A Theory of Wages and Labour Demand with Intra-firm Bargaining and Matching Frictions

Firms are the field of several strategic interactions that standard neo-classical analysis often ignores. Such strategic considerations concern relations between capital owner and labour, relations between marginal employees and incumbents and more generally all relations between different groups within the firm with different bargaining positions. This Paper provides a synthetic model of the labour market equilibrium with search frictions in a dynamic framework where wage bargaining is influenced by within-firm strategic interactions, with explicit closed form solutions. We then explore systematically within-firm strategic interactions and shed new light on the micro- and macroeconomic consequences of conflicts on wages, unemployment and capital accumulation. First, we recover the partial equilibrium over-employment phenomenon put to the fore by Stole and Zwiebel (1996a,b) at the firm level, according to which the bargaining power of workers increases employment. Further, with heterogeneous labour, higher relative bargaining power for some groups leads quite generally to over-employment relative to other groups, those other groups being under-employed if they have a lower relative bargaining power. The over-employment results do not necessarily hold at the macroeconomic level, however. Quantitative exercises suggest that the bargaining power of workers is actually detrimental to employment when labour is considered as an homogeneous input. Finally, the hold-up problem between capital owners and employees does not necessarily lead to under-investment in physical capital as it is usually the case. Actually, strategic over-employment can induce over-investment when employees substitutable to capital have strong bargaining power.