1 As the ituitio ay suggest, if the lic fir is tacelberg leader, pricig at the argial cost is ot optial ( P M > ; this is because thas to the tacelberg leadership, the lic fir is able to ove soe of its productio to the ate producers De Fraja ad Delboo (1989. I fact it is also: q > q P > P Q > Q As the cosuers surplus is a decreasig fuctio of the price, cosuers are better off whe a lic fir is a tacelberg leader ad worse off whe it is a ourot copetitor. ouicatios of the IBIMA Volue 11, 9 IN:

8 Najiba Beabess.. opariso I a ope ecooy, the lic fir should atize oly if it acts as a ourot player before ad after atizatio ad oly whe the aret is copetitive eough (large ad. 5. oclusio The literature o the welfare effects of atizatio i ixed oligopolies is issig three relevat cases (table A1, therefore this paper fills the gap i this literature by ivestigatig these cases. Table A represets the copleted table that suarizes the effects of atizatio o welfare for six differet cases. I observe that two out of six cases show a egative effect of atizatio o welfare which are: i tacelberg to ourot i a closed ecooy; ii tacelberg to ourot i a ope ecooy. Two cases out of six show o- positive effect of atizatio o welfare, which are iii tacelberg to tacelberg i a closed ecooy; ad tacelberg to tacelberg i a ope ecooy. Ad two out of six cases show ideteriate effect of atizatio o welfare which are the ourot to ourot i both a closed ad ope ecooy. I coclude that a lic tacelberg leader should ot becoe a ate tacelberg leader uder ay exaied circustaces. Whether the ecooy is closed or ope, the social welfare decreases with atizatio. I additio, a lic tacelberg leader should ot becoe a ourot copetitor i ay of the cases preseted because welfare either decreases or is uaffected with atizatio. O the other had, a lic ourot player should be atized oly whe the doestic aret is copetitive eough because atizatio icreases social welfare. Moreover, I observe that the effects of atizatio o welfare i a closed ecooy are idetical to the oes i a ope ecooy. I coclude that the presece of foreig copetitio does t affect the qualitative ifluece of atizatio o social welfare. 6. Appedix Table A1: Results o the Ifluece of Privatizatio o Welfare. losed Ecooy Ope Ecooy 1.ourot to ourot: 1.ourot to ourot: De Fraja &Delboo (1989? /-.tacelberg to ourot: De Fraja & Delboo ( tacelberg to ourot?. tacelberg to tacelberg?.tacelberg to tacelberg (Fjell ad Heywood -* Key: (/- Meas that the chage i welfare depeds o the uber of doestic firs i the aret. - Meas that welfare decreases with atizatio.? Meas that the result is issig ad will be covered i this paper. -* Meas that the chage i welfare is o- positive ouicatios of the IBIMA Volue 11, 9 IN:

9 Privatizatio i losed ad Ope Mixed Oligopolies 1 Table A : The copleted table represets the effects of atizatio o welfare. losed Ecooy Ope Ecooy 1.ourot to 1.ourot to ourot: ourot: Beabess De Fraja &Delboo (1989 /- /-.tacelberg to ourot: De Fraja & Delboo ( tacelberg to tacelberg Beabess -*.tacelberg to ourot Beabess -.tacelberg to tacelberg (Fjell ad Heywood -* Key: (/- Meas that the chage i welfare depeds o the uber of doestic firs i the aret. - Meas that welfare decreases with atizatio. Meas that the welfare does t chage with atizatio. -* Meas that the chage i welfare is o- positive Figure B1. tacelberg to tacelberg i a closed ecooy. Delta (the chage i welfare fuctios as a fuctio of whe a1 ad 1. Figure B: ourot to ourot i a ope ecooy. *( at 1,, ad 6. ouicatios of the IBIMA Volue 11, 9 IN:

10 Najiba Beabess < 1 6 > ouicatios of the IBIMA Volue 11, 9 IN:

11 Privatizatio i losed ad Ope Mixed Oligopolies 7. Refereces [1[ De-Fraja G., Delboo F. (1989. Alterative trategies of a lic Eterprise i Oligopoly, Oxford Ecooic Paper. 1,P.-11. [] Dieter Bös, "Privatizatio i Europe: A opariso of Approaches," Oxford Review of Ecooic Policy," Vol. 9 No. 1 (199 pp [] Fjell K. &Pal D. (1996. A ixed Oligopoly i the presece of Foreig Private Firs aadia Joural of Ecooics, 9,P [] Fjell K.& Heywood J. (. Public tacelberg Leadership Australia Ecooic Papers.P67-8. [5] Fjell K. & Heywood J. (. Mixed Oligopoly, subsidizatio ad the order of fir s oves: the relevace of atizatio. Ecooics Letters, 8, pp [6] Hodge, Graee. (. Privatizatio: A Iteratioal Review of Perforace. Boulder olorado: Westview Press. [7] Jeffrey R. Heig. (Witer, Privatizatio i the Uited tates: Theory ad Practice. Political ciece Quarterly, Vol. 1, No., pp [8] Myles G. (. Mixed Oligopoly, ubsidizatio ad Order of Firs Moves: a Irrelevace Result for the Geeral ase. Ecooic Bulleti, 1 (1, P 1-6. [9] Pal D. & White M. (1998. Mixed Oligopoly, Privatizatio, ad trategic Trade Policy. outher Ecooics Joural, 65 (, P [1] epahvad M. (. Public Etreprise trategies i a Maret Ope to Doestic ad Iteratioal opetitio. Aales D ecooie Et De tatistique-#75/76, P [11] George Yarrow, "Privatizatio i Theory ad Practice," Ecooic Policy, Vol. (April 1986, pp [1] Paygo Theoy,Joaa, (1 Mixed Oligopoly, ubsidizatio ad the order of firs oves: a irrelevace result. Ecooic Bulleti, Vol.1,No. pp.1-5 opyright 9 by the Iteratioal Busiess Iforatio Maageet Associatio (IBIMA. All rights reserved. Authors retai copyright for their auscripts ad provide this joural with a licatio perissio agreeet as a part of IBIMA copyright agreeet. IBIMA ay ot ecessarily agree with the cotet of the auscript. The cotet ad proofreadig of this auscript as well as ay errors are the sole resposibility of its author(s. No part or all of this wor should be copied or reproduced i digital, hard, or ay other forat for coercial use without writte perissio. To purchase reprits of this article please e-ail: adi@ibia.org. ouicatios of the IBIMA Volue 11, 9 IN: