"Will That be Pickup or Delivery?": An Alternative Spatial Pricing Strategy

Abstract

This article demonstrates that when consumers are offered a choice between pickup and delivery, afirm can increase profits relative to the case when no choice is tendered, as in the mill or uniform spatial pricing models. Further, this choice yields a lower level of welfare than that obtained under mill pricing. These results hold in models where market size is endogenous as well as exogenous to the firm's decisions, and with tastes and technology that are fairly standard in the spatial literature. ? Three spatial pricing strategies are preeminent in the literature: mill pricing, uniform pricing, and discriminatory pricing (Beckmann, 1968). At bottom, the distinction among these strategies arises from the assumption of which agent pays for transportation services. This note presents the implications of an alternative and?as casual observation suggests? widely employed spatial pricing strategy in which the firm allows consumers a choice between pickup and delivery (i.e., between a mill price and a uniform price). This practice is prevalent in the take-out food industry such as pizza, where discounts are often given on pickup orders. However, the problem appears applicable in the broader context where a commodity can be sold f.o.b. or c.i.f. Several assumptions?fairly common in the spatial literature?are invoked: (1) there is a linear market in which consumers are spatially distributed at constant unit density; (2) each consumer has an identical demand for some commodity: q = a ? bPF, where PF is the full price paid by a consumer and may include transportation costs; (3) a firm is located at the extreme of the market; (4) production occurs with constant marginal cost,1 c; and (5) tr is the transportation cost per unit of output, where / is the transport rate and r is the distance between the firm and consumer. Under any pricing regime the firm chooses its profit-maximizing price Pi9 where i = M9 U, D for mill, uniform, and discriminatory pricing, respectively. The firm which adopts pickup or delivery (hereafter PD) pricing simultaneously chooses a pickup price Px and a delivery price P2 to maximize profits. Further, the market length under any regime may be alternatively modeled as an additional choice variable available to the firm or assumed exogenously determined.2