Non-Linear Demand in a Linear Town
-
Mohammad Torshizi
,
Murray E. Fulton
Abstract
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.
Acknowledgements
The authors would like to thank Professor Vic Adamowicz and Professor James Rude for their valuable comments on this paper.
Appendix
In what follows we show that even when the two distributions are uniform but have different ranges (i. e. non-identical), the independence of preferences still results in a more elastic demand. Assume preferences for goods 1 and 2 are uniformly distributed over different ranges as follows:
Figure 6 illustrates the distribution of preferences for the two cases of independent and perfectly negatively correlated characteristics.
Allocation of consumers to two products with unrelated and related characteristics.
Figure 7 illustrates the corresponding CDFs.
CDFs of buying product 1.
Figure 8 illustrates the corresponding demand curves.
Demand for product 1.
Expected demand curve with unrelated characteristics can be found from Panel a of Figure 6. Given the uniform density of the preference box,
The length of the flat portion of the demand curve, where
The equation for the demand curve with correlated preferences presented in Panel b of Figure 8 can be easily found as follows:
The slope of the demand curve in Equation 13, which represents perfectly negatively correlated preferences, is as follows:
Comparison of Equations 12 and 14 reveals that for any
As illustrated in the above figures, even when the preference distributions for the two products are both uniform but have different ranges, a great portion of the demand curve, which corresponds to the centre of the preferences box, is still more elastic with independent preferences than with perfectly negatively correlated preferences. Therefore, although the demand curve does not have a single high-elasticity point, as long as equilibrium price is within the more elastic portion of the demand curve, markups are lower for independent preferences than for negatively correlated. However, the difference between markups with independent and perfectly negatively correlated preferences may not be as great as the case presented in Figure 5.
As pointed out by a reviewer, when all consumers have a constant WTP level for one of the two products (i. e. independent preferences) demand curve becomes linear. This is a special case where demand curve is linear although preferences are independent. Nevertheless, this demand curve is more elastic than other cases discussed in this paper where there are variations in consumers’ WTP for that product.
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Articles in the same Issue
- Articles
- Non-Linear Demand in a Linear Town
- Illegitimate or Legitimate Non-Tariff Measures
- The Trade Impacts of a Food Scare: The Fonterra Contamination Incident
- The Contribution of Marketing and Branding Efforts in Food Exports: Evidence from Panel Data
- Aflatoxins and Health Considerations in Consumer Food Choices in Ghana
- Linear and Nonlinear Causality between Corn Cash and Futures Prices
Articles in the same Issue
- Articles
- Non-Linear Demand in a Linear Town
- Illegitimate or Legitimate Non-Tariff Measures
- The Trade Impacts of a Food Scare: The Fonterra Contamination Incident
- The Contribution of Marketing and Branding Efforts in Food Exports: Evidence from Panel Data
- Aflatoxins and Health Considerations in Consumer Food Choices in Ghana
- Linear and Nonlinear Causality between Corn Cash and Futures Prices
