To examine the interaction between buyer power and competition intensity in a downstream market, we consider four variations of a model in which oligopolistic retailers compete in the downstream market and one of them is a large retailer that has its own exclusive supplier. We demonstrate that an increase in the buyer power of the large retailer against its supplier leads to a fall in retail price and an improvement in consumer welfare, and this is true even in the extreme case where the large retailer is a monopoly in the downstream market. More interestingly, we find that the beneficial effects of an increase in buyer power are large when the intensity of downstream competition is low, with the effects being the largest in the case of downstream monopoly.