A Hotelling Duopoly Model That Views Transportation Cost As an Inverse Predictor of Sales Volume

We introduce and investigate a Hotelling duopoly model where the price of undifferentiated products is fixed and transportation cost is viewed as an inverse predictor of sales volume. In this model, vendors can increase sales by establishing equilibrium locations away from the center of the street. Assuming linear costs, an equilibrium occurs at locations 1/3 and 2/3, providing each vendor with an additional 44% in sales. For a street 50% longer than Main Street, where initial demand equals zero near the ends, the equilibrium locations are 0.28 and 0.72 for an 86% increase in sales. For a street half the length of Main Street, where demand never falls to zero, an equilibrium occurs at locations 0.31 and 0.69 for a 16% increase in sales. Assuming sub-linear transportation costs, vendors can increase Main Street sales by 36%, and with super-linear costs, they can achieve an increase of 73%. In general, the greater the penalty for distance from a vendor, the more vendors have to gain by spreading out.We close by presenting equilibria for three and also for four Main Street vendors.