# Bargaining over productivity and wages when technical change is induced: implications for growth, distribution, and employment

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## Abstract

I study a model of growth and income distribution in which workers and firms bargain *à la* Nash (Econometrica 18(2):155–162, 1950) over wages and productivity gains, taking into account the trade-offs faced by firms in choosing factor-augmenting technologies. The aggregate environment resulting from self-interested, objective function-maximizing decision rules on wages, productivity gains, savings and investment, is described by a two-dimensional dynamical system in the employment rate and output/capital ratio. The economy converges cyclically to a long-run equilibrium involving a Harrod-neutral profile of technical change, a constant rate of employment of labor, and constant input shares. The type of oscillations predicted by the model is qualitatively consistent with the available data on the United States (1963–2003), replicates the dynamics found in earlier models of growth cycles such as Goodwin (A growth cycle, in C.H. Feinstein (ed). Socialism, Capitalism and Economic Growth. Cambridge University Press, Cambridge 1967. Cambridge University Press, Cambridge, 1967); Shah and Desai (Econ J 91:1006–1010, 1981); van der Ploeg (J Macroecon 9:1–12, 1987); Flaschel (J Econ: Zeitschrift für Nationalökonomie 44:63–69, 1984) and Sportelli (J Econ: Zeitschrift für Nationalökonomie 61(1):35–64, 1995), and can be verified numerically in simulations. Institutional change, as captured by variations in workers’ bargaining power, has a positive effect on the long-run rate of growth of output per worker but a negative effect on long-run employment. Economic policy can also affect the growth and distribution pattern through changes in the unemployment compensation, which also have a positive long-run impact on labor productivity growth but a negative long-run impact on employment. In both cases, employment can overshoot its new equilibrium value along the transitional dynamics.

## Keywords

Goodwin growth cycle Bargaining Induced technical change Factor shares Employment## JEL Classification

E24 E25 J52 O31## Notes

### Acknowledgments

I thank Rudi von Arnim, Guido Cozzi, Peter Flaschel, Michalis Nikiforos, Christian Proaño, Codrina Rada, Rick van der Ploeg, Peter Skott, Luca Zamparelli, participants to the 2010 Eastern Economic Association Meetings, and two anonymous referees for extremely valuable comments and suggestions. I am most indebted to Duncan Foley for his guidance and constructive criticism.

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