Cournot-Bertrand equilibria under two-part tariff contract

We consider a vertically related market where one quantity setting and another price setting downstream firm negotiate the terms of a two-part tariff contract with an upstream input supplier. In contrast to the traditional belief, we show that when bargaining is decentralised, the price setting firm produces a higher output and earns a higher profit than the quantity setting firm. And, when bargaining is centralised, both firms produce the same output whereas the profit is higher under the price setting firm than the quantity setting firm.