Abstract
In this paper, we present a cooperative model of a hierarchically structured firm to study wage differences between different levels in such a firm. We consider a class of wage functions that are based on marginal contributions to production. It turns out that the wage of a manager is always at least as high as the wage of its subordinates. On the other hand, the wage of a manager never exceeds the sum of the wages of its direct subordinates. These bounds are sharp in the sense that we can characterize for which production processes they are reached. For the class of constant elasticity of substitution (CES) production functions this implies that the wage differences are maximal for linear production functions, and they are minimal for Cobb–Douglas production functions.
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References
Alchian AA, Demsetz H (1972) Production, information costs, and economic organization. Am Econ Rev 62:777–795
Banzhaf JF (1965) Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Rev 19:317–343
Ben-Yashar R, Nitzan S (2001) The robustness of optimal organizational architectures: a Note on hierarchies and polyarchies. Soc Choice Welfare 18:155–163
Brânzei R, Fragnelli V, Tijs S (2002) Tree connected peer group situations and peer group games. Math Methods Oper Res 55:93–106
van den Brink R (1997) An axiomatization of the disjunctive permission value for games with a permission structure. Int J Game Theory 26:27–43
van den Brink R, Gilles RP (1996) Axiomatizations of the conjunctive permission value for games with Permission Structures. Games Econ Behav 12:113–126
van den Brink R, van der Laan G (1998) Axiomatizations of the normalized Banzhaf value and the Shapley value. Soc Choice Welfare 15:567-582
van den Brink R, Ruys PHM (2005) Positional wages, market wages and firm size. Tinbergen Discussion Paper 05/020-1, Tinbergen Institute and Free University, Amsterdam
van den Brink R, Ruys PHM, Semenov R (2007) Governance of clubs and firms with cultural dimensions. Mimeo, Tinbergen Institute and Free University, Amsterdam
Calvo GA, Wellisz S (1978) Supervision, loss of control, and the optimum size of the firm. J Pol Econ 86:943–952
Calvo GA, Wellisz S (1979) Hierarchy, ability and income distribution. J Pol Econ 87:991–1010
Carlson NW (1982) Time rates tighten their grip on manufacturing industries. Mon Labor Rev 15–22
Dubey P, Shapley LS (1979) Mathematical properties of the Banzhaf power index. Math Oper Res 4:99–131
Gilles RP, Owen G (1994) Games with permission structures: The disjunctive approach. Mimeo, Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia
Gilles RP, Owen G, van den Brink R (1992) Games with permission structures: the conjunctive approach. Int J Game Theory 20:277–293
Grossman SJ, Hart OD (1983) An analysis of the principal-agent problem. Econometrica 51:7–45
Grossman SJ, Hart OD (1986) The costs and benefits of ownership: a theory of vertical and lateral integration. J Pol Econ 94:691–719
Hart O, Moore J (1990) Property rights and the nature of the firm. J Polit Econ 98:1119–1158
Hart O, Moore J (1999) Foundations of incomplete contracts. Rev Econ Stud 66:115–138
Hofstede G (1980) Culture’s consequences. International differences in work-related values. Sage Publications, Beverly Hills
Holmström B (1979) Moral hazard and observability. Bell J Econ 10:74–91
Ichiishi T (1993) The cooperative nature of the firm. Cambridge University Press, Cambridge
Kalai E, Samet D (1987) On weighted Shapley values. Int J Game Theory 16:205–222
Keren M, Levhari D (1979) The optimum span of control in a pure hierarchy. Manage Sci 25:1162–1172
Keren M, Levhari D (1983) The internal organization of the firm and the shape of average costs. Bell J Econ 14:474–486
Koh WTH (2005) Optimal sequential decision architectures and the robustness of hierarchies and polyarchies. Soc Choice Welfare 24:397–411
van der Laan G, van den Brink R (1998) An axiomated class of share functions for N-person games. Theory Decision 44:117–148
Maskin E, Tirole J (1999) Unforeseen contingencies and incomplete contracts. Rev Econ Stud 66:83–114
Milgrom P, Roberts J (1994) The economics of modern manufacturing: technology, strategy and organization. Am Econ Rev 80:511–528
Owen G (1975) Multilinear extensions and the Banzhaf value. Nav Res Logis Q 22:741–750
Radner R (1992) Hierarchy: the economics of managing. J Econ Lit 30:1382–1415
Rajan RG, Zingales L (1998) Power in a theory of the firm. Q J Econ 113:387–432
Rajan RG, Zingales L (2001) The firm as a dedicated hierarchy: a Theory of the origins and growth of firms. Q J Econ 116:805–851
Sah RK, Stiglitz JE (1986) The architecture of economic systems: hierarchies and polyarchies. Am Econ Rev 76:716–727
Shapley LS (1953) A value for n-person games. In: Kuhn HW, Tucker AW (eds) Ann Math Stud 28 (Contributions to the theory of games Vol. 2). Princeton University Press, Princeton, pp 307–317
Simon HA (1957) The compensation of executives. Sociometry 20:32–35
Weber RJ (1988) Probabilistic values for Games. In: Roth AE (ed) The Shapley value: Essays in Honor of Lloyd S. Shapley. Cambridge University Press, Cambridge
Williamson OE (1967) Hierarchical control and optimum firm size. J Pol Econ 75:123–138
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van den Brink, R. Vertical wage differences in hierarchically structured firms. Soc Choice Welfare 30, 225–243 (2008). https://doi.org/10.1007/s00355-007-0230-7
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DOI: https://doi.org/10.1007/s00355-007-0230-7