Accessible Requires Authentication Published by De Gruyter July 20, 2019

Efficiency Wages in Cournot-Oligopoly

Marco de Pinto and Laszlo Goerke

Abstract

In a Cournot-oligopoly with free but costly entry and business stealing, output per firm is too low and the number of competitors excessive, assuming labor productivity to depend on the number of employees only or to be constant. However, a firm can raise the productivity of its workforce by paying higher wages. We show that such efficiency wages accentuate the distortions occurring in oligopoly. Specifically, excessive entry is aggravated and the welfare loss due to market power rises.

JEL Classification: D43; J31; L13

Acknowledgements

We are grateful for helpful comments by an anonymous referee, Florian Baumann, Michael Neugart, Alexander Rasch, Philipp Weinschenk and Ulrich Zierahn. We also thank participants of the European Society of Population Economics annual meeting 2018 (held in Antwerp) and seminar participants in Trier for inspiring discussions and Andreas Jung for his excellent research assistance.

Appendix

A

Throughout the Appendix, we consider the case of a linear production function, i. e. F=1. For simplicity, we suppress the respective underline notation (as employed in the main text).

A.1 Derivation of Eqs. (19) and (20)

Using (18), we can rewrite (15) as:

(22)xopt=n+1nopt+1x=(nopt+1)1.5nopt+1x=(nopt+1)0.5x,

which is identical to Eq. (19). To compute (20), note that in case of a linear production function, the social planner’s objective can be rewritten as:

(23)W=0.5(qp)nx+nπ=qnxnwl0.5(nx)2nk=(n(γ)+1)xnx0.5(nx)2nk,

where we have used (1), (3) and (10). Combining (23) with (22) and (9) yields,

(24)Wopt=(n+1)xnoptxopt0.5(noptxopt)2noptk=(nopt+1)xoptnoptxopt0.5(noptxopt)2noptk=(noptxopt)2+xoptnoptxopt0.5(noptxopt)2noptk=xoptnoptxoptnoptk+0.5(noptxopt)2=((xopt)2k)nopt+0.5(noptxopt)2=((xopt)2(x)2)nopt+0.5(noptxopt)2.

A.2 Derivation of Proposition 2 Part (I)

Differentiating (10) with respect to γ yields:

(25)dndγ=1x[dwdγe(w)γ+wddγe(w(γ))γ].

The second derivative in square brackets can be expressed as:

(26)ddγe(w(γ))γ=e(w)γ[ln(e(w))γe(w)de(w(γ))dγ].

Inserting de(w(γ))/dγ=de/dw×dw/dγ into (26) and substituting the result into (25) yields:

(27)dndγ=1x[dwdγe(w)γwe(w)γ(ln(e(w))+γe(w)dedwdwdγ)]=1xe(w)γ[dwdγγdedwdwdγwe(w)wln(e(w))]=1xe(w)γ[dwdγ(1γdedwwe(w))wln(e(w))].

Using the Solow-condition implies:

(28)dndγ=1xe(w)γwln(e(w))>0.

Differentiating (18) with respect to γ yields:

(29)dnoptdγ=23(n+1)1/3<1dndγ>0>0.

This shows that:

(30)d(nnopt)dγ=dndγdnoptdγ>0,

which proves the first part of Proposition 2.

A.3 Derivation of Proposition 2 Part (II)

From (9) and (19), we obtain dx/dγ=0 and dxopt/dγ>0. This immediately proves the second part of Proposition 2.

A.4 Derivation of Proposition 2 Part (III)

Using (11) and (20), we can write the welfare loss as:

(31)WWopt=((xoptxoptxx)nopt+0.5((noptxopt)2(nx)2))=((xopt+x)(xoptx)nopt+0.5(noptxopt+nx)(noptxoptnx)).

From (18) and (19), we find:

(32)xoptx=(nopt+1)0.5,
(33)n=(nopt+1)1.51.

This leads to:

(34)noptxoptnx=x(noptxoptxn)=x(nopt(nopt+1)0.5(nopt+1)1.5+1)=x+x(nopt(nopt+1)0.5(nopt+1)1.5)=xx(nopt+1)0.5=(xoptx).

Given (32), (33) and (34), we can rewrite (31) as:

(35)WWopt=(xoptx)((xopt+x)nopt0.5(noptxopt+nx))=(xoptx)(0.5xoptnopt+xnopt0.5nx)=(xoptx)x(0.5(nopt+1)0.5nopt+nopt0.5(nopt+1)1.5+0.5)=(xoptx)x(0.5(nopt+1)0.5nopt+nopt+10.5(nopt+1)1.50.5)=(xoptx)x((nopt+1)(1+0.5(nopt+1)0.5nopt0.5(nopt+1)0.5)0.5)=(xoptx)x((nopt+1)(10.5(nopt+1)0.5)0.5)

Defining Θ(nopt(γ)+1)[10.5(nopt(γ)+1)0.5]0.5>0, we can calculate:

(36)WWopt=(xopt(γ)x)xΘ(γ),
(37)d(WWopt)dγ=x(dxoptdγ>0Θ+(xoptx)dΘdnopt>0dnoptdγ>0)<0,

which proves the last part of Proposition 2.

References

Akerman, A., I. Gaarder and M. Mogstad. 2015. “The Skill Complementarity of Broadband Internet.” The Quarterly Journal of Economics 130 (4): 1781–824.10.1093/qje/qjv028 Search in Google Scholar

Altenburg, L., and M. Straub. 1998. “Efficiency Wages, Trade Unions, and Employment.” Oxford Economic Papers 50 (4): 726–46.10.1093/oep/50.4.726 Search in Google Scholar

Amable, B., and D. Gatti. 2002. “Macroeconomic Effects of Product Market Competition in a Dynamic Efficiency Wage Model.” Economics Letters 75 (1): 39–46.10.1016/S0165-1765(01)00583-3 Search in Google Scholar

Amable, B., and D. Gatti. 2004. “Product Market Competition, Job Security, and Aggregate Employment.” Oxford Economic Papers 56 (4): 667–86.10.1093/oep/gpf068 Search in Google Scholar

Amir, R., and C. Burr. 2015. “Corruption and Socially Optimal Entry.” Journal of Public Economics 123: 30–41.10.1016/j.jpubeco.2014.12.012 Search in Google Scholar

Amir, R., L. De Castro, and L. Koutsougeras. 2014. “Free Entry Versus Socially Optimal Entry.” Journal of Economic Theory 154: 112–25.10.1016/j.jet.2014.09.003 Search in Google Scholar

Ara, T., A. Ghosh, and H. Zhang. 2017. “Tariffs, Vertical Oligopoly and Market Structure.” Working Paper. Search in Google Scholar

Autor, D., and D. Dorn. 2013. “The Growth of Low-Skill Service Jobs and the Polarization of the US Labor Market.” The American Economic Review 103 (5): 1553–97.10.1257/aer.103.5.1553 Search in Google Scholar

Autor, D., D. Dorn, L. F. Katz, C. Patterson, and J. Van Reenen. 2017. “Concentrating on the Fall of the Labor Share.” The American Economic Review 107 (5): 180–85.10.1257/aer.p20171102 Search in Google Scholar

Bachmann, R., G. Demir, and H. Frings. 2019. “Labour Market Polarisation and Monopsonistic Competition.” Working Paper. Search in Google Scholar

Basak, D., and A. Mukherjee. 2016. “Social Efficiency of Entry in a Vertically Related Industry.” Economics Letters 139: 8–10.10.1016/j.econlet.2015.12.003 Search in Google Scholar

Bernard, A. B., S. J. Redding, and P. K. Schott. 2007. “Comparative Advantage and Heterogeneous Firms.” The Review of Economic Studies 74 (1): 31–66.10.1111/j.1467-937X.2007.00413.x Search in Google Scholar

Chao, A. C., J.-Y. Lee, and L. F. Wang. 2017. “Stackelberg Competition, Innovation and Social Efficiency of Entry.” The Manchester School 85 (1): 1–12.10.1111/manc.12130 Search in Google Scholar

Chen, Z., and B. Zhao. 2014. “Unemployment and Product Market Competition in a Cournot Model with Efficiency Wages.” Canadian Journal of Economics 47 (2): 555–79.10.1111/caje.12081 Search in Google Scholar

Corchon, L. C., and I. Fradera. 2002. “Comparative Statics in Cournot Free Entry Equilibrium.” Mathematical Social Sciences 44 (2): 155–68.10.1016/S0165-4896(02)00026-4 Search in Google Scholar

Dauth, W., S. Findeisen, J. Südekum, and N. Woessner. 2017. “German Robots - the Impact of Industrial Robots on Workers.” Working Paper. Search in Google Scholar

Davidson, C., and A. Mukherjee. 2007. “Horizontal Mergers with Free Entry.” International Journal of Industrial Organization 25 (1): 157–72.10.1016/j.ijindorg.2006.03.003 Search in Google Scholar

de Pinto, M., and L. Goerke. 2016. “Welfare-Enhancing Trade Unions in an Oligopoly with Excessive Entry.” IAAEU Discussion Paper 03/2016. Search in Google Scholar

Dustmann, C., J. Ludsteck, and U. Schönberg. 2009. “Revisiting the German Wage Structure.” The Quarterly Journal of Economics 124 (2): 843–81.10.1162/qjec.2009.124.2.843 Search in Google Scholar

Etro, F. 2014. “The Theory of Endogenous Market Structures.” Journal of Economic Surveys 28 (5): 804–30.10.1111/joes.12020 Search in Google Scholar

Ghosh, A., and H. Morita. 2007a. “Free Entry and Social Efficiency Under Vertical Oligopoly.” The RAND Journal of Economics 38 (2): 541–54.10.1111/j.1756-2171.2007.tb00083.x Search in Google Scholar

Ghosh, A., and H. Morita. 2007b. “Social Desirability of Free Entry: A Bilateral Oligopoly Analysis.” International Journal of Industrial Organization 25 (5): 925–34.10.1016/j.ijindorg.2007.02.002 Search in Google Scholar

Ghosh, A., and S. Saha. 2007. “Excess Entry in the Absence of Scale Economies.” Economic theory 30 (3): 575–86.10.1007/s00199-005-0072-4 Search in Google Scholar

Gielen, A. C., M. J. Kerkhofs, and J. C. Van Ours. 2010. “How Performance Related Pay Affects Productivity and Employment.” Journal of Population Economics 23 (1): 291–301.10.1007/s00148-009-0252-9 Search in Google Scholar

Hamada, K., T. Ohkawa, and M. Okamura. 2018. “Insufficient Entry of Employee-Controlled Firms in a Free-Entry Oligopoly.” Annals of Public and Cooperative Economics 89 (2): 437–48.10.1111/apce.12179 Search in Google Scholar

Haruna, S., and R. K. Goel. 2011. “R&D, Free Entry, and Social Inefficiency.” Economics of Innovation and New Technology 20 (1): 89–101.10.1080/10438599.2010.533534 Search in Google Scholar

Head, K., and B. J. Spencer. 2017. “Oligopoly in International Trade: Rise, Fall and Resurgence.” Canadian Journal of Economics 50 (5): 1414–44.10.1111/caje.12303 Search in Google Scholar

Hershbein, B., and C. Macaluso. 2018. “Labor Market Concentration and the Demand for Skills.” Working Paper. Search in Google Scholar

Lavy, V. 2009. “Performance Pay and Teachers’ Effort, Productivity, and Grading Ethics.” The American Economic Review 99 (5): 1979–2011.10.1257/aer.99.5.1979 Search in Google Scholar

Layard, R., S. Nickell, and R. Jackmann. 1991. Unemployment. Macroeconomic Performance and the Labour Market. Oxford: Oxford University Press. Search in Google Scholar

Lazear, E. P. 2000. “Performance Pay and Productivity.” The American Economic Review 90 (5): 1346–61.10.1257/aer.90.5.1346 Search in Google Scholar

Mankiw, N. G., and M. D. Whinston. 1986. “Free Entry and Social Inefficiency.” The RAND Journal of Economics 17 (1): 48–58.10.2307/2555627 Search in Google Scholar

Marjit, S., and A. Mukherjee. 2013. “Foreign Competition and Social Efficiency of Entry.” Economic Modelling 32: 108–12.10.1016/j.econmod.2013.01.032 Search in Google Scholar

Matsumura, T., and Y. Okumura. 2014. “Comparison Between Specific Taxation and Volume Quotas in a Free Entry Cournot Oligopoly.” Journal of Economics 113 (2): 125–32.10.1007/s00712-013-0365-1 Search in Google Scholar

McKinsey & Company. 2017. “Transforming Operations Management for a Digital World.” McKinsey Global Institute – Operations. Search in Google Scholar

Michaels, G., A. Natraj, and J. Van Reenen. 2014. “Has ICT Polarized Skill Demand? Evidence From Eleven Countries Over Twenty-Five Years.” Review of Economics and Statistics 96 (1): 60–77.10.1162/REST_a_00366 Search in Google Scholar

Mizuno, T. 2003. “On the Existence of a Unique Price Equilibrium for Models of Product Differentiation.” International Journal of Industrial Organization 21 (6): 761–93.10.1016/S0167-7187(03)00017-1 Search in Google Scholar

Mukherjee, A. 2012a. “Endogenous Cost Asymmetry and Insufficient Entry in the Absence of Scale Economies.” Journal of Economics 106 (1): 75–82.10.1007/s00712-011-0255-3 Search in Google Scholar

Mukherjee, A. 2012b. “Social Efficiency of Entry with Market Leaders.” Journal of Economics & Management Strategy 21 (2): 431–44.10.1111/j.1530-9134.2012.00333.x Search in Google Scholar

Nickell, S. 1999. “Product Markets and Labour Markets.” Labour Economics 6 (1): 1–20.10.1016/S0927-5371(99)00005-6 Search in Google Scholar

Novshek, W. 1985. “On the Existence of Cournot Equilibrium.” The Review of Economic Studies 52 (1): 85–98.10.2307/2297471 Search in Google Scholar

Okuno-Fujiwara, M., and K. Suzumura. 1993. “Symmetric Cournot Oligopoly and Economic Welfare: A Synthesis.” Economic Theory 3 (1): 43–59.10.1007/BF01213691 Search in Google Scholar

Perry, M. K. 1984. “Scale Economies, Imperfect Competition, and Public Policy.” The Journal of Industrial Economics 32 (3): 313–33.10.2307/2098020 Search in Google Scholar

Schlicht, E. 2016. “Efficiency Wages: Variants and Implications.” IZA World of Labor 2016 (275). https://doi.org/10.15185/izawol.275. Search in Google Scholar

Seade, J. 1980. “On the Effects of Entry.” Econometrica 48 (2): 479–89.10.2307/1911111 Search in Google Scholar

Shapiro, C., and J. E. Stiglitz. 1984. “Equilibrium Unemployment as a Worker Discipline Device.” The American Economic Review 74 (3): 433–44. Search in Google Scholar

Shearer, B. 2004. “Piece Rates, Fixed Wages and Incentives: Evidence from a Field Experiment.” The Review of Economic Studies 71 (2): 513–34.10.1111/0034-6527.00294 Search in Google Scholar

Solow, R. M. 1979. “Another Possible Source of Wage Stickiness.” Journal of Macroeconomics 1 (1): 79–82.10.1016/0164-0704(79)90022-3 Search in Google Scholar

Suzumura, K. 1995. Competition, Commitment, and Welfare. Oxford: Oxford University Press. Search in Google Scholar

Suzumura, K., and K. Kiyono. 1987. “Entry Barriers and Economic Welfare.” The Review of Economic Studies 54 (1): 157–67.10.2307/2297451 Search in Google Scholar

Varian, H. R. 1985. “Price Discrimination and Social Welfare.” The American Economic Review 75 (4): 870–75. Search in Google Scholar

Published Online: 2019-07-20

© 2019 Walter de Gruyter GmbH, Berlin/Boston