Home Privatizing Multi-subsidiary Public Firm in Location Model
Article
Licensed
Unlicensed Requires Authentication

Privatizing Multi-subsidiary Public Firm in Location Model

  • Jingliang Chen and Jie Shuai EMAIL logo
Published/Copyright: September 19, 2017
The B.E. Journal of Theoretical Economics
From the journal The B.E. Journal of Theoretical Economics Volume 19 Issue 1

Abstract

This paper examines a different way of privatization from existing literature. In a mixed duopoly Hotelling type model in which the public firm consists of multiple subsidiaries, instead of privatizing the public firm as its entirety, the government may privatize only one of the subsidiaries (for example the manufacturing subsidiary). We find that this kind of privatization always improves social welfare comparing to no privatization at all. And comparing to privatizing the public firm in its entirety, privatizing only the manufacturing subsidiary always results in larger consumer welfare and results in larger social welfare when transport cost or R&D cost is sufficiently large.

Keywords: privatization; multi-subsidiary; mixed oligopoly
JEL Classification: L13; L32; L33

Acknowledgements

We would like to thank the editor Yuk-Fai Fong, and two anonymous referees for helpful comments and suggestions. We also thank participants at the Xiangzhang Workshop at Jinan University and 2016 Asia Meeting of Econometric Society. Financial support from the National Science Foundation of China (71603283) is gratefully acknowledged. The usual disclaimers apply.

Appendix

Linear Price

In the paper, we have assumed that a two-part tariff contract is employed after privatization. As many marketing literature, such as McGuire and Staelin (1983), Coughlan (1985), and Rey and Stiglitz (1995) suggested, linear pricing, or a wholesale-price contract as is called, is quite common in practice. In this appendix we discuss the case that the manufacturer and the retailer sign a linear price contract. As the two-part tariff, we discuss two cases: wholesale price set by the manufacturer (wholesale-price contract) and wholesale price set by the retailer (inverse wholesale-price contract). When the contract is determined by the retailer, the linear price contract and the two-part tariff contract are the same. The reason is that the retailer only cares the social welfare, on which the franchise fee has no effect. We thus only need to discuss the wholesale price case. We present the equilibrium as following proposition.

Proposition 8

When the manufacturer trades with the retailer under a wholesale-price contract, in equilibrium,

p0LP=c+t(5t2γ2−30tγ+48)4(t2γ2−2tγ−16),p1LP=c+t(t2γ2−6tγ+8)t2γ2−2tγ−16,
wLP=c+t(−t3γ3+15t2γ2−66tγ+80)4(t2γ2−2tγ−16),
SSLP=V−c−t(3t5γ5−80t4γ4+956t3γ3−5152t2γ2+11776tγ−8192)48(t2γ2−2tγ−16)2
CSLP=V−c−t(13t4γ4−100t3γ3+8t2γ2+1216tγ−2048)12(t2γ2−2tγ−16)2
πM
∂πM∂w=−γ(−t4γ3+4ct2γ2+15t3γ2−4t2γ2w−8ctγ−66t2γ+8tγw−64c+80t+64w)2(t2γ2−6tγ+4)2=0

Proof

We use backward induction to solve the game. The manufacturer sets R&D investment to maximize its own (subsidiary) profit. This part of analysis is the same as the proof of Proposition 3, and we skip it. We next analyze the wholesale price decision stage. Different from the two-part tariff contract, in linear price contract, there is no franchise fee to extract surplus from the retailer. The manufacturer thus uses the wholesale price to maximize its own profit (wLP=c+t(−t3γ3+15t2γ2−66tγ+80)4(t2γ2−2tγ−16)). We can write down the first order condition as following:

wLP

Solving the first condition we have:

■

Substitute p0 back into cost, location and price, we have our equilibrium results.w

As some literature suggested (for example, Ishida and Matsushima 2009), the public sector cannot operate at a loss. This requires that the retail price (p0LP−wLP=t(γ3t3−10γ2t2+36γt−32)4(γ2t2−2γt−16),) should be higher than the wholesale price (tγ>8). It can be verified that

SSRD−SSLP=A+B16γ(t2γ2−9tγ+32)(t2γ2−2tγ−16)2>0,

which is always positive, given A=t8γ8−36t7γ7+588t6γ6−5424t5γ5,. That is to say, at equilibrium, the state-owned retailer will not operate at a loss.

We compare the two cases: the wholesale-price contract and the inverse wholesale-price contract.

B=29776t4γ4−93312t3γ3+146688t2γ2−86016tγ+16384.

where

CSRD−CSLP=C+D16γ(t2γ2−9tγ+32)2(t2γ2−2tγ−16)2>0,
C=9t9γ9−276t8γ8+3684t7γ7−25472t6γ6+80112t5γ5,
D=53888t4γ4−1252608t3γ3+3608576t2γ2−3686400tγ+1048576.

where

C=9t9γ9−276t8γ8+3684t7γ7−25472t6γ6+80112t5γ5,
D=53888t4γ4−1252608t3γ3+3608576t2γ2−3686400tγ+1048576.

From both consumer welfare and social welfare perspective, inverse wholesale-price contract is better than wholesale-price contract. Since the privatization decision is made by the government, it is reasonable to believe that it will choose the scheme that is the best for the social welfare or (and) consumer welfare: the state-owned retailer determines the contract, either linear pricing or two-part tariff.

Proposition 9

When the manufacturer is privatized, in consideration of the social welfare, it is better to allow the retailer to determine the contract, whether it is a linear price contract or a two-part tariff contract. Furthermore, when it is determined by the retailer, these two contracts result in the same social welfare and consumer welfare.

References

Anderson, S. P., de Palma A., and Thisse J.-F. 1997. “Privatization and Efficiency in a Differentiated Industry.” European Economic Review 41 (9):1635–1654.10.1016/S0014-2921(97)00086-XSearch in Google Scholar

Barcena-Ruiz, J., and Garzon M. 2017. “Privatization of State Holding Corporations.” Journal of Economics 120 (2):171–188.10.1007/s00712-016-0498-0Search in Google Scholar

Bárcena-Ruiz, J. C., and Casado-Izaga F. J. 2014. “Zoning Under Spatial Price Discrimination.” Economic Inquiry 52 (2):659–665.10.1111/ecin.12071Search in Google Scholar

Bassi, M., Pagnozzi M., and Piccolo S. 2015. “Product Differentiation by Competing Vertical Hierarchies.” Journal of Economics and Management Strategy 24 (4):904–933.10.1111/jems.12115Search in Google Scholar

Bennett, J., and Maw J. 2003. “Privatization, Partial State Ownership, and Competition.” Journal of Comparative Economics 31 (1):58–74.10.1016/S0147-5967(02)00008-2Search in Google Scholar

Bonanno, G., and Vickers J. 1988. “Vertical Separation.” The Journal of Industrial Economics 36 (3):257–265.10.2307/2098466Search in Google Scholar

Cardenas, O. J. 2007. “Mixed Oligopoly and Spatial Agglomeration: A Comment.” Canadian Journal of Economics/Revue canadienne d’conomique 40 (1):340–346.10.1111/j.1365-2966.2007.00394.xSearch in Google Scholar

Chao, C.-C., and Yu E. S. 2006. “Partial Privatization, Foreign Competition, and Optimum Tariff.” Review of International Economics 14 (1):87–92.10.1111/j.1467-9396.2006.00562.xSearch in Google Scholar

Coughlan, A. T. 1985. “Competition and Cooperation in Marketing Channel Choice: Theory and Application.” Marketing Science 4 (2):110–129.10.1287/mksc.4.2.110Search in Google Scholar

Cremer, H., Marchand M., and Thisse J.-F. 1991. “Mixed Oligopoly with Differentiated Products.” International Journal of Industrial Organization 9 (1):43–53.10.1016/0167-7187(91)90004-5Search in Google Scholar

Du, N., Heywood J. S., and Ye G. 2013. “Strategic Delegation in an Experimental Mixed Duopoly.” Journal of Economic Behavior & Organization 87:91–100.10.1016/j.jebo.2013.01.006Search in Google Scholar

George, K., and La Manna M. M. A. 1996. “Mixed Duopoly, Inefficiency, and Public Ownership.” Review of Industrial Organization 11:853–860.10.1007/BF00174411Search in Google Scholar

Gupta, S., and Loulou R. 1998. “Process Innovation, Product Differentiation, and Channel Structure: Strategic Incentives in a Duopoly.” Marketing Science 17 (4):301–316.10.1287/mksc.17.4.301Search in Google Scholar

Heywood, J. S., and Ye G. 2009. “Mixed Oligopoly and Spatial Price Discrimination with Foreign Firms.” Regional Science and Urban Economics 39 (5):592–601.10.1016/j.regsciurbeco.2009.03.004Search in Google Scholar

Heywood, J. S., and Ye G. 2010. “Optimal Privatization in a Mixed Duopoly with Consistent Conjectures.” Journal of Economics 101 (3):231–246.10.1007/s00712-010-0156-xSearch in Google Scholar

Inoue, T., Kamijo Y., and Tomaru Y. 2009. “Interregional Mixed Duopoly.” Regional Science and Urban Economics 39 (2):233–242.10.1016/j.regsciurbeco.2008.10.001Search in Google Scholar

Ishibashi, I., and Matsumura T. 2006. “R&D Competition Between Public and Private Sectors.” European Economic Review 50 (6):1347–1366.10.1016/j.euroecorev.2005.04.002Search in Google Scholar

Ishida, J., and Matsushima N. 2009. “Should Civil Servants be Restricted In Wage Bargaining? A Mixed-Duopoly Approach.” Journal of Public Economics 93 (3):634–646.10.1016/j.jpubeco.2008.11.004Search in Google Scholar

Kamijo, Y., and Tomaru Y. 2014. “The Endogenous Objective Function of a Partially Privatized Firm: A Nash Bargaining Approach.” Economic Modelling 39:101–109.10.1016/j.econmod.2014.02.014Search in Google Scholar

Kitahara, M., and Matsumura T. 2013. “Mixed Duopoly, Product Differentiation and Competition.” The Manchester School 81 (5):730–744.10.1111/j.1467-9957.2012.02329.xSearch in Google Scholar

Kumar, A., and Saha B. 2008. “Spatial Competition in a Mixed Duopoly with One Partially Nationalized Firm.” Journal of Comparative Economics 36 (2):326–341.10.1016/j.jce.2007.03.001Search in Google Scholar

Matsumura, T. 1998. “Partial Privatization in Mixed Duopoly.” Journal of Public Economics 70 (3):473–483.10.1016/S0047-2727(98)00051-6Search in Google Scholar

Matsumura, T., and Matsushima N. 2004. “Endogenous Cost Differentials Between Public and Private Enterprises: A Mixed Duopoly Approach.” Economica 71, No. 284:671–688.10.1111/j.0013-0427.2004.00394.xSearch in Google Scholar

Matsumura, T., and Matsushima N. 2012. “Locating Outside a Linear City Can Benefit Consumers.” Journal of Regional Science 52 (3):420–432.10.1111/j.1467-9787.2011.00735.xSearch in Google Scholar

Matsumura, T., Matsushima N., and Ishibashi I. 2009. “Privatization and Entries of Foreign Enterprises in a Differentiated Industry.” Journal of Economics 98 (3):203–219.10.1007/s00712-009-0091-xSearch in Google Scholar

McGuire, T. W., and Staelin R. 1983. “An Industry Equilibrium Analysis of Downstream Vertical Integration.” Marketing Science 2 (2):161–191.10.1287/mksc.2.2.161Search in Google Scholar

Merrill, W. C., and Schneider N. 1966. “Government Firms in Oligopoly Industries: A Short-run Analysis.” Quarterly Journal of Economics 80 (3):400–412.10.2307/1880727Search in Google Scholar

Pal, D., and White M. D. 1998. “Mixed Oligopoly, Privatization, and Strategic Trade Policy.” Southern Economic Journal 65:264–281.10.2307/1060667Search in Google Scholar

Rey, P., and Stiglitz J. E. 1995. “The Role of Exclusive Territories in Producers’ Competition.” RAND Journal of Economics 26 (3):431–451.10.2307/2555997Search in Google Scholar

Shuai, J., and Tomaru Y. 2017. “On Privatization of Public Firms: A Subsidiary Privatization Approach.” working paper.10.2139/ssrn.2880573Search in Google Scholar

Shuai, J. 2016. “Mixed Duopoly with Subcontracting.” Managerial and Decision Economics 37 (1):37–49.10.1002/mde.2687Search in Google Scholar

Shuai, J. 2017. “Mixed Duopoly with a Partial-Delegated-Public Firm,” Manchester School forthcoming.10.1111/manc.12150Search in Google Scholar

Tian, G. 2000. “Property Rights and the Nature of Chinese Collective Enterprises.” Journal of Comparative Economics 28 (2):247–268.10.1006/jcec.2000.1658Search in Google Scholar

Published Online: 2017-09-19

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Articles
  2. Privatizing Multi-subsidiary Public Firm in Location Model
  3. Efficient Combinatorial Allocations: Individual Rationality versus Stability
  4. On Decay Centrality
  5. Sequential Auctions with Decreasing Reserve Prices
  6. The core of a strategic game
  7. Targeted Advertising on Competing Platforms
  8. Representation in Multi-Issue Delegated Bargaining
  9. Endogenous Mergers in Markets with Vertically Differentiated Products
  10. Standards of Proof and Civil Litigation: A Game-Theoretic Analysis
  11. Retained Earnings, Interest Rates and Lending Relationship
  12. Uniform Price Auctions with Asymmetric Bidders
  13. Conformity and Influence
  14. Sellouts, Beliefs, and Bandwagon Behavior
  15. Notes
  16. Eco-Firms and the Sequential Adoption of Environmental Corporate Social Responsibility in the Managerial Delegation
  17. Vertical Contract and Competition Intensity in Hotelling’s Model
  18. Constrained Allocation of Projects to Heterogeneous Workers with Preferences over Peers
  19. Irrelevance of the Strategic Variable in the Case of Relative Performance Maximization
  20. Critical Efficiencies as Upward Pricing Pressure with Feedback Effects
  21. On the Openness of Unique Pure-Strategy Nash Equilibrium
  22. Forecast Dispersion in Finite-Player Forecasting Games
https://doi.org/10.1515/bejte-2017-0056
Keywords for this article
privatization; multi-subsidiary; mixed oligopoly

Articles in the same Issue

  1. Articles
  2. Privatizing Multi-subsidiary Public Firm in Location Model
  3. Efficient Combinatorial Allocations: Individual Rationality versus Stability
  4. On Decay Centrality
  5. Sequential Auctions with Decreasing Reserve Prices
  6. The core of a strategic game
  7. Targeted Advertising on Competing Platforms
  8. Representation in Multi-Issue Delegated Bargaining
  9. Endogenous Mergers in Markets with Vertically Differentiated Products
  10. Standards of Proof and Civil Litigation: A Game-Theoretic Analysis
  11. Retained Earnings, Interest Rates and Lending Relationship
  12. Uniform Price Auctions with Asymmetric Bidders
  13. Conformity and Influence
  14. Sellouts, Beliefs, and Bandwagon Behavior
  15. Notes
  16. Eco-Firms and the Sequential Adoption of Environmental Corporate Social Responsibility in the Managerial Delegation
  17. Vertical Contract and Competition Intensity in Hotelling’s Model
  18. Constrained Allocation of Projects to Heterogeneous Workers with Preferences over Peers
  19. Irrelevance of the Strategic Variable in the Case of Relative Performance Maximization
  20. Critical Efficiencies as Upward Pricing Pressure with Feedback Effects
  21. On the Openness of Unique Pure-Strategy Nash Equilibrium
  22. Forecast Dispersion in Finite-Player Forecasting Games
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 18.11.2025 from https://www.degruyterbrill.com/document/doi/10.1515/bejte-2017-0056/pdf
Scroll to top button