Consider now the second stage. In a competitive labour market, each firm chooses labour input to maximize net revenue Y+z^-wL if production is taken up. This simply yields the marginal productivity condition YL=w. The equilibrium wage rate obviously satisfies w$c. The wage rate may exceed c if L=N in the equilibrium, i.e. no voluntary unemployment exists. For the following analysis, it is useful to concentrate on the case of an interior solution, where the labour market clears with L
We finally turn to the first stage where the firms choose K. For the analysis of investment behaviour, suppose for the sake of the argument that all firms decide to take up production, that is |ic=0. We show below that this conjecture is indeed correct. Expected profits of a firm i are thus given by
Equations (3)-(5) and the condition w=c completely describe the competitive equilbibrium, i.e. the equilibrium values of L,K,w and the liquidation probability |ic. The competitive equilibrium also represents a first-best outcome in this economy and will serve as a benchmark for the following analysis.
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The Equilibrium with Union-Firm Bargaining
We now introduce a trade union which represents the interests of the workers. As the number of firms is normalised to unity, we also consider one representative trade union. In line with the assumption of risk-neutral workers, it is the objective of the union to maximize expected labour income of workers (U) which is given by
where ц* now denotes the probability that a firm is closed. Of course, the union essentially has the function to raise the wage rate above the competitive wage c.
The labour market is now characterized by union-firm bargaining, which takes place at stage two in the sequence of decisions. As in Grout (1984), the union is assumed to know the capital stock (K). The (representative) union and the (representative) firm bargain over wages (w) and employment per firm (L). The outcome of this bargaining process specifies a wage-employment contract which determines w and L.
The expected profit (P) of the representative firm in stage 2, where the capital stock is given, can be written as
The first term in (7) captures the profit of a firm which takes up production. The latter occurs with probability (1-ц*). The second term is the revenue from a liquidation, which occurs with probability ц*.