不完全契约下PPP项目剩余控制权配置模型研究

28 2 2013 4JOURNAL OF SYSTEMS ENGINEERINGV ol.28No.4Apr.2013PPP,( , 300072): (public-private partnership,PPP) ( ) . PPP , , PPP .PPP , , .: ; ; ; ;:F270 :A :1000−5781(2013)02−0227−07Study of the allocation of residual control rights in the public-privatepartnership under incomplete contractsSun Hui,Ye Xiuxian(College of Management and Economics,Tianjin University,Tianjin300072,China)Abstract:PPP(public-private partnership)is an important model that the public sectors and private ones col-laborate to supply the public goods and public services.This paper believes that the genuine nature of PPP is the contract,and researches the affect of the residual control rights allocation on the parties’investment level from the perspective of the incomplete contracts.A mathematical model is used to analyze the relationship be-tween residual control rights allocation and the motivation of both parties’investments under the background of PPP.The paperfinds that the optimal allocation of residual control rights depends on the parties’respective degrees of optimism of the expectation on thefinal return,both parties’technological factors,and the allocation of income provided by the initial contract when there is a proposal of income allocation in the initial contract.Key words:public-private partnership;contractual incompleteness;allocation of residual control rights;allocation of income;investment incentives1(PPP) ( ) [1], . PPP , , ( ) , . , , , , [2,3]. PPP ,228 28 , . , , , . ,PPP , [4−11].PPP . , , [12−14].Grossman [15],Hart [16,17] , ( GHM ), . GHM ,Hart [18] ( HSV ) , ( ) , HSV . HSV ,Besley [19] ( BG ), , ( ). BG , , ( ) . ,BG PPP . [20] BG 0/1 , . , , , PPP .Francesconi [21] , ( ) , ( ) ( ) . PPP , . [22] PPP . [23] , PPP BOT , BOT [24]. GHM BG , FM , , , . GHM , ( ) . , , PPP .. , .1) , ;2) , ;3) , , ( ) , .22.1(g) (n) , , . ( ) , . , , .Grossman [15] , 1. :2 : PPP 229 , ( 0); ( 1), . : , ( 2); , ( 3). , , . 2 .1Fig.1Timeline of the model2.1.1 0, , . θg, θn θg+θn= 1. [20,21], π . π(π∈[0,1]) ,1−π . π=1(π=0), ( ) ; π∈(0,1), .2.1.2 1, , . y g, y n. y i(i=g,n) C i(y i), C g(y g) C n(y n), C i(i=g,n) ,, C′i >0,C′′i0, C i(0)=0.2.1.3 2. , : , B(y,π), y≡(y g,y n); , b(y), b(y)>B(y,π), . π=0 B n(y),π=1 B n(y). B(y,π)=πB g(y)+(1−π)B g(y).1)b y i(i=g,n) , , b(0,0)>0;2)B i(i=g,n) y i(i=g,n) , , B i(0,0) 0;3) y,b′1(y) B′g1(y)>B′n1(y),b′2(y) B′n2(y)>B′g2(y)( 1,2 , );4) y,b′′12(y) B′′g12(y) 0,b′′12(y) B′′n12(y) 0;5) y,|b′′11(y)|>|B′′g11(y)|,|b′′11(y)|>|B′′n11(y)|,|b′′22(y)|>|B′′g22(y)|,|b′′22(y)|>|B′′n22(y)|;6) y,|b′′11(y)|−|b′′12(y)|>|B′′g11(y)|−|B′′g12(y)| 0,|b′′11(y)|−|b′′12(y)|>|B′′n11(y)|−|B′′n12(y)| 0, |b′′22(y)|−|b′′21(y)|>|B′′g22(y)|−|B′′g21(y)| 0,|b′′22(y)|−|b′′21(y)|>|B′′n22(y)|−|B′′n21(y)| 0.3) , , . 4) (weak complements)[21].5) 6) (standard regularity conditions)[21].230 28 2.1.4 3, , u g(y)=θg b(y)+t, u n(y)=θn b(y)−t, t , . , , ¯u g(y)=θg(πB g(y)+(1−π)B n(y)),¯u n(y)=θn(πB n(y)+(1−π)B n(y)). (b(y)−B(y,π)), r g=π(b(y)−B(y,π)), r n=(1−π)(b(y)−B(y,π)).,V g(y,π)=θg(πB g(y)+(1−π)B n(y))+π(b(y)−(πB g(y)+(1−π)B n(y))),(1) V n(y,π)=θn(πB g(y)+(1−π)B n(y))+(1−π)(b(y)−(πB g(y)+(1−π)B n(y))).(2) 2.20 θi π, 1 ,i ( V g(y,π) C g(y g)) 1 y i, i . , y e=(y e g(π),y e n(π)) (3) (4) .V g1(y,π)=C′g(y g),(3)V n2(y,π)=C′n(y n).(4)(3) (4) π ,V g 12∂y en∂π=−V g13,(5)V n 12∂y eg∂π=−V n23.(6)(5) (6)∂y egA (V n23V g12−V g13(V n22−C′′n)),(7)∂y enA(V g13V n12−V n23(V g11−C′′g)),(8)(V n22−C′′n),(V g11−C′′g)<0( ),V g12,V n12 0( ),A=(V n22−C′′n)(V g11−C′′g)−V g 12V n12,A>0( ).,∂y eg∂π( ), V n23,V g13(),V g 13=∂∂y g =(θg−2π)(B g1(y)−B n1(y))+(b1(y)−B n1(y)),(9)V n 23=∂∂y n =(θg−2π)(B n2(y)−B g2(y))+(b2(y)−B n2(y)).(10)(9) (10) 2π θg+b1(y)−B n1(y)B g1(y)−B n1(y),V g130; 2π θg+b2(y)−B n2(y)B n2(y)−B g2(y),V n230.2 : PPP 231Besley [19] , B n1(y)B n2(y)=βn∈(0,1),B n1(y)b2(y)=γ2∈(0,1), γ1 βg,γ2 βn.βg βn y , i[12];γ1 γ2 .γi , i(b k ,k=1,2), i .(9) (10), .1 2π θg+βg(1−γ1)∂π0,∂y en2 θg+βg(1−γ1)∂π 0,∂y e n γ2(1−βn),2(1−π) θn+βn(1−γ2)∂π∂y en2 θn+βn(1−γ2)∂π 0,∂y e n 2 θg+βg(1−γ1)2 θg−βn(1−γ2)2 θg−βn(1−γ2)2θg+βg(1−γ1)∂π,∂y e n 2 θg−βn(1−γ2)2θg+βg(1−γ1)γ1<1βg−1 θn 1βn+ 12 θg+βg(1−γ1)γ1>1βg−1)θn1βn+ 12 θg−βn(1−γ2)2 , γ1,γ212βg12βn, 3232 28 π∈ 3γ2−2βn−γ2βn4γ1(1−βg) .3 , , .3PPP , . PPP , . , ; , ; , : , , . , , . , , ., , , PPP . , , , , , , PPP .:[1]Eric M,Jean T.Public-private partnerships and government spending limits[J].Internationnal Journal of Industrial Organnization,2008,26(2):412–420.[2]Bank W.Bureaucrats in Business:The Economics and Politics of Government Ownership[M].New York:Oxford University Press,1995.[3]Bank W.World Development Report2004:Making Services Work for Poor People[R].NewYork:Oxford University Press,2004.[4]Hart O.Incomplete contracts and public ownership:Remarks and an application to public-private partnerships[J].The EconomicJournal,2003,113(486):69–76.[5]Hardy C,Phillips N,Lawrence T B.Resources knowledge and influence:The organization effects of inter-organizational collabora-tion[J].Journal of Management Studies,2003,40(2):321–347.[6]De Bettignies J E,Ross T W.The economics of public-private partnerships[J].Canadian Public Policy,2004,30(2):135–154.[7]Bennett J,Iossa E.Contracting out public service provision to not-for-profitfirms[J].Oxford Economic Papers:New Series,2005,62(4):784–802.[8]Ramiah I,Reich M.Building effective public-private partnerships:Experiences and lessons from the African comprehensiveHIV/AIDS partnerships[J].Social Science and Medicine,2006,63(2):397–408.[9]Martimort D,Pouyet J.To build or not to build:Normative and positive theories of public-private partnerships[J].InternationalJournal of Industrial Organization,2008,26(2):393–411.[10]Bettignies J E,Ross T W.Public-private partnerships and the privatization offinancing:An incomplete contracts approach[J].International Journal of Industrial Organization,2009,27(3):358–368.[11]Roy J,Chowdhury P R.Public-private partnerships in micro-finance:Should NGO involvement be restricted[J].Journal of Develop-ment Economics,2009,90(2):200–208.[12]Maskin E,Tirole J.Unforeseen contingencies and incomplete contracts[J].Review of Economic Studies,1999,66(1):83–114.2 : PPP 233 [13]Douglas G B,Robert K R.Control rights,priority rights,and the conceptual foundations of corporate reorganizations[J].VirginiaLaw Review,2001,87(5):921–959.[14]Anderlini L,Felli L.Incomplete contracts and complexity costs[J].Theory and Decision,1999,46(1):23–50.[15]Grossman S,Hart O.The costs and benefits of ownership:A theory of vertical and lateral integration[J].Political Economy,1986,94(4):691–719.[16]Hart O,Moore J.Property rights and nature of thefirm[J].Journal of Political Economy,1990,98(6):1119–1158.[17]Hart O,Moore J.Foundations of incomplete contracts[J].Review of Economic Studies,1999,66(1):115–138.[18]Hart O,Shleifer A,Vishny R W.The proper scope of government:Theory and an application to prisons[J].Quarterly Journal ofEconomics,1997,112(4):1127–1161.[19]Timothy B,Ghatak ernment versus private ownership of public goods[J].Quarterly Journal of Economics,2001,116(4):1343–1372.[20] , , .PPP [J]. ,2009 23(3):23–29Theoretical Study on the Efficient Allocation of Control Rights in the Public-Private Partnership(PPP)[J].Journal of Industry Engi-neering and Engineering Management,2011,23(3):23–29 (in Chinese)[21]Francesconi M,Muthoo A.Control Rights in Complex Partnerships[R].Coventry,UK:University of Warwick,2010.[22] , , .PPP : PPP[J] ,2009,21(9):29–38Zhang Zhe,Jia Ming,Wan Difang.A Theoretical and Empirical Study of Allocation of Control Rights and Its Influence towards the Cooperation Efficiency in PPP:Exemplified by PPPs in China s medical and healthfields[J].Management Review,2009,21(9): 29–38 (in Chinese)[23] , , .PPP [J]. ,2011,3(1):154–158Sun hui,Fan zhiqing,Shi Ye.Research on the optimal ownership structure of an expressway under a PPP scheme[J].Journal of Industry Engineering and Engineering Management,2011,3(1):154–158 (in Chinese)[24] , , .BOT [J]. ,2011,26(1):68–73Sun hui,Fan zhiqing,Shi Ye.Research on effect of exclusive condition on pricing and social welfare of road under BOT scheme[J].Journal of Systems Engineering,2011,26(1):68–73 (in Chinese):(1968—), , , , , : ,Email:bighui2000@;(1986—), , , , : ,Email:tiandayxx@.1) π∈(0,1) (V n22−C′′n),(V g11−C′′g)<0.V g1=θg B1+π(b1−B1) V n2=θn B2+(1−π)(b2−B2) V g11=θg B11+π(b11−B11) 1, (1), (2) (5) B11=πB g11+(1−π)B n11 0,B11=πB g11+(1−π)B n11>πb11+(1−π)b11=b11,B11 0,b11−B11<0 V g11 0.(π=0 ,V g11<0),V n22=θn B22+(1−π)(b22−B22).1, (1), (2) (5) ,B22=πB g22+(1−π)B n22 0,B22=πB g22+(1−π)B n22>πb22+(1−π)b22=b22,B22 0,b22−B22<0, V n22 0,(π=1,V n22<0). .2) y, V g12(y,π) 0,V n12(y,π) 0.V g12=θg B12+π(b12−B12), 1 (4) ,B12=πB g12+(1−π)B n12 0,B12=πB g12+(1−π)B n12 πb12+(1−π)b12=b12, B12 0,b12−B12 0, V g12 0, V n12 0. .3)A=(V g11−C”g)(V n22−C”n)−V g12V n12=V g11V n22−V g12V n12−V g11C′′n−V n22C′′g,A>0.|V g11|>|V g12|,|V n22|>|V n12|,V g11=θg B11+π(b11−B11),V g12=θg B12+π(b12−B12),|V g11|= |θg−π||B11|+π|b11|,|V g12|=|θg−π||B12|+π|b12|.1 (6) |b11|−|b12|>|B g11|−|B g12| 0,|b11|−|b12|>|B n11|−|B n12| 0,|V g11|−|V g12|=|θg−π|(|B11|−|B12|)+π(|b11|−|b12|) π[(|b11|−|b12|)−(|B11|−|B12|)]+θg(|B11|−|B12|).|B11|=π|B g11|+(1−π)|B n11|,|B12|=π|B g12|+(1−π)|B n12|,|B11|−|B12|=π(|B g11|−|B g12|)+(1−π)(|B n11|−|B n12|) 0,|B11|−|B12|=π(|B g11|−|B g12|)+(1−π)(|B n11|−|B n12|)<π(|b11|−|b12|)+(1−π)(|b11|−|b12|)=|b11|−|b12|.π∈(0,1) |V g11|−|V g12|>0 |V n22|−|V n12|>0.A=(V g11−C”g)(V n22−C”n)−V g12V n12=V g11V n22−V g12V n12−V g11C′′n−V n22C′′g.V g 11 0,V g220 V g11C′′n+V n22C′′g 0.V g12(y,π) 0,V n12(y,π) 0, |V g11|−|V g12|>0,|V n22|−|V n12|>0,V g11V n22−V g12V n12>0,A>0. .。