Multi-purchasing in the linear city

This paper allows for the purchase of both goods in the Hotelling model with linear transport costs. Price competition disappears as a result, and we have a stable linear model with the Principle of Minimum Differentiation intact. Stability is dependent on equal marginal costs for the two producers.

The new model lends itself well to bundling. Treating the multi-purchase Hotelling framework under a monopoly, we find that mixed bundling leads to an intermediate level of differentiation with at least half the line between the two goods. Variety is thus greater under a monopoly than under the ordinary duopoly.

Media markets, popularly modelled using two-sided markets, are an example of when purchases of multiple brands are common. This paper fills a gap in the literature on multi-homing in two-sided markets.