Comparing Cournot and Bertrand Competition in a Unionized Mixed Duopoly

Choi, Kangsik (2008): Comparing Cournot and Bertrand Competition in a Unionized Mixed Duopoly.

Abstract

We investigate a differentiated mixed duopoly in which private and public firms can choose to strategically set prices or quantities by facing a union bargaining process. For the case of a unionized mixed duopoly, only the public firm is able to choose a type of contract irrespective of whether the goods are substitutes or complements in the equilibrium. Thus, we show that social welfare under Bertrand competition is always determined by the public firm's dominant strategy, wherein the Bertrand competition entails higher social welfare than the Cournot competition. Moreover, there are multiple Nash equilibria in the contract stage of the game. Finally, our main results hold irrespective of the nature of goods, with the exception of when a sufficiently large parameter of complements is employed, the ranking of private firm's profit is not reversed, which is contrast to the standard findings.

• Item Type: MPRA Paper
• Language: English
• Keywords: Wage Bargaining, Union, Cournot-Bertrand Competition, Mixed Duopoly.
• Subjects: J - Labor and Demographic Economics > J5 - Labor-Management Relations, Trade Unions, and Collective Bargaining > J51 - Trade Unions: Objectives, Structure, and Effects; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D43 - Oligopoly and Other Forms of Market Imperfection; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; H - Public Economics > H4 - Publicly Provided Goods > H44 - Publicly Provided Goods: Mixed Markets

References

Amir, R, and J, Y, Jin, 2001,``Cournot and Bertrand Equilibria Compared: Substitutability, Complementarity and Convavity," International Journal of Industrial Organization 19, 303-317.

Barcena-Ruiz, J.C. 2007,``Endogenous Timing in a Mixed Duopoly: Price Competition," Journal of Economics 91, 263-272.

Cheng, L, 1985, ``Comparing Bertrand and Cournot Equilibria: A Geometric Approach," RAND Journal of Economics, 16, 146-152.

Correa-Lopez, M, 2007, ``Price and Quantity Competition in a Differentiated Duopoly with Upstream Suppliers," Jouranl of Economics and Management Strategy, 16, 469-505.

Dastidar, K, G. 1997, ``Comparing Cournot and Bertrand in Homogenous Product Market," Journal of Economic Theory, 75, 205-212.

De Fraja, G. 1993, ``Union and Wages in Public and Private Firms: A Game Theoretic Analysis," Oxford Economic Papers, 45, 457-469.

De Fraja, G. and Delbono F., 1989, ``Alternative Strategies of a Public Enterprise in Oligopoly," Oxford Economic Papers, 41, 302-311.

De Fraja, G. and Delbono F., 1990, ``Game Theoretic Models of Mixed Oligopoly," Journal of Economic Surveys, 4, 1-17.

Ghosh, A, and M., Mitra, 2008, ``Comparing Bertrand and Cournot Outcomes in the Presence of Public Firm," University of New South Wales, Australian School of Business, Scool of Economics Discussion Paper: 2008-18

Hackner, J, 2000, ``A Note on Price and Quantity Competition in Differentiated Oligopolies," Journal of Economic Theory, 93, 233-239.

Haskel, J, and A, Sanchis, 1995, ``Privatisation and X-Inefficiency: A Bargaining Approach," Journal of Industrial Economics, 43, 301-321.

Haskel, J, and S, Szymanski, 1993, ``Privatization, Liberalization, Wages and Employment: Theory and Evidence for the UK," Economica, 60, 161-182.

Haucap, J. and C. Wey, 2004,``Unionisation Structures and Innovation Incentives," Economic Journal, 114, C149-C465.

Ishida, J, and N., Matsushima, 2008a, ``Should Civil Servants be Restricted in Wage Bargaining? A Mixed-Duopoly Approach," Kobe University, GSBA Discussion Paper Series 2008-49. forthcoming in Journal of Public Economics.

Ishida, J, and N., Matsushima, 2008b, ``Outward FDI in Unionized Oligopoly: Welfare and Policy Implications," Osaka University, OSIPP Discussion Paper DP-2008-E-005.

Lambertini, L, 1997, ``Prisoners' Dilemma in Duopoly (Super)Games," Journal of Economic Theory, 77, 181-191.

Leahy, D, and C, Montagna, 2000, ``Unionisation and Foreign Direct Investment: Challenging Conventional Wisdom?" Economic Journal, 110, C80-C92.

Lommerud K, E., F, Meland, and L, Sorgard 2003,``Unionised Oligopoly, Trade Liberalisation and Location Choice," Economic Journal, 113, 782-800.

Lopez, C, M, 2007, ``Price and Quantity Competition in a Differentiated Duopoly with Upstream Suppliers," Jouranl of Economics and Management Strategy, 16, 469-505.

Lopez, C, M, and R, Naylor, 2004, ``The Cournot-Bertrand Profit Differential: A Reversal Result in a Dfferentiated Duopoly with Wage Bargaining," European Economic Review, 48, 681-696.

Lu, Y. and S., Poddar, 2006, ``The Choice of Capacity in Mixed Duopoly under Demand Uncertainty," The Manchester School, 74, 266-272.

Manasakis, C, and M, Vlassis, 2006, ``Equilibrium Mode of Competition in Unionize Oligopolies: Do Unions Act as Commitment Device to Cournot Outcomes," Working Papers No. 2006-3, University of Crete.

Matsumura. T, 1998, ``Partial Privatization in Mixed Duopoly," Journal of Public Economics, 70, 473-483.

Matsumura, T, and O, Kanda, 2005,``Mixed Oligopoly at Free Entry Markets," Journal of Economics, 84, 27-48.

Matsumura, T., and N. Matsushima, 2004, ``Endogenous Cost Differentials between Public and Private Enterprises: A Mixed Duopoly Approach," Economica, 71, 671-688.

Matsushima, N, and T, Matsumura, 2006,``Mixed Oligopoly and Spatial Agglomeration," Canadian Journal of Economics, 36, 62-87.

Mukherjee, A, and K, Suetrong, 2007,``Unionisation Structure and Strategic Foreign Direct Investment," GEP Research Paper Series 2007/22, University of Nottingham.

Naylor, R, A, 2002,``Industry Profits and Competition under Bilateral Oligopoly," Economics Letters, 77, 169-177.

Naylor, R, A, 1998,``International Trade and Economic Integration when Labour Markets are Generally Unionised," European Economic Review, 42, 1251-1267.

Naylor, R, A, 1999,``Wage Union Strategies and International Trade," Economic Journal, 109, 102-125.

Nett, L., 1993, ``Mixed Oligopoly with Homogeneous Goods," Annals of Public and Cooperative Economics, 64, 367-393.

Okuguchi, K., 1987, ``Equilibrium Prices in the Bertrand and Cournot Oligopolies," Journal of Economic Theory, 42, 213-229.

Oswald, A, J., and P., Turnbull, 1995, ``Pay and Employment Determination in Britain: What are Labour Contracts Really Like," Oxford Review of Economic Policy, 1, 80-97.

Qiu, L, D. 1997, ``On the Dynamic Efficiency of Bertrand and Cournot Equilibria," Journal of Economic Theory, 75, 213-229.

Schmidt, K, M., 1996, ``The Costs and Benefits of Privatization - An Incomplete Contracts Approach," Journal of Law, Economics and Organization, 12, 1-24.

Singh, N., and Vives, X., 1984, ``Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, 15, 546-554.

Skaksen, M, Y,, and J. R. Sorensen, 2001, ``Should Trade Union Appreciate Foreign Direct Investment?" Journal of International Economics, 55, 379-390.

Straume, O. R., 2003, ``International Merger and Trade Liberalization: Implications for Unionized Labour," International Journal of Industrial Organization, 21, 717-735.

Zanchettin, P., 2006, ``Differentiated Duopoly with Asymmetirc Costs: New Results from a Seminal Model," Journal of Economics and Management Strategy, 15, 999-1015.

Zhao, L., 1995, ``Cross-Hauling Direct Foreign Investment and Unionized Oligopoly," European Economic Review, 39, 379-390.

Wang, X. H, 2008, ``Price and Quantity Competition Revisited," Economics Bulletin, 4, 1-7.