Differentiated products are the central economic focus of competition in consumer goods products such as cereal, soda, and beer. We first estimate demand models which do not restrict unduly the pattern of consumer preferences as does much previous research in the area of differenciated products. Using recently available transactions data we estimate own and cross price elasticities in a relatively unrestricted manner. We next turn to competitive analysis using our estimated demand system. We consider two applications in this paper. The main economic factor that we consider is that the firms which produce the differentiated products almost always tend to be multi-product firms in the given industry. Our first application is competitive analysis when two firms are allowed to merge. The other application that we consider is inference on the competitive structure in an industry. In both applications we consider the effect of a multi-product firm where its competitive decisions for one brand affects it sales and prices for other brands that it produces.