First, for linear demand, the optimal plan as given by Equation 9 is an average of an F.O.B. origin and a uniform delivered plans.
It is shown in Technical Appendix E that for the constant elasticity demand rate function, the best F.O.B. origin plan generates greater profit than the best uniform delivered plan, i.e., [[Phi].sub.F] [is greater than] [[Phi].sub.U].
We therefore examine: (1) whether the menu plan can generate a higher profit than the F.O.B. origin plan; and (2) the extent of suboptimality of the menu plan.
Since demand never declines to zero, all the three plans under consideration (F.O.B. origin, menu, optimal) serve all locations.
The best F.O.B. origin plan and the best menu plan could not be determined in closed form.
However, it is also clear that unless spatial dispersion is high, the gain obtained from using a menu plan instead of an F.O.B. origin plan alone is quite small.
As shown in Figure 3, [P.sup.*] (x) in the present case is a linear function of x with slope greater than 1, while the price for an F.O.B. origin plan has a slope of 1.
Retailers typically use either a uniform delivered plan or an F.O.B. origin plan, and customers can either accept the plan offered or not patronize the store at all.
Thus, to generate demand from the high cost segment, the optimal pricing plan charges the customer a base price plus half the cost of transportation, i.e., the optimal price schedule falls at the mid-point between the F.O.B. origin plan and the uniform delivered plan.
Thus, the optimal plan converges to the F.O.B. origin plan as price sensitivity increases.
When demand is a linear function of price, a retailer can increase profit substantially by offering the customer a choice between a uniform delivered and an F.O.B. origin plans rather than using only one of these plans.
In fact, in a menu plan, customers, by choosing between a uniform delivered and an F.O.B. origin plans, reveal their true cost of transportation.