Volume 3, Issue 1 Partal prvatzaton n prce-settng mxed duopoly Kazuhro Ohnsh Insttute for Basc Economc Scence, Japan Abstract Ths paper nvestgates a prce-settng mxed model nvolvng a prvate frm and a publc frm to reassess the welfare effect of partal prvatzaton. Frst, the government chooses the level of prvatzaton to maxmze socal welfare. Second, observng the level of prvatzaton, the frms non-cooperatvely choose prces. The paper then demonstrates that partal prvatzaton s not an optmal choce for the government. Ctaton: Kazuhro Ohnsh, (1) ''Partal prvatzaton n prce-settng mxed duopoly'', Economcs Bulletn, Vol. 3 no.1 pp. 39-314. Submtted: Aug 1 9. Publshed: January 8, 1.
1. Introducton In recent years, the theoretcal analyss of partal prvatzaton of state-owned publc frms has been deeply and extensvely studed by many economsts. For example, Matsumura (1998) nvestgates a quantty-settng duopoly model nvolvng a proft-maxmzng prvate frm and a state-owned publc frm. Frst, the government wshes to maxmze socal welfare and chooses the degree of prvatzaton of the state-owned publc frm. Second, the prvate frm and the partally prvatzed frm non-cooperatvely choose quanttes. He then shows that nether full prvatzaton (the government does not hold any shares) nor full natonalzaton (the government holds all of the shares) s optmal for socal welfare; that s, partal prvatzaton s optmal. There are also many other excellent studes such as Chang (5), Matsumura and Kanda (5), Chao and Yu (6), Tomaru (6), Fujwara (7), Lu and Poddar (7), Han and Ogawa (8), Ishbash and Kaneko (8), and Roy chowdhury (9). Most theoretcal studes demonstrate that the optmal degree of prvatzaton exhbts nether full prvatzaton nor full natonalzaton but partal prvatzaton. Ths paper nvestgates a prce-settng mxed model nvolvng a prvate frm and a publc frm to reassess the welfare effect of partal prvatzaton. The tmng of the game runs as follows. In the frst stage, the government chooses the level of prvatzaton to maxmze socal welfare. Observng the level of prvatzaton, the frms non-cooperatvely choose prces n the second stage. The purpose of the paper s to assess the welfare effect of partal prvatzaton by examnng a prce-settng mxed duopoly model and to show that partal prvatzaton s not optmal n the prce-settng mxed competton. Ths result s n marked contrast to that of the quantty-settng mxed competton. The remander of the paper s organzed as follows. In Secton, we formulate the model. Secton 3 assesses the welfare effect of partal prvatzaton n prce-settng mxed duopoly. Fnally, Secton 4 concludes the paper.. The model In ths secton, we consder a prce-settng mxed model wth two frms (frm and frm 1) and the government. These frms produce mperfectly substtutable goods. There s no possblty of entry or ext. On the consumpton sde, there s a contnuum of consumers of the same type whose utlty functon s lnear. Subscrpts and 1 denote frm and frm 1, respectvely. Followng Bárcena-Ruz (7), we assume that the representatve consumer maxmzes U ( q, q1 ) - pq - p1q1, where q s the amount of good and p s ts prce (,1). The functon U ( q, q 1) s quadratc, strctly concave and symmetrc n q and q 1 :
1 U ( q, q1) a( q + q1 ) - ( q + bqq1 + q1 ), (1) where a s a constant and bî (,1) s a measure of the degree of substtutablty among products. The demand functon s gven by a(1 - b) - p + bp j q 1- b (, j,1; ¹ j). () For smplcty, we assume that a 1 and b.5. Each frm s proft s p ( p - c ) q (,1), (3) where c s the margnal cost of frm. Snce the result of ths paper s not affected by c, we normalze t to zero. Frm 1 ams to maxmze ts proft. Furthermore, socal welfare, whch s the sum of consumer surplus and profts, s gven by W CS + p + p1. (4) The objectve functon of frm s gven by V lp + (1 - l) W, (5) where l Î [,1] s the level of prvatzaton. That s, f l frm becomes purely prvate, whereas f l 1 t becomes purely publc. The game s constructed by the followng two-stage decson-makng. In the frst stage, the government chooses the level of prvatzaton, l, to maxmze socal welfare. Observng l, the frms non-cooperatvely choose prces n the second stage. The subgame perfect Nash equlbrum of the prce-settng mxed game s examned. 3. The man result In ths secton, we examne the welfare effect of partal prvatzaton n the prce-settng mxed game. We obtan the reacton functons n prces of the two frms: R R 1- l + p1, (6) ( - l) 1+ p 4 1. (7) From (6) and (7), the equlbrum can be derved as follows: p q 5-4l 15-8l (1-3 l) 3(15-8 l), p1, q1 5-3l, 15-8l 4(5-3 l). 3(15-8 l) Furthermore, the profts, consumer surplus, and socal welfare can be expressed as follows: 3
(5-4 l)(1-3 l) p, (8) 3(15-8 l) 4(5-3 l) p 3(15-8 l) 1 CS W (1-9l + 1 l ) 3(15-8 l) ( - 5l + 51 l ) 3(15-8 l), (9), (1). (11) The maxmzaton of (11) wth respect to l s derved from dw / dl. That s, we have l 5/» 1.136. W s llustrated n Fgure 1 as a functon of l. When l 1, W s a strctly ncreasng functon of l. Ths can be stated n the followng proposton. Proposton 1. In the prce-settng mxed model, partal prvatzaton s not a reasonable choce for the government that wshes to maxmze socal welfare. W 9.66 147» 16.593 7» 1 α Fgure 1. Prvatzaton and Socal Welfare 4
4. Concluson We have nvestgated a prce-settng mxed model nvolvng a prvate frm and a publc frm to reassess the welfare effect of partal prvatzaton and have shown that partal prvatzaton s not optmal n the prce-settng mxed competton. We have found that our result s n marked contrast to that of the quantty-settng mxed competton. We have used a mxed model wth a publc frm and a domestc prvate frm and have examned the welfare effect of partal prvatzaton. However, what f publc and foregn prvate frms compete aganst each other? Ths s one of varous extensons of ths study that reman to be consdered n future research. References Bárcena-Ruz, J. C. (7) Endogenous tmng n a mxed duopoly: prce competton Journal of Economcs 91, 63-7. Bös, D. (1) Prvatzaton: A Theoretcal Treatment, Clarendon Press: Oxford. Chang, W. W. (5) Optmal trade and prvatzaton polces n an nternatonal duopoly wth cost asymmetry Journal of Internatonal Trade and Economc Development 14, 19-4. Chao, C. C. and E. S. H. Yu (6) Partal prvatzaton, foregn competton, and optmal tarff Revew of Internatonal Economcs 14, 87-9. Cremer, H., M. Marchand, and J.-F. Thsse (1991) Mxed olgopoly wth dfferentated products Internatonal Journal of Industral Organzaton 9, 43-53. Fjell, K. and J. S. Heywood () Publc Stackelberg leadershp n a mxed olgopoly wth foregn frms Australan Economc Papers 41, 67-81. Fjell, K. and D. Pal (1996) A mxed olgopoly n the presence of foregn prvate frms Canadan Journal of Economcs 9, 737-743. Fujwara, K. (7) Partal prvatzaton n a dfferentated mxed olgopoly Journal of Economcs 9, 51-65. George, K. and M. La Manna (1996) Mxed duopoly, neffcency, and publc ownershp Revew of Industral Organzaton 11, 853-86. Gupta, N. (5) Partal prvatzaton and frm performance Journal of Fnance 6, 987-115. Han, L. and H. Ogawa (8) Economc ntegraton and strategc prvatzaton n an nternatonal mxed olgopoly FnanzArchv 64, 35-363. Ishbash, K. and T. Kaneko (8) Partal prvatzaton n mxed duopoly wth prce and quantty competton Journal of Economcs 95, 13-31. 5
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