In an imperfectly competitive industry, differentiated products compete with each other with price rather than quantity as the strategic variable. Several previous studies have employed a generalized Nash-Bertrand model: Liang (1989), Cotterill (1994), Cotterill et al. (2000), and Kinoshita et al. (2002); however, only Liang has explored the theoretical foundations of that model. This article generalizes the Liang two-good model to three goods. A surprising and important result follows. Price-conjectural variations do not exist in models with three or more goods. Price-reaction functions, however, exist in multiple-good models. We estimate them jointly with a brand-level demand system to evaluate the total impact of a brand manager's price change on own quantity. In a differentiated product market, this is a useful addition to a partial demand elasticity approach, because a change in one brand's price typically engenders a price reaction by other brands that affects own quantity via substantial cross-price elasticities among substitutes. Strategic pricing in the Boston fluid milk market was also influenced by the existence of a raw milk price support program, the Northeast Dairy Compact. We find that the advent of the Compact was a focal point event that crystallized a shift away from Nash-Bertrand to more cooperative pricing. If the downstream market is not competitive, one needs to consider strategic price reactions when designing and evaluating agricultural price programs.