Abstract
We extend Hotelling’s model of spatial competition by adding an outside good, provided by a webshop. Unlike the commonly used reservation price, the price of the webshop is endogenous. We establish that a Nash equilibrium exists if the outside good is not too different from the goods sold by the bricks-and-mortar shops. Equilibrium prices positively depend on transport costs, which would not be the case for an exogenous reservation price. If the webshop serves an alternative market as well, the price of that market is partly imported into the local market. The bricks-and-mortar shops compete only with the the webshop. The lower the webshop’s delivery costs are relative to the transport cost parameter, the wider the feasible range for locations of the bricks-and-mortar shops.
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Notes
This is clearly different from delivered pricing in the Hotelling model, where the firm bears the transport costs that depend on the customer’s location.
In the context of product space, we can also think of the webshop as an outside good, where \(\theta \) represents the utility loss of buying the imperfect substitute rather than the good the consumer was looking to buy.
It is fairly straightforward to show that this theorem also holds in our model. The solution found by Hinloopen and van Marrewijk (1999) for ‘intermediate’ values of the reservation price does not apply here, as it requires a zero market share for the webshop.
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Lijesen, M. Hotelling’s webshop. J Econ 109, 193–200 (2013). https://doi.org/10.1007/s00712-012-0303-7
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DOI: https://doi.org/10.1007/s00712-012-0303-7