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Efficient Bargaining in a Dynamic Macroeconomic Model

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Essays on Wage Bargaining in Dynamic Macroeconomics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 689))

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Abstract

This chapter analyzes the implications of efficient wage–employment bargaining in a closed monetary macroeconomic model of the AS–AD type with a government sector and fiat money. The consumption sector is made up of heterogeneous consumers—shareholders and workers—with endogenous labor supply and an endogenous reservation wage.

Unique temporary equilibria exist for all levels of bargaining power. These induce the determination of real allocations as well as nominal prices, wages, savings, and deficits. The comparative-statics analysis shows in particular that an increase of union power induces negative output and employment effects under a negative general-equilibrium price feedback. Equilibria under efficient bargaining are not Second-Best optimal.

The chapter concludes describing the evolution of such economies under perfect foresight and discusses the role of union power for existence and stability. Due to endogenous budget deficits/surpluses, stationary states fail to exist generically. The stability analysis distinguishes between the dynamics in nominal terms and the evolution of the real economy. The associated concepts of convergence to characterize balanced monetary expansion are introduced. Fiscal policy parameters and union power exhibit structural tradeoffs for the existence of balanced paths and their stability.

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Notes

  1. 1.

    There are some contributions dealing with specific dynamic or policy issues within nonmonetary models of capital accumulation, as for example Devereux and Lockwood (1991), Kaas and von Thadden (2004), Gerber and Upmann (2006), and Koskela and Puhakka (2006). Gertler and Trigari (2009) present an interesting combination of a market with matching and staggered Nash bargaining in an empirically oriented model. Ellis and Fender (1985, 1987) analyze a fixed-price macroeconomy with efficient bargaining and rationing, with an extension to an open economy.

  2. 2.

    The model is a standard version of an AS–AD model with fiat money whose consumption sector consists of cohorts of overlapping generations of heterogeneous consumer types (see for example Böhm 2017).

  3. 3.

    To save on notation, the government parameters g, τ w, and τ π are omitted wherever possible.

  4. 4.

    This assumption is made for simplicity only, the extension to multiple homogeneous firms organized in a producers association is straightforward, but would not qualitatively change any results of this chapter.

  5. 5.

    More general situations when workers consume in both periods can be analyzed within the same framework—with homothetic preferences in consumption and time separability between consumption and leisure—without changing the labor supply behavior in an essential way.

  6. 6.

    For any function f, its elasticity at x is denoted as E f(x).

  7. 7.

    The employment decision under efficient bargaining is the same as in a bilateral monopoly between the union and the producer maximizing the joint net gain.

  8. 8.

    For such bargaining problems, the generalized Zeuthen solution for half-space games coincides with the generalized Nash solution, yet requires less properties (see Peters 1992; Rosenmüller 2000).

  9. 9.

    See Böhm (2017) for more details; the macroeconomic implications are shown in Sect. 2.4.

  10. 10.

    For a more detailed discussion see Sect. 2.4.1.

  11. 11.

    If workers consume in the current period as well (cf. footnote 5), a term consisting of the net consumption propensity times the wage share (2.9) is added.

  12. 12.

    All diagrams are calculated and drawn to scale with isoelastic functions for the same set of parameters, unless otherwise indicated.

  13. 13.

    This is the same level of union power as in Corollary 2.3.1. It can be defined explicitly by evaluating the natural level of bargaining power λ nat(L) from (2.8) at \(L=h_{\mathrm {eff}}(p^e/\mathcal {P}_{\mathrm {com}}(M,p^e))={\mathcal {L}_{\mathrm {eff}}}(M,p^e)\).

  14. 14.

    Note that this discussion argues only about efficiency in terms of the payoff between the firm and the union and not in welfare terms with respect to the two groups of consumers and their indirect utility. A welfare comparison should use their utility functions. In this case, the effects stemming from underemployment/overemployment would have to be accounted for as well. Moreover, the intertemporal structure of overlapping generations requires additional criteria between old and young consumers and their position in the temporary equilibrium, for which a Pareto criterion is not universally defined.

  15. 15.

    Strictly speaking, the set also contains the boundary point (L crit, w crit) since there exists an unbounded interval of positive prices which induce positive profits.

  16. 16.

    Selten and Güth (1982) treat a simplified real macro model which is one of the rare attempts of sequential bargaining in a dynamic general equilibrium. An alternative endogenous mechanism could use adaptive intertemporal procedures to determine union power (as an agent-based approach) by using, for example, aspiration levels and adjusting them to the sequence of economic data achieved.

  17. 17.

    See Böhm and Wenzelburger (1999) and Böhm (2017) for a general discussion of perfect predictors.

  18. 18.

    The general case can be dealt with using Lemma 2.3.1.

  19. 19.

    For simplicity, it is assumed that the average tax rate is independent of real balances. This occurs in the isoelastic example or under one common tax rate.

  20. 20.

    The government consumption parameter g has been set such that the balanced paths are evenly spread. This has no qualitative effect on stability/instability in general which is induced by the uniform tax rates.

  21. 21.

    Selten and Güth (1982) presents such a sequential bargaining solution in a dynamic nonmonetary economy and Blanchard and Fischer (1993) discusses intertemporal issues without analyzing a complete dynamic model.

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  1. Center for Mathematical Economics, Bielefeld University, Bielefeld, Germany

    Oliver Claas

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Claas, O. (2019). Efficient Bargaining in a Dynamic Macroeconomic Model. In: Essays on Wage Bargaining in Dynamic Macroeconomics. Lecture Notes in Economics and Mathematical Systems, vol 689. Springer, Cham. https://doi.org/10.1007/978-3-319-97828-4_2

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