We consider a linear city model where both firms and consumers have to incur transport
costs. Following a standard Hotelling (1929) type framework we analyze a duopoly
where firms facing a continuum of consumers choose locations and prices, with the
transportation rate being linear in distance. From a theoretical point of view such
a model is interesting since mill pricing and uniform delivery pricing arise as special
cases. Given the complex nature of the profit function for the two-stage transport
cost sharing game, we invoke simplifying assumptions and solve for two different
games. We provide a complete characterization for the equilibrium of the location
game between the duopolists by removing the price choice from the strategy space.
We then find that if the two firms are constrained to locate at the same spot, the
resulting price competition leads to a mixed strategy equilibrium with discriminatory
rationing. In equilibrium both firms always have positive expected profits. Finally,
we derive a pure strategy equilibrium for the two-stage game. Results are then compared
with the mill pricing and uniform delivery pricing models.