Non-Linear Demand in a Linear Town

In Hotelling’s linear town model characteristics are implicitly assumed to be related in such a way that preferences for them can be mapped into a one-dimensional town. This results in perfectly correlated willingness to pay levels. Many differentiated products, however, embody characteristics that are functionally at least somewhat unrelated to other characteristics. This paper makes the implicit assumption of perfectly correlated preferences in the original Hotelling model explicit, and examine the implications of this assumption for the economics of competition. We develop a simple theoretical model to show that shape of the demand curve for differentiated products depends on distribution of consumers’ preferences, which is determined by the nature of the relationship between the corresponding characteristics. Misrepresentation of correlated preferences in differentiated product models impacts demand elasticity and can result in unreliable outcomes. This issue is particularly important in agricultural and food markets where many factors such as expectations about weather and information on social media can impact consumer ranking of one product versus another in ways that are not fully observable or measurable by the researcher.