Price vs. quantity competition in a vertically related market revisited

In a recent paper, Alipranti et al. (2014) show that, in a vertically related market, Cournot competition yields higher social welfare than Bertrand competition if the upstream firm subsidises the downstream firm’s production via negative wholesale input prices. However, the assumption of a negative input price is not economically viable as it encourages the downstream firms to buy an unbounded amount of inputs. We show that the welfare ranking is reversed once we introduce a non-negativity constraint on the input prices.