The Cournot–Bertrand profit differential: A reversal result in a differentiated duopoly with unions’ fairness concerns

This paper revisits the classic Cournot–Bertrand profit differential in a differentiated duopoly with firm-specific labor unions. Departing from the standard assumption of rent-maximizing unions, we introduce a new dimension by modelling unions that institutionalize workers’ fairness concerns. These concerns are formalized along two distinct, empirically grounded arguments: vertical fairness concerns (VFC), where unions care about the intra-firm distribution of surplus between labor (wage bill) and capital (profits); and horizontal fairness concerns (HFC), where unions engage in inter-firm wage comparisons driven by envy/pride. The intensity of each concern reshapes the union’s utility function from simple rent extraction to a more complex objective that includes relative payoff comparisons.