Residual Claimancy and Monitoring for Regulating Multiple Agents* Shinji Kobayashi Graduate School of Economics Nihon University Shigemii Oba Graduate School of Economics Nihon University January 2009 Abstract In this paper we examine the optimal incentive contracts with two-dimensional uncertainty in which a government selects residual claimancy and monitoring instrument under a decentralized or a consolidated industry structure. We consider the same quality of public facilities supplied by a government in the two di¤erent regions. In each region, these facilities are procured from a …rm which has private information about the cost. We show that optimal industry structure is contingent on residual claimancy and monitoring instrument. 1 Introduction We consider the same quality of public facilities, such as toll expressways, supplied by a government in the two di¤erent regions. In each region, these facilities are procured from a …rm which has private information about the cost. We focus on the following three issues. The …rst issue is industry structure: decentralization versus consolidation. The second issue is privatization versus nationalization. The third issue is optimal monitoring instrument. We analyze three industry structures. The …rst structure is a decentralized industry in which the government procures the facilities from two separate …rms. The second structure is a consolidate industry with a decentralized organization. The government procures from a single …rm, the *Preliminary 1 organization of which is decentralized. The third structure is a consolidate industry with an integrated organization. The government procures from a single …rm, the organization of which is integrated. Analyzing the privatization versus nationalization, we assume that the government can determine residual claimancy. When the …rm is privatized, it seeks pro…t and is a residual claimant. When the …rm is nationalized, it does not seek pro…t and the government is a residual claimant. Analyzing the optimal monitoring instrument, we assume the government can decide to implement input monitoring or output monitoring. In either structure, we show, the government prefers to be a residual claimant and implement input monitoring. Furthermore, we show that the optimal industry structure is contingent on who is a residual claimant and which of monitoring instruments is implemented. For instance, when implementing output monitoring, the government prefers a consolidated industry with a decentralized organization. A decentralized industry yields the intermediate payo¤ and a consolidated industry with an integrated industry yields the lowest payo¤ for the government. This paper is related to the literature on information integration and decentralization. Dana (1993) analyzes the identical optimal problem. He concludes that the optimal industry structure is contingent on whether two production costs are su¢ ciently positively correlated or not. Also, Baron, Besanko (1992), Gilbert and Riordan (1995) analyze the optimal problem, in which a producer composes a …nal output from two inputs provided by one or two suppliers. They conclude that the optimal supplier contract is contingent on the degree of complementarity or substitutability between the two inputs. This paper is also related to Khalil and Lawarree (1995). They explore the asymmetric information model where a principal can design a residual claimant and a monitoring instrument. They analyze the four cases contingent on residual claimancy and monitoring instrument. They conclude that input monitoring with a principal as a residual claimant yields the highest payo¤ and that input monitoring with an agent as a residual claimant yields the lowest. Also, regardless of who is a residual claimant, output monitoring yields the intermediated payo¤. We are motivated by the fact that Japanese state-owned gigantic monopolistic companies have been privatized and divided under the Administrative and Fiscal Reforms since the end of the twentieth century. In 1985 Nippon Telegraph and Telephone Public Corporation was privatized and in 1999 this privatized company was divided into the two regional companies. In 1987 Japan National Railways was privatized and divided into the seven regional railway companies. Furthermore, in 2005 Japan Highway Public Corpora2 tion (JH) was divided into the three privatized expressway companies and a government institution. This paper is organized as follows. In Section 2, we present the model and basic assumptions. In Section 3, we characterize the optimal contracts under the three industry structures. In each structure, we analyze four cases contingent on a residual claimant and a monitoring instrument. In Section 4, we make comparative analyses about these three structures. In Section 5, we conclude. 2 Model We consider the public facilities which are supplied by a government in two di¤erent regions: region A and B. In each region, the government procures these facilities, the quality of which is …xed, from a …rm. The facilities yield R S and revenue ; which are observable and veri…able, in consumer surplus 2 2 each region. The …rm’s production cost depends on the productivity , which is determined by the regional environment, and the …rm’s cost reduction e¤ort e: The cost function is given by C= e; where we have with 2 f 1 ; 2 g and 0 < 1 < 2 : Probability distribution over 1 or 2 is respectively p or 1 p with 0 < p < 1: We denote the productivities in region A and B as iA and jB respectively with i; j = 1 or 2: For simplicity, we assume iA and jB are independent. The …rm’s cost e2 reduction e¤ort e is the disutility for the …rm given by (e) = . These 2 parameters and e are the …rm’s private information. We analyze two industry structures. One structure is a decentralized industry. The government procures from two …rms, each of which produces the facility in the respective region. The other structure is a consolidated industry. The government procures from a single …rm which produces the facilities in the two separate regions. Under the consolidated industry, the …rm is assumed to have either a decentralized organization or an integrated organization. With a decentralized organization, the …rm exerts e¤ort in the 2 2 eA eB ij ij two regional divisions and its disutility is given by + : With an 2 2 integrated organization, the …rm exerts e¤ort in an integrated division and (eij )2 its disutility is given by : 2 3 Under each structure, the government can determine a residual claimant (the government or the …rm) and a monitoring instrument (input or output). When the government is a residual claimant, it obtains the pro…t, R C. When the …rm is a residual claimant, it obtains the pro…t. With input monitoring, the government can observe e and enforce the optimal e¤ort level. With output monitoring, the government can verify the realized cost. We suppose the following timing of events: (Stage 1) The government decides on an industry structure (a decentralized industry, a consolidated industry with a decentralized organization or a consolidated industry with an integrated organization). Also, the government determines a residual claimant (a government or a …rm) and a monitoring instrument (input or output monitoring). (Stage 2) In each region, nature decides on the regional productivity and the …rm responsible for each region observes it. (Stage 3) The government o¤ers a contract contingent on what is monitored. The …rm signs the contract if it guarantees at least reservation utility. (Stage 4) The …rm exerts cost reduction e¤ort e. (Stage 5)The …rm completes the production and the cost C is realized. At the end of this stage, the monetary transfer between the government and the …rm is realized. 3 Optimal Contracts under the Three Industry Structures In this section, under the respective industry structure, we analyze the government’s optimal contract for the following four cases: Case 1: Government is a residual claimant and monitors …rm’s e¤ort. Case 2: Government is a residual claimant and monitors …rm’s cost. Case 3: Firm is a residual claimant and its e¤ort is monitored. Case 4: Firm is a residual claimant and its cost is monitored. 3.1 3.1.1 Decentralized Industry Government as Residual Claimant Case 1: Input Monitoring The government’s problem is to maximize X A B B G eB =S+R pij ( iA eA ij + tij + j ij + tij ): The government faces with the following interim incentive compatibility constraints: 4 X and " eA 1j 2 2 2 pi1 tB i1 eB i1 2 p1j tA 1j X " # X # X " eA 2j 2 pi1 tB i2 eB i2 2 p1j tA 2j " 2 2 # # ; and the following individual rationality constraints: eA 2j 2 B ei2 2 tA 2j tB i2 and 2 0 2 0: Rewriting the problem with the binding conditions and taking the …rst order B conditions with respect to eA ij and eij ; we obtain B fb eA = 1: ij = eij = e GI The government’s expected payo¤ GI =S+R 2p is given by 2(1 1 p) 2 + 1: Case 2: Output Monitoring The government’s problem is identical. It faces with the following interim incentive compatibility constraints and individual rationality constraints: X " eA 1j 2 2 2 pi1 tB i1 eB i1 2 p1j tA 1j X " # X # X eA 2j 2 B ei2 2 tA 2j and tB i2 5 " e^A 2j 2 pi1 tB i2 e^B i2 2 p1j tA 2j " 2 0 2 0; 2 2 # # A B where we have ebA bB 2 + 1 and e 2 + 1 . Rewriting the 2j = e2j i2 = ei2 problem with the binding conditions and taking the …rst order conditions B with respect to eA ij and eij ; we have B B A eA 11 = e12 = e11 = e21 = 1 and Since 0 < e and 0 < eA 2j 2 + 1 = eB i2 2 GO =S+R 2 GO 2 2 <1 1 The government’s expected payo¤ 3.1.2 p B A B eA 21 = e12 = e22 = e22 = 1 1 + 1; p ( 1 ): 2 we must satisfy p: is given by +1+ p 1 p ( 2 2 1) : Firm as Residual Claimant Case 3: Input Monitoring The government’s problem is to maximize X F =S+ pij ijA + ijB subject to X " R p1j 2 " X R pi1 2 ( ( 1 1 2 eA 1j ) eA 1j 2 2 eB i1 ) eB i1 2 A 1j B i1 # # X X p1j pi1 " " 2 R 2 R 2 ( ( 1 1 eA 2j ) eA 2j 2 eB i2 ) eB i2 2 2 A 2j 2 eA R 2j A A ( 2 e2j ) 0 2j 2 2 2 eB R i2 B B and ( 2 ei2 ) 0: i2 2 2 Rewriting the problem with the binding conditions and taking the …rst order B condition with respect to eA ij and eij , we have B fb = 1: eA ij = eij = e The government’s payo¤ FI FI is represented as =S+R 6 2 2 + 1: B i2 # # Case 4: Output Monitoring The government’s problem is identical. It faces with the following interim incentive compatibility constraints and individual rationality constraints: X " R p1j 2 " X R pi1 2 ( 1 ( 1 2 eA 1j ) eA 1j 2 2 eB i1 ) eB i1 2 R 2 R 2 and A 1j B 1j ( X # pi1 eA 2j 2 eB i2 2 eB i2 ) 2 p1j X eA 2j ) 2 ( # " " R 2 ( R 2 ( 1 1 eA 2j ) e^A 2j 2 eB i2 ) e^B i2 2 2 A 2j 2 2 A 2j 0 B i2 0: 2 A B where we have ebA bB 2 + 1 and e 2 + 1 . Rewriting the 2j = e2j i2 = ei2 problem with the binding conditions and taking the …rst order conditions B with respect to eA ij and eij ; we obtain A B B eA 11 = e12 = e11 = e21 = 1 p B A B and eA 21 = e12 = e22 = e22 = 1 Since 0 < e and 0 < eA 2j 2 + 1 = eB i2 2 The government’s payo¤ is FO 3.1.3 FO =S+R 2 <1 1 1 + p ( 1 ): 2 we must satisfy 1; p: is given by 2 2 +1+ p 1 p ( 2 2 1) : Comparison By the comparison of the government’s payo¤s, we have GO and GI FI FI p = 1 p = 2p( 2 7 ( 2 1) 2 1) > 0: >0 B i2 # # Since 2 1 GI <1 GO p; we have = p( 1) 2 1 2 ( 1 p = FO 2 1) < GI > p( 1) 2 > 0: We conclude that FI 3.2 3.2.1 GO < : Consolidated Industry with Decentralized Organization Government as Residual Claimant Case 1: Input Monitoring The government’s problem is to maximize X G B =S+R pij ( iA eA eB ij + j ij + tij ): The government faces with the following ex post incentive compatibility constraints: 2 eA 1j + eB 1j 2 2 eA + eB i1 i1 2 A 2 e11 + eB 11 2 t1j ti1 and t11 2 t2j 2 ti2 2 t22 eA 2j 2 2 + eB 2j 2 2 2 eA + eB i2 i2 2 2 A 2 e22 + eB 22 : 2 Since the …rm can coordinate its announcement, we have the last constraint. The individual rationality constraint is represented by eA 22 2 2 + eB 22 0: t22 2 Rewriting the problem with the binding conditions and taking the …rst order B conditions with respect to eA ij and eij ; we have B jb eA ij = eij = e = 1: The government’s payo¤ GI GI is given by =S+R 2p 1 8 2(1 p) 2 + 1: Case 2: Output Monitoring The government’s problem is identical. It faces with the following ex post incentive compatibility constraints and individual rationality constraints: eA 1j t1j ti1 t11 2 2 + eB 1j 2 A 2 ei1 + eB i1 2 2 eA + eB 11 11 2 e^A 2j 2 + eB 2j 2 2 A 2 ei2 + e^B i2 2 2 A 2 e^22 + e^B 22 2 t2j 2 ti2 2 t22 eA 22 2 2 2 + eB 22 and t22 0; 2 B A bB where we have ebA 2 + 1. 2 + 1 and e i2 = ei2 2j = e2j We have two scenarios whether the last incentive compatibility constraint is binding or not. When the last constraint is not binding, we have B A B eA 11 = e11 = e12 = e21 = 1 p B A B and eA 21 = e12 = e22 = e22 = 1 The government’s payo¤ GO1 GO1 (1 p)2 ( 2 1 ): is given by =S+R 2 p ( 1 p When the last constraint is binding, we obtain 2 +1+ 2 2 1) : B A B A B eA 11 = e11 = e12 = e21 = e21 = e12 = 1 p B ( 2 and eA 1 ): 22 = e22 = 1 (1 p)2 Since 0 < e and 0 < eA 22 2 + 2 The government’s payo¤ GO2 Since GO1 < GO2 ; we have 2 + 1; we must satisfy (1 p)2 : p2 p + 1 is given by 1 GO2 =S+R = eB 22 1 < p (p2 2 2+1+ (1 GO2 = GO 9 : p + 1) ( p)2 2 2 1) : 3.2.2 Firm as Residual Claimant Case 3: Input Monitoring The government’s problem is to maximize X F =S+ pij ij subject to R ( eA 1j ) 1 R R ( ( R ( ( ( ( i ( eA 22 ) eB i1 ) ( ( ( 1 1 2 eA i1 eB i2 ) eB 11 ) 1 eA 1j eB 2j ) j 1 eA 22 ) 1 2 ( eA i2 ) eA 11 ) 1 R and R eA i1 ) ( j eA 2j ) 1 i R ( eB 1j ) eA 11 eB 22 ) 2 1j 2 2j 2 2 + eB i1 2 A 2 ei2 + eB i2 2 2 i1 2 i2 2 + eB 11 2 2 eA + eB 22 22 2 eA 22 eB 22 ) 2 + eB 1j 2 2 + eB eA 2j 2j 2 2 + eB 22 2 11 2 22 2 22 0: Rewriting the problem with the binding conditions and taking the …rst order B conditions with respect to eA ij and eij ; we obtain B fb = 1: eA ij = eij = e The government’s payo¤ FI FI is represented as =S+R 10 2 2 + 1: Case 4: Output Monitoring The government’s problem is identical. It faces with the following ex post incentive compatibility constraints and individual rationality constraints: R ( eA 1j ) 1 R R ( ( R ( ( ( 1 ( eA 22 ) ( e^B i2 ) 1 eA 11 eB 11 ) 1 e^A 22 ) eA i1 eB i1 ) ( ( eB 2j ) j 1 eA i2 ) i 2 ( ( eA 11 ) 1 R and R eA i1 ) ( j e^A 2j ) 1 i R ( eA 1j eB 1j ) e^B 22 ) 1 eB 22 ) 2 2 2 + eB 1j 2 2 e^A + eB 2j 2j 2 2 1j 2 2j 2 + eB i1 2 A 2 ei2 + e^B i2 2 2 i1 2 i2 2 + eB 11 2 A 2 e^22 + e^B 22 2 2 eA 22 2 + 2 22 2 + eB 22 2 B A bB where we have ebA 2 + 1 and e i2 = ei2 2j = e2j Since the last constraint is binding, we have 11 22 1. B A B A B eA 11 = e11 = e12 = e21 = e21 = e12 = 1 p B ( 2 and eA 1 ): 22 = e22 = 1 (1 p)2 Since 0 < e and 0 < eA 22 2 + 2 The government’s payo¤ FO =S+R FO 1 = eB 22 1 < 2 + 1; we must satisfy (1 p)2 : p2 p + 1 is given by 2 2+1+ 11 p (p2 (1 p + 1) ( p)2 2 2 1) : 0: 3.2.3 Comparison By the comparison of the government’s payo¤s, we have and Also, since GI 2 GO 1 < = p( GO FI GI FI p (p2 (1 = 2p( 2 = p + 1) ( 2 p)2 1 ) > 0: 2 1) >0 (1 p)2 ; we have p2 p + 1 2 1) 2 p2 p + 1 ( (1 p)2 < GO 1) 2 > p( 2 1) > 0: We conclude that FI 3.3 3.3.1 = FO < GI : Consolidated Industry with Integrated Organization Government as Residual Claimant Case 1: Input Monitoring The government’s problem is to maximize X G =S+R pij ( i + j eij + tij ): The government faces with the following ex post incentive compatibility constraints and individual rationality constraint: t1j ti1 t11 (e1j )2 2 (ei1 )2 2 (e11 )2 2 t2j ti2 t22 (e2j )2 2 (ei2 )2 2 (e22 )2 2 (e22 )2 0: 2 Rewriting the problem with the binding conditions and taking the …rst order conditions, we have eij = 1: and t22 12 GI The government’s expected payo¤ GI =S+R 2p is given by 2(1 1 p) 2 1 + : 2 Case 2: Output Monitoring The government’s problem is identical. It faces with the following ex post incentive compatibility constraints and individual rationality constraints: (e1j )2 2 (ei1 )2 2 (e11 )2 2 t1j ti1 t11 t2j ti2 t22 (^ e2j )2 2 (^ ei2 )2 2 (^ e22 )2 2 (e22 )2 0: 2 where we have eb2j = e2j bi2 = ei2 2 + 1 and e Since the last constraint is binding, we obtain and t22 e11 = e12 = e21 = 1 2p and e22 = 1 ( (1 p)2 Since 0 < e and 0 < e^22 = e22 2 2 The government’s payo¤ GO 3.3.2 GO =S+R + 1 1; < 2 2 + 1. 1 ): we have (1 p)2 : p2 + 1 is given by 1 p(1 + p2 ) 2 2+ + ( 2 (1 p)2 2 2 1) : Firm as Residual Claimant Case 3: Input Monitoring The government’s problem is to maximize X F =S+ pij ij 13 subject to R ( R R 1 + ( i+ ( 1+ j 1 1 e1j ) (e1j )2 2 ei1 ) (ei1 )2 2 e11 ) (e11 )2 2 1j R ( i1 R ( i+ 11 R ( 1 + 1+ j e2j ) (e2j )2 2 1 ei2 ) (ei2 )2 2 1 e22 ) (e22 )2 2 2j i2 22 (e22 )2 and R ( 2 + 2 e22 ) 0: 22 2 Rewriting the problem with the binding conditions and taking the …rst order condition with respect to eij ; we obtain eij = 1: The government’s payo¤ FI is represented as FI =S+R 2 2 1 + : 2 Case 4: Output Monitoring The government’s problem is identical. It faces with the following ex post incentive compatibility constraints and individual rationality constraints: R ( R R 1 + ( i+ ( 1 + j 1 1 e1j ) ei1 ) e11 ) (e1j )2 2 (ei1 )2 2 (e11 )2 2 1j R ( + j e^2j ) i1 R ( i+ 1 e^i2 ) 11 R ( 1 e^22 ) 1 1 + e^2j 2 (^ ei2 )2 2 (^ e22 )2 2 2j i2 22 (e22 )2 and R ( 2 + 2 e22 ) 0: 22 2 where we have eb2j = e2j bi2 = ei2 2 + 1 and e 2 + 1. Since the last incentive compatibility constraint is binding, we have 14 e11 = e12 = e21 = 1 2p and e22 = 1 ( (1 p)2 FO Then, the government’s payo¤ FO 3.3.3 =S+R 2 1 ): 2 is represented as 2+ 1 p(1 + p2 ) + ( 2 (1 p)2 2 1) : 2 Comparison By the comparison of the government’s payo¤s, we have and p(1 + p2 ) 2 ( 2 1) > 0 (1 p)2 = 2p( 2 1 ) > 0: GO FI GI FI 1) 2 p(1 + p2 ) ( (1 p)2 = Also, we have GI GO = p( where we satisfy 2 2 1 < > p( 2 1 ) (2 p) > 0: (1 p)2 : We conclude that p2 + 1 FI 4 1) 2 GO < FO = GI < : Optimal Industry Structure We have analyzed optimal contracts in a decentralized industry, a consolidated industry with a decentralized organization, and a consolidated industry with an integrated organization. In either structure, we have and FI < GO = FI < GO = FI < GO and obtain the following proposition. 15 = FO FO < < FO < GI GI GI ; Proposition 1 Whether a government is under a decentralized industry with two …rms or under a consolidated industry with a single …rm, it selects to be a residual claimant and implements input monitoring. Next, we compare the government’s payo¤s, when it implements output monitoring. We obtain GO GO and Since GO = p (p2 (1 = FO p + 1) p)2 < GO = p 1 FO < (1 p)2 ; we must satisfy ( 1 + p2 GO GO = and GO = 2 1 p = p3 (1 p)2 >0 : 2 1) < 2 (1 p)4 : Then, we (1 + p2 )2 have p2 (1 + p) ( (1 p)2 1 2 FO < GO = 2 1) 2 FO > p2 (1 + p)(1 p)2 >0 (1 + p2 )2 1 2 : We conclude GO = FO < GO = FO < GO = FO and obtain the following proposition. Proposition 2 Under output monitoring, residual claimancy is not an issue. The government prefers a consolidated industry with a decentralized organization. When the government implements input monitoring, we obtain GI GI FI FI GI and Since 2 1 < FI 1 >0 2 1 = >0 2 < GI = = < (1 p)2 ; we also have 1 + p2 16 FI = GI FI : FI and GI = GI < 1 2 2p( FI 1) 2 4p3 + 9p2 4p + 1 >0 2 (p2 + 1) > : We have FI GI < < FI = FI < GI GI = ; and following proposition. Proposition 3 When a government implements input monitoring, it selects to be a residual claimant under a decentralized industry or under a consolidated industry with a decentralized organization. We compare the government’s payo¤s, when a residual 2p(1 p)2 (1 p)2 and 0 < < government. Since 2 < 1 1 + p2 1 + p2 GO GI GI and p 1 + ( 2 1 p 1 p > + ( 2 1 p < GO : = claimant is the 1 ; we have 2 2 2 1) 2p( 2 2 1) 2p(1 p)2 >0 1 + p2 1) 2 Hence, when the government is a residual claimant, we have GO GI < < GO < GO GI < = GI ; and following proposition. Proposition 4 When a government is a residual claimant, it selects input monitoring under a decentralized industry or under a consolidated industry with a decentralized organization. We compare the payo¤s when a residual claimant is the …rm. Since (1 p)4 p(1 p)2 1 2 ( 2 and 0 < < ; we have 1) < 2 2 2 1+p 2 (1 + p ) FI FO = and FO < p(1 + p2 ) ( (1 p)2 1 2 FI 2 : 17 2 1) > 1 2 p(1 p)2 >0 (1 + p2 ) Hence, when the …rm is a residual claimant, we have FI < FO < FI = FI < FO < FO and following proposition. Proposition 5 When a …rm is a residual claimant, a government selects output monitoring under a consolidated industry with a decentralized organization. 5 Conclusion Finally, we discuss the privatization and division of state-owned monopolistic companies such as Japan Highway Public Corporation (JH). Before the privatization and division, the state-owned companies supplied the same quality of nationwide services. It implies that the government faced with an integrated industry. Since these companies were not allowed to pursue pro…ts, the government was a residual claimant. In this scenario, as discussed above, we have GO < GI < GO < GI : The government selects to implement input monitoring and make the …rm to have a decentralized organization. After the privatization and division of these state-owned companies, the multiple private companies supply these services. Also, each private company pursues pro…t and is a residual claimant. In this case, as discussed above, we have FI < FO : The government selects to implement output monitoring. In general, output monitoring is less costly and more accurate than input monitoring. When output monitoring is implemented, as discussed above, we have GO = FO < GO = FO < GO = FO : The government selects the integrated industry with the decentralized organization. Under this structure, whichever is a residual claimant, the government obtains the highest payo¤. 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