American Institute of Mathematical Sciences

• Previous Article
Markowitz's mean-variance optimization with investment and constrained reinsurance
• JIMO Home
• This Issue
• Next Article
Ordering policy for non-instantaneously deteriorating products under price adjustment and trade credits
January  2017, 13(1): 349-373. doi: 10.3934/jimo.2016021

Impact of price cap regulation on supply chain contracting between two monopolists

 Institute of Systems Engineering, Tianjin University, Tianjin 300072, China

* Corresponding author: Yanfei Lan, Email: lanyf@tju.edu.cn

Received  August 2013 Published  March 2016

This paper considers a supply chain with an unregulated upstream monopolist (she) supplying a kind of products to a regulated downstream monopolist (he). The upstream monopolist's production efficiency, which represents her type, is only privately known to herself. When the downstream monopolist trades with the upstream monopolist, his pricing discretion is constrained by price cap regulation (PCR). We model this problem as a game of adverse selection with the price cap constraint. In this model, the downstream monopolist offers a menu of contracts, each of which consists of two parameters: the transfer payment and the retail price. We show that private information can weaken PCR's impact on the optimal contract, and PCR can dampen the effects of private information. We also shed light on the influences of private information and PCR on the optimal contract, the downstream monopolist's profit, the upstream monopolist's profit, the consumers' surplus and the social total welfare, respectively. Finally, a numerical example is given to illustrate the proposed results.

Citation: Jing Feng, Yanfei Lan, Ruiqing Zhao. Impact of price cap regulation on supply chain contracting between two monopolists. Journal of Industrial and Management Optimization, 2017, 13 (1) : 349-373. doi: 10.3934/jimo.2016021
References:
 [1] M. Armstrong and J. Vickers, Multiproduct price regulation under asymmetric information, J. Ind. Econ., 8 (2000), 137-160.  doi: 10.1111/1467-6451.00115. [2] M. Armstrong and J. Vickers, Welfare effects of price discrimination by a regulated monopolist, Rand J. Econ., 22 (1991), 571-580. [3] M. Armstrong and D. Sappington, Recent developments in the theory of regulation, in Handbook of Industrial Organization, Elsevier Science Publishers, Ⅲ (2007), 1557-1700. [4] Armstrong1994 M. Armstrong, S. Cowan and J. Vickers, Regulatory Reform: Economic Analysis and the British Experience, MIT Press, Cambridge, MA, 1994. [5] M. Armstrong, Multiproduct nonlinear pricing, Econometrica, 64 (1996), 51-76.  doi: 10.2307/2171924. [6] D. Baron and R. Myerson, Regulating a monopolist with unknown costs, Econometrica, 50 (1982), 911-930.  doi: 10.2307/1912769. [7] R. Barlow and F. Proschan, Mathematical Theory of Reliability, John Wiley and Sons, New York, 1965. [8] M. Bagnoli and T. Bergstrom, Log-concave probability and its applications, Econ. Theor., 26 (2005), 445-469.  doi: 10.1007/s00199-004-0514-4. [9] A. Burnetas, S. Gilbert and C. Smith, Quantity discount in single period supply contracts with asymmetric demand information, IIE Trans., 39 (2007), 465-479. [10] M. Cakanyildirim, Q. Feng, X. Gan and S. Sethi, Contracting and coordination under asymmetric production cost information, Prod. Oper. Manag., 21 (2012), 345-360. [11] G. Cachon, Competitive supply chain inventory management, in Quantitative Models for Supply Chain Management, Kluwer, Boston, MA, 1998, 111–146. doi: 10.1007/978-1-4615-4949-9-5. [12] G. Cachon, Supply chain coordination with contracts, in Handbook in Operations Research and Management Science: Supply Chain Management, Elsevier Science Publishers, North Holland, The Netherlands, 2003, 227–339. doi: 10.1016/S0927-0507(03)11006-7. [13] G. Cachon and M. Lariviere, Contracting to assure supply: How to share demand forecasts in supply chain, Manage. Sci., 47 (2001), 629-646. [14] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. [15] C. Corbett and X. Groote, A supplier's optimal quantity discount policy under asymmetric information, Manage. Sci., 46 (2000), 444-450. [16] C. Corbett, D. Zhou and C. Tang, Designing supply contracts: Contract type and information asymmetry, Manage. Sci., 50 (2004), 550-559. [17] A. Ha, Supplier-buyer contracting: Asymmetric cost information and cutoff policy for buyer participation, Nav. Res. Log., 48 (2001), 41-64. [18] E. Inssa and F. Stroffolini, Price-cap regulation, revenue sharing and information acquisition, Inf. Econ. Policy, 17 (2005), 217-230. [19] E. Inssa and F. Stroffolini, Price-cap regulation and information acquisition, Int. J. Ind. Organ., 20 (2002), 1013-1036. [20] A. Iozzi, J. Poritz and E. Valentini, Socal preferences and price cap regualtion, J. Public Econ. Theory, 4 (2002), 95-114. [21] J. Kang, D. Weisman and M. Zhang, Do consumers benefit from tighter price cap regulation?, Econ. Lett., 67 (2000), 113-119.  doi: 10.1016/S0165-1765(99)00252-9. [22] P. Law, Tighter average revenue regulation can reduce consumer welfare, J. Ind. Econ., 43 (1995), 399-404.  doi: 10.2307/2950551. [23] J. Laffont and D. Mortimort The Theory of Incentive: The Principal-Agent Model, Princeton University Press, Princeton, NJ, 2002. [24] J. Laffont and J. Rochet, Regulation of a risk averse firm, Game. Econ. Behav., 25 (1998), 149-173.  doi: 10.1006/game.1998.0639. [25] T. Lewis and C. Garmon, Fundamentals of Incentive Regulation, 12th PURC/World Bank International Training Program on Utility Regulation and Strategy, Gainesville, 2002. [26] C. Liston, Price cap versus rate of return regulation, J. Regul. Econ., 5 (1993), 25-48.  doi: 10.1007/BF01066312. [27] M. Lariviere, A note on probability distributions with increasing generalized failure rates, Oper. Res., 54 (2006), 602-604.  doi: 10.1287/opre.1060.0282. [28] R. Myerson, Incentive compatibiltiy and the bargaining problem, Econometrica, 47 (1979), 61-74.  doi: 10.2307/1912346. [29] Ö. Özer and W. Wei, Strategic commitment for optimal capacity decision under asymmetric forecast information, Manage. Sci., 52 (2006), 1238-1257. [30] Ö. Özer and G. Raz, Supply chain sourcing under asymmetric information, Prod. Oper. Manag., 20 (2011), 92-115. [31] J. Reitzes, Downstream price-cap regulation and upstream market power, J. Regul. Econ., 33 (2008), 179-200. [32] D. Sappington and D. Weisman, Price cap regulation: What have we learned from 25 years of experience in the telecommunications industry?, J. Regul. Econ., 38 (2010), 227-257. [33] Y. Shen and S. Willems, Coordinating a channel with asymmetric cost information and the manufactures' optimality, Int. J. Prod. Econ., 135 (2012), 125-135. [34] D. Sibley, Asymmetric information, incentives and price cap regulation, Rand J. Econ., 20 (1989), 392-404.  doi: 10.2307/2555578. [35] G. Voigt and K. Inderfurth, Supply chain coordination and setup cost reduction in case of asymmetric information, OR Spectrum, 33 (2011), 99-122.

show all references

References:
 [1] M. Armstrong and J. Vickers, Multiproduct price regulation under asymmetric information, J. Ind. Econ., 8 (2000), 137-160.  doi: 10.1111/1467-6451.00115. [2] M. Armstrong and J. Vickers, Welfare effects of price discrimination by a regulated monopolist, Rand J. Econ., 22 (1991), 571-580. [3] M. Armstrong and D. Sappington, Recent developments in the theory of regulation, in Handbook of Industrial Organization, Elsevier Science Publishers, Ⅲ (2007), 1557-1700. [4] Armstrong1994 M. Armstrong, S. Cowan and J. Vickers, Regulatory Reform: Economic Analysis and the British Experience, MIT Press, Cambridge, MA, 1994. [5] M. Armstrong, Multiproduct nonlinear pricing, Econometrica, 64 (1996), 51-76.  doi: 10.2307/2171924. [6] D. Baron and R. Myerson, Regulating a monopolist with unknown costs, Econometrica, 50 (1982), 911-930.  doi: 10.2307/1912769. [7] R. Barlow and F. Proschan, Mathematical Theory of Reliability, John Wiley and Sons, New York, 1965. [8] M. Bagnoli and T. Bergstrom, Log-concave probability and its applications, Econ. Theor., 26 (2005), 445-469.  doi: 10.1007/s00199-004-0514-4. [9] A. Burnetas, S. Gilbert and C. Smith, Quantity discount in single period supply contracts with asymmetric demand information, IIE Trans., 39 (2007), 465-479. [10] M. Cakanyildirim, Q. Feng, X. Gan and S. Sethi, Contracting and coordination under asymmetric production cost information, Prod. Oper. Manag., 21 (2012), 345-360. [11] G. Cachon, Competitive supply chain inventory management, in Quantitative Models for Supply Chain Management, Kluwer, Boston, MA, 1998, 111–146. doi: 10.1007/978-1-4615-4949-9-5. [12] G. Cachon, Supply chain coordination with contracts, in Handbook in Operations Research and Management Science: Supply Chain Management, Elsevier Science Publishers, North Holland, The Netherlands, 2003, 227–339. doi: 10.1016/S0927-0507(03)11006-7. [13] G. Cachon and M. Lariviere, Contracting to assure supply: How to share demand forecasts in supply chain, Manage. Sci., 47 (2001), 629-646. [14] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. [15] C. Corbett and X. Groote, A supplier's optimal quantity discount policy under asymmetric information, Manage. Sci., 46 (2000), 444-450. [16] C. Corbett, D. Zhou and C. Tang, Designing supply contracts: Contract type and information asymmetry, Manage. Sci., 50 (2004), 550-559. [17] A. Ha, Supplier-buyer contracting: Asymmetric cost information and cutoff policy for buyer participation, Nav. Res. Log., 48 (2001), 41-64. [18] E. Inssa and F. Stroffolini, Price-cap regulation, revenue sharing and information acquisition, Inf. Econ. Policy, 17 (2005), 217-230. [19] E. Inssa and F. Stroffolini, Price-cap regulation and information acquisition, Int. J. Ind. Organ., 20 (2002), 1013-1036. [20] A. Iozzi, J. Poritz and E. Valentini, Socal preferences and price cap regualtion, J. Public Econ. Theory, 4 (2002), 95-114. [21] J. Kang, D. Weisman and M. Zhang, Do consumers benefit from tighter price cap regulation?, Econ. Lett., 67 (2000), 113-119.  doi: 10.1016/S0165-1765(99)00252-9. [22] P. Law, Tighter average revenue regulation can reduce consumer welfare, J. Ind. Econ., 43 (1995), 399-404.  doi: 10.2307/2950551. [23] J. Laffont and D. Mortimort The Theory of Incentive: The Principal-Agent Model, Princeton University Press, Princeton, NJ, 2002. [24] J. Laffont and J. Rochet, Regulation of a risk averse firm, Game. Econ. Behav., 25 (1998), 149-173.  doi: 10.1006/game.1998.0639. [25] T. Lewis and C. Garmon, Fundamentals of Incentive Regulation, 12th PURC/World Bank International Training Program on Utility Regulation and Strategy, Gainesville, 2002. [26] C. Liston, Price cap versus rate of return regulation, J. Regul. Econ., 5 (1993), 25-48.  doi: 10.1007/BF01066312. [27] M. Lariviere, A note on probability distributions with increasing generalized failure rates, Oper. Res., 54 (2006), 602-604.  doi: 10.1287/opre.1060.0282. [28] R. Myerson, Incentive compatibiltiy and the bargaining problem, Econometrica, 47 (1979), 61-74.  doi: 10.2307/1912346. [29] Ö. Özer and W. Wei, Strategic commitment for optimal capacity decision under asymmetric forecast information, Manage. Sci., 52 (2006), 1238-1257. [30] Ö. Özer and G. Raz, Supply chain sourcing under asymmetric information, Prod. Oper. Manag., 20 (2011), 92-115. [31] J. Reitzes, Downstream price-cap regulation and upstream market power, J. Regul. Econ., 33 (2008), 179-200. [32] D. Sappington and D. Weisman, Price cap regulation: What have we learned from 25 years of experience in the telecommunications industry?, J. Regul. Econ., 38 (2010), 227-257. [33] Y. Shen and S. Willems, Coordinating a channel with asymmetric cost information and the manufactures' optimality, Int. J. Prod. Econ., 135 (2012), 125-135. [34] D. Sibley, Asymmetric information, incentives and price cap regulation, Rand J. Econ., 20 (1989), 392-404.  doi: 10.2307/2555578. [35] G. Voigt and K. Inderfurth, Supply chain coordination and setup cost reduction in case of asymmetric information, OR Spectrum, 33 (2011), 99-122.
Information structure's impact on the optimal contract
Price cap's impact on the optimal contract under full information
Price cap's impact on the revenue under full information
Price cap's impact on the optimal contract under private information
Price cap's impact on the revenue under private information
Information structure's impact on contract
 $Scenario$ $p$ $t$ $full$ $information$ $0.5x+13$ $-0.7x^{2}+6.5x+7$ $private$ $information$ $x+8$ $-0.5x^{2}-x+63.3$
 $Scenario$ $p$ $t$ $full$ $information$ $0.5x+13$ $-0.7x^{2}+6.5x+7$ $private$ $information$ $x+8$ $-0.5x^{2}-x+63.3$
Price cap's impact on the optimal contact under full information
 $Scenario$ $p^{**}$ $t^{**}$ $RPCR$ $0.5x+13$ $-0.7x^{2}+6.5x+7$ $TPCR$ $16.75$ $-0.2x^{2}+3.25x+3.25$ $MPCR\,when\,x\geq x_{0}$ 17.75 $-0.2x^{2}+2.25x+2.25$ $MPCR\,when\, x < x_{0}$ $0.5x+13$ $-0.7x^{2}+6.5x+7$
 $Scenario$ $p^{**}$ $t^{**}$ $RPCR$ $0.5x+13$ $-0.7x^{2}+6.5x+7$ $TPCR$ $16.75$ $-0.2x^{2}+3.25x+3.25$ $MPCR\,when\,x\geq x_{0}$ 17.75 $-0.2x^{2}+2.25x+2.25$ $MPCR\,when\, x < x_{0}$ $0.5x+13$ $-0.7x^{2}+6.5x+7$
Price cap's impact on the optimal contact under private information
 $Scenario$ $p_{1}^{**}$ $t_{1}^{**}$ $RPCR$ $x+8$ $-0.5x^{2}-x+63.3$ $TPCR$ $16.75$ 16.3 $MPCR\, when\, x\geq x_{1}$ $17.75$ 5.175 $MPCR\,when\, x< x_{1}$ $x+8$ $-0.5x^{2}-x+63.3$
 $Scenario$ $p_{1}^{**}$ $t_{1}^{**}$ $RPCR$ $x+8$ $-0.5x^{2}-x+63.3$ $TPCR$ $16.75$ 16.3 $MPCR\, when\, x\geq x_{1}$ $17.75$ 5.175 $MPCR\,when\, x< x_{1}$ $x+8$ $-0.5x^{2}-x+63.3$
Price cap's impacts on the downstream monopolist's profit, the consumers' surplus and the social total welfare under full information
 $Scenario$ $U^{**}$ $S^{**}$ $W^{**}$ $RPCR$ $0.45x^{2}\!-\!7x+49$ $0.125x^{2}\!-\!3.5x\!+\!24.5$ $0.575x^{2}\!-\!10.5x\!+\!73.5$ $TPCR$ $0.2x^{2}\!-\!3.25x\!+\!34.94$ $5.28$ $0.2x^{2}\!-\!3.25x\!+\!40.22$ $MPCR\,when\,x\geq x_{0}$ $0.2x^{2}\!-\!2.25x\!+\!26.44$ $2.53$ $0.2x^{2}\!-\!2.25x\!+\!28.97$ $MPCR\,when\, x < x_{0}$ $0.45x^{2}\!-\!7x\!+\!49$ $0.125x^{2}\!-\!3.5x\!+\!24.5$ $0.575x^{2}\!-\!10.5x\!+\!73.5$
 $Scenario$ $U^{**}$ $S^{**}$ $W^{**}$ $RPCR$ $0.45x^{2}\!-\!7x+49$ $0.125x^{2}\!-\!3.5x\!+\!24.5$ $0.575x^{2}\!-\!10.5x\!+\!73.5$ $TPCR$ $0.2x^{2}\!-\!3.25x\!+\!34.94$ $5.28$ $0.2x^{2}\!-\!3.25x\!+\!40.22$ $MPCR\,when\,x\geq x_{0}$ $0.2x^{2}\!-\!2.25x\!+\!26.44$ $2.53$ $0.2x^{2}\!-\!2.25x\!+\!28.97$ $MPCR\,when\, x < x_{0}$ $0.45x^{2}\!-\!7x\!+\!49$ $0.125x^{2}\!-\!3.5x\!+\!24.5$ $0.575x^{2}\!-\!10.5x\!+\!73.5$
Price cap's impacts on the downstream monopolist's profit, the upstream monopolist's profit, the consumers surplus and the social total welfare under private information
 $Scenario$ $U_{1}^{**}$ $\pi_{1}^{**}$ $S_{1}^{**}$ $W_{1}^{**}$ $RPCR$ $22.53$ $0.7x^{2}\!-\!12x\!+\!51.3$ $0.5x^{2}\!-\!12x\!+\!72$ $1.2x^{2}\!-\!24x\!+\!145.83$ $TPCR$ $21.89$ $0.2x^{2}\!-\!3.25x\!+\!13.05$ $5.28$ $0.2x^{2}\!-\!3,25x\!+\!40.22$ $MPCR\,when\, x\geq x_{1}$ $22.52$ $0.2x^{2}\!-\!2.25x\!+\!2.93$ 2.53 $0.2x^{2}\!-\!2,25x\!+\!27.98$ $MPCR\,when\, x < x_{1}$ $22.52$ $0.7x^{2}\!-\!12x\!+\!51.3$ $0.5x^{2}\!-\!12x\!+\!72$ $1.2x^{2}\!-\!24x\!+\!145.82$
 $Scenario$ $U_{1}^{**}$ $\pi_{1}^{**}$ $S_{1}^{**}$ $W_{1}^{**}$ $RPCR$ $22.53$ $0.7x^{2}\!-\!12x\!+\!51.3$ $0.5x^{2}\!-\!12x\!+\!72$ $1.2x^{2}\!-\!24x\!+\!145.83$ $TPCR$ $21.89$ $0.2x^{2}\!-\!3.25x\!+\!13.05$ $5.28$ $0.2x^{2}\!-\!3,25x\!+\!40.22$ $MPCR\,when\, x\geq x_{1}$ $22.52$ $0.2x^{2}\!-\!2.25x\!+\!2.93$ 2.53 $0.2x^{2}\!-\!2,25x\!+\!27.98$ $MPCR\,when\, x < x_{1}$ $22.52$ $0.7x^{2}\!-\!12x\!+\!51.3$ $0.5x^{2}\!-\!12x\!+\!72$ $1.2x^{2}\!-\!24x\!+\!145.82$
 [1] Qingguo Bai, Jianteng Xu, Fanwen Meng, Niu Yu. Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3417-3444. doi: 10.3934/jimo.2020126 [2] Chun-xiang Guo, Dong Cai, Yu-yang Tan. Outsourcing contract design for the green transformation of manufacturing systems under asymmetric information. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021158 [3] Yafei Zu. Inter-organizational contract control of advertising strategies in the supply chain. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021126 [4] Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial and Management Optimization, 2022, 18 (1) : 487-510. doi: 10.3934/jimo.2020165 [5] Juliang Zhang, Jian Chen. Information sharing in a make-to-stock supply chain. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1169-1189. doi: 10.3934/jimo.2014.10.1169 [6] Feimin Zhong, Wei Zeng, Zhongbao Zhou. Mechanism design in a supply chain with ambiguity in private information. Journal of Industrial and Management Optimization, 2020, 16 (1) : 261-287. doi: 10.3934/jimo.2018151 [7] Honglin Yang, Jiawu Peng. Coordinating a supply chain with demand information updating. Journal of Industrial and Management Optimization, 2022, 18 (2) : 843-872. doi: 10.3934/jimo.2020181 [8] Yang Yang, Guanxin Yao. Fresh agricultural products supply chain coordination considering consumers' dual preferences under carbon cap-and-trade mechanism. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022032 [9] Mitali Sarkar, Young Hae Lee. Optimum pricing strategy for complementary products with reservation price in a supply chain model. Journal of Industrial and Management Optimization, 2017, 13 (3) : 1553-1586. doi: 10.3934/jimo.2017007 [10] Min Li, Jiahua Zhang, Yifan Xu, Wei Wang. Effect of disruption risk on a supply chain with price-dependent demand. Journal of Industrial and Management Optimization, 2020, 16 (6) : 3083-3103. doi: 10.3934/jimo.2019095 [11] Han Zhao, Bangdong Sun, Hui Wang, Shiji Song, Yuli Zhang, Liejun Wang. Optimization and coordination in a service-constrained supply chain with the bidirectional option contract under conditional value-at-risk. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022021 [12] Mingyong Lai, Hongzhao Yang, Erbao Cao, Duo Qiu, Jing Qiu. Optimal decisions for a dual-channel supply chain under information asymmetry. Journal of Industrial and Management Optimization, 2018, 14 (3) : 1023-1040. doi: 10.3934/jimo.2017088 [13] Suresh P. Sethi, Houmin Yan, Hanqin Zhang, Jing Zhou. Information Updated Supply Chain with Service-Level Constraints. Journal of Industrial and Management Optimization, 2005, 1 (4) : 513-531. doi: 10.3934/jimo.2005.1.513 [14] Man Yu, Erbao Cao. Trade credit and information leakage in a supply chain with competing retailers. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022042 [15] Apostolis Pavlou. Asymmetric information in a bilateral monopoly. Journal of Dynamics and Games, 2016, 3 (2) : 169-189. doi: 10.3934/jdg.2016009 [16] Kun Fan, Wenjin Mao, Hua Qu, Xinning Li, Meng Wang. Study on government subsidy in a two-level supply chain of direct-fired biomass power generation based on contract coordination. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022049 [17] Tinggui Chen, Yanhui Jiang. Research on operating mechanism for creative products supply chain based on game theory. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1103-1112. doi: 10.3934/dcdss.2015.8.1103 [18] Yadong Shu, Ying Dai, Zujun Ma. Evolutionary game theory analysis of supply chain with fairness concerns of retailers. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022098 [19] Bibhas C. Giri, Bhaba R. Sarker. Coordinating a multi-echelon supply chain under production disruption and price-sensitive stochastic demand. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1631-1651. doi: 10.3934/jimo.2018115 [20] Dingzhong Feng, Xiaofeng Zhang, Ye Zhang. Collection decisions and coordination in a closed-loop supply chain under recovery price and service competition. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021117

2021 Impact Factor: 1.411