Copies and originals in a horizontally and vertically differentiated market with habit and quality differences

This paper models the interaction of copies and originals (e.g. MP3s and CDs, generally called flavors) in a dynamic, horizontally (stylistic variety) and vertically (distribution technology) differentiated market. The Johnson (1985) household copying model is at the root of this model. Quality differences were added because they appeared to play an important role in the market for music, but previous economic research has ignored them. Habit was added to allow for current consumption to affect later consumption. The paper argues extensively for these additions. The model is generalized to one, two and N flavors, its properties are carefully studied, and various examples are presented. The model is then used to find whether deceasing costs of obtaining MP3s can have a long run positive influence on the demand for CDs. If that were the case, CDs and MP3s would be substitutes in the short run and complements in the long run. The paper shows that this can happen, provided that the habit effect is very strong. For the quadratic utility version of the model, explicit bounds on the habit effect are found. The paper then exploits a symmetry between demand and supply in the model to explore optimal pricing of CDs, and best responses to decreasing costs of copying. Lastly, the paper models the introduction of a third flavor, a legitimate alternative to copying, such as Apple's iTunes Music Store.