Interesting, what assumptions would you say are being made with this model? E.g., Why should price be modeled as the log of the rank?
The relative importance of a product or asset in a market is not directly related to its position in the market. The relative importance of a product is determined by the fact that the most expensive product ranks first, and the second most expensive product ranks second. Using such a model, it can often be analyzed that the higher the price of a product item, the more important it is, and the lower its importance.