Endogenous input price and collusion sustainability in the output market

We analyze collusion sustainability in a duopoly where firms compete on quantities, labor is the only input, and the wage is endogenously defined by the match between the industry labor demand and an upward-sloping labor supply. In this framework, the equilibrium wage is positively correlated with the industry level of output and, to expand production, firms have to attract additional employees offering them a higher wage. We prove that the more sensitive to the industry demand of labor the wage is, the higher is the industry critical discount factor, i.e. the harder it is to sustain collusion. Thus, when the equilibrium wage is very sensitive to the industry demand of labor, punishment in the Nash reversion stage may be not credible; this makes collusion never sustainable.