Wage bargaining as an optimal control problem: A dynamic version of the efficient bargaining model

Guerrazzi, Marco (2020): Wage bargaining as an optimal control problem: A dynamic version of the efficient bargaining model.

Abstract

In this paper, I develop a dynamic version of the efficient bargaining model grounded on optimal control in which a firm and a union bargain over the wage in a continuous-time environment under the supervision of an infinitely lived mediator. Overturning the findings achieved by means of a companion right-to-manage framework, I demonstrate that when employment is assumed to adjust itself in the direction of the contract curve implied by the preferences of the two bargainers, increases in the bargaining power of the firm (union) accelerate (delay) the speed of convergence towards the stationary solution. In addition, confirming the reversal of the results obtained when employment moves over time towards the firm's labour demand, I show that the dynamic negotiation of wages tends to penalize unionized workers and favour the firm with respect to the bargaining outcomes retrieved with a similar static wage-setting model.

• Item Type: MPRA Paper
• Language: English
• Keywords: Wage-employment bargaining; Optimal control; Local dynamics.
• Subjects: E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E24 - Employment ; Unemployment ; Wages ; Intergenerational Income Distribution ; Aggregate Human Capital ; Aggregate Labor Productivity; J - Labor and Demographic Economics > J5 - Labor-Management Relations, Trade Unions, and Collective Bargaining > J52 - Dispute Resolution: Strikes, Arbitration, and Mediation ; Collective Bargaining

References

Ambrus, A., En Lu, S., (2015), A Continuous-Time Model of Multilateral Bargaining, American Economic Journal: Microeconomics, Vol. 7, No. 1, pp. 208-249.

Binmore, K., Rubinstein, A., (1986), The Nash Bargaining Solution in Economic Modelling, Rand Journal of Economics, Vol. 17, No. 2, pp. 176-188.

Booth, A.L. (1995), The Economics of Trade Unions, Cambridge University Press, Cambridge.

Castaner, A., Marin-Solano, J., Ribas, C., (2018), A Time Consistent Dynamic Bargaining Procedure in Continuous Time, Mimeo.

de la Croix, D., Palm, F.C., Pfann, G.A., (1996), A Dynamic Contracting Model for Wages and Employment in Three European Economies, European Economic Review, Vol. 40, No. 2, pp. 429-448.

Dobbelaere, S., Luttens, R.I., (2016), Gradual Collective Wage Bargaining, Labour Economics, Vol. 40, pp. 37-42.

Espinoza, M.P., Rhee, C., (1989), Efficient Wage Bargaining as a Repeated Game, Quarterly Journal of Economics, Vol. 104, No. 3, pp. 565--588.

Fellner, W., (1947), Prices and Wages Under Bilateral Monopoly, Quarterly Journal of Economics, Vol. 61, No. 4, pp. 503-532.

Gerber, A., Upmann, T., (2006), Bargaining Solutions at Work: Qualitative Differences in Policy Implications, Mathematical Social Sciences, Vol. 52, No. 2, pp. 162--175.

Guerrazzi, M., (2011), Wage Bargaining as an Optimal Control Problem: A Dynamic Version of the Right-to-Manage Model, Optimal Control Applications and Methods, Vol. 32, Vol. 5, pp. 609-622.

Johnson, G.E., (1990), Work Rules, Featherbedding, and Pareto-Optimal Union-Management Bargaining, Journal of Labor Economics, Vol. 8, No. 1, pp. S237-S259.

Layard, R., Nickell, S., (1990), Is Unemployment Lower if Unions Bargain Over Employment?, Quarterly Journal of Economics, Vol. 105, No. 3, pp. 773-787.

Leontief, W., (1946), The Pure Theory of the Guaranteed Annual Wage Contract, Journal of Political Economy, Vol. 54, No. 1, pp. 76-79.

Lockwood, B., Manning A., (1989), Dynamic Wage-Employment Bargaining with Employment Adjustment Costs, Economic Journal, Vol. 99, No. 398, pp. 1143-1158.

McDonald, I.M., Solow, R.M., (1981), Wage Bargaining and Employment, American Economic Review, Vol. 71, No. 5, pp. 896-908.

Muthoo, A., (1999), Bargaining Theory with Applications, Cambridge University Press, Cambridge.

Nash, J., (1953), Two-Person Cooperative Games, Econometrica, Vol. 21, No. 1, pp. 128-140.

Nash, J., (1950), The Bargaining Problem, Econometrica, Vol. 18, No. 2, pp. 155-162.

Oswald, A.J., (1985), The Economic Theory of Trade Unions: An Introductory Survey, Scandinavian Journal of Economics, Vol. 87, No. 2, pp. 160-193.

Petrakis, E., Vlassis, M., (2000), Endogenous Scope of Bargaining in a Union--Oligopoly Model: When Will Firms and Unions Bargain Over Employment?, Labour Economics, Vol. 7, No. 3, pp. 261-281.

Pohjola, M., (1987), Profit-Sharing, Collective Bargaining and Employment, Journal of Institutional and Theoretical Economics, Vol. 143, No. 2, pp. 334-342.

Raiffa, H., (1953), Arbitration Schemes for Generalized Two Person Games, in Kuhn, H., Tucker, A., (eds.), Contributions to the Theory of Games II, Princeton University Press, Princeton, pp. 361-387.

Ravn, M., Simonelli, S., (2007), Labor Market Dynamics and the Business Cycle: Structural Evidence for the United States, Scandinavian Journal of Economics, Vol. 109, No. 4, pp. 743-777.

Shimer, R., (2004), The Consequences of Rigid Wages in Search Models, Journal of the European Economic Association, Vol. 2, No. 2/3, pp. 469-479.

Stole, L.A., Zwiebel, J., (1996), Intra-Firm Bargaining under Non-Binding Contracts, Review of Economic Studies, Vol. 63, No. 3, pp. 375-410.

Strand, J., (1989), Monopoly Unions versus Efficient Bargaining: A Repeated Game Approach, European Journal of Political Economy, Vol. 5, No. 4, pp. 473-486.