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Project Description
Quick model overview
The aim of the application is to model the results of the article The Importance of Consumer Multihoming (Joint Purchases) for Market Performance: Mergers and Entry in Media Markets. Therefore, the article focuses on the study of consumer multihoming. Consumer multihoming models a situation in which a consumer buys an equivalent good from two different companies, for example by subscribing to both a Netflix subscription and a Disney+ subscription. The model is based on Salop's model, which is itself an extension of Hotelling's model, representing a beach on which two ice cream vendors are present, and consumers are distributed all along this beach. Hotelling therefore asks the question of where the two vendors will position themselves, knowing that consumers incur a transportation cost to get to a merchant and therefore they will prefer the closest merchant. Salop seeks to overcome the main weakness of this model, namely the edge effects due to the fact that the model is based on a segment. Salop will therefore implement a new model based, not on a segment, but on a circle, with consumers distributed all around it. Here is the circular city model, which will serve as the basis for this homing model.
The differentiation of consumer preferences is modeled by the parameter $\theta$
, the lower it is, the stronger consumers will have a preference for a good, and therefore will be single homes. Conversely, a high $\theta$ will make consumers less dependent on one of the two goods, so they will be multihomers.
Application overview
The application allows a user to get the distribution of consumers in each group (singlehomer and multihomer) based on a $\theta$
and a price specified by the user. The panel studied is restricted to a market configuration in which there are only 3 companies, the number of consumers displayed in each group only represents the demand for company 1. That is, if the application shows you that there are 5 multihomers and 4 singlehomers, it is only about consumers who are singlehomers of company 1 (they only consume at its place) or multihomers of company 1 (they consume at least the good of company 1). On the circle, the model is represented, the three companies are symmetrically distributed around it, as well as consumers who are indifferent between singlehomer and multihomer. These consumers represent a limit beyond which consumers will switch from one class to another (multihomer becomes singlehomer or vice versa). The positions of these indifferent consumers are likely to be modified by price parameters or $\theta$.
Project progress
Currently, the application accurately represents the location of firms and consumers who are indifferent between singlehomer and multihomer. It also displays the number of singlehomer and multihomer consumers for company 1. The implementation of constraints so that the positions of indifferent consumers respect the problems of the model is currently under study. A first version is currently applied to the application but it is buggy. This is the main goal to achieve to allow a potential further improvement, since as you will see, the number of singlehomers and multihomers suffers from it.
Once this problem is resolved, it could be interesting to allow the user to modify the prices of other companies, allow to add a company to the market or carry out a merger.