Price and Quantity Contracts in a Mixed Duopoly with a Socially Concerned Firm

I study the endogenous choice of a price or quantity contract in a mixed duopoly with a socially concerned firm which maximizes a combination of profit and consumer welfare. Contrasting the literature, I find that equilibria where firms adopt price contracts and quantity contracts might coexist. Welfare under price competition might be lower than under quantity competition. Finally, the profit ranking of the firms might be different from that of a private duopoly or a mixed duopoly with a public firm