The original hotelling model with linear and quadratic firms logistics costs

We introduce a modified Hotelling model setup that incorporates the original model and considers logistics' related costs incurred by the firms. Both the linear and quadratic logistics related costs cases are studied. We find that the relative magnitudes of firms' logistics costs to customers' transportation and/or search costs have significant effects on firms' decisions in terms of location choices. In the linear case, we show, under a large set of cost structures, that substantial differentiation exists and is stable. In the quadratic case, maximum differentiation is the only equilibrium for all cost structures in the model but firms' profits are higher than in the original case. We also consider the case where customers transportation costs are quadratic while firms logistics costs are linear.