We examine how the confluence of competition and upstream innovation influences downstream firms' profit-maximizing strategies. In particular, we analyze how, in light of these forces, the downstream firm sets the price of the product over its life cycle. We focus on personal computers (PCs) and introduce two novel data sets that describe prices and sales in the industry. Our main result is that a vintage-capital model that combines a competitive market structure with a rapid rate of innovation is well able to explain the observed paths of prices, as well as sales and consumer income, over a typical PC's product cycle. The analysis implies that rapid price declines are not caused by upstream innovation alone, but rather by the combination of upstream innovation and a competitive environment.