Wage Bargaining and Capital Accumulation: A Dynamic Version of the Monopoly Union Model

In this paper, I explore the relationship between wage bargaining and capital accumulation by developing a differential game in which a monopolistic union sets the wage of its members by taking as given the optimal employment strategy of a representative firm and the way in which capital is evaluated over time. Under the assumption that investment amounts to a constant share of output, I show that a meaningful open-loop Stackelberg equilibrium implies a positive union wage premium that achieves a maximum for a critical value of the elasticity of output with respect to capital which is a decreasing (increasing) function of the discount (depreciation) rate. Moreover, relying on some numerical simulations, I show that capital accumulation displays a non-monotonic pattern along which the union wage premium and the capital share follow a declining path.