Using Lorenz curves to represent firm heterogeneity in Cournot games

We derive several comparative-static results for Cournot games when firms have nonconstant marginal-cost curves which shift exogenously. The results permit us to rank certain vectors of equilibrium marginal costs with the same component sum according to their associated social surplus or industry profit. We arrange the components of each vector in ascending order and then construct from the resulting ordered vector its associated Lorenz curve. We show that if two Lorenz curves do not cross, the one reflecting greater inequality is associated with higher social surplus and industry profit. A duality result permits a corresponding ranking of equilibrium output vectors. The same partial ordering is used in the literature on income inequality to rank certain distributions of income and in the literature on decision-making under uncertainty to compare the riskiness of certain probability distributions with the same mean.