As none of the plans under consideration (F.O.B. origin, uniform delivered, and menu) requires extensive monitoring of the costs of shipment to customers, the costs of implementing these three plans should be minimal.
To illustrate pricing plans, we now briefly discuss the F.O.B. origin and the uniform delivered plans.
The F.O.B. origin plan charges the customer a base price (i.e., the price of the product) plus x.
In an F.O.B. origin plan, on the other hand, the unit contribution margin is the same, ([P.sub.f] - c), at all levels of delivery cost.
Consider the menu plan which lets the customer choose between an F.O.B. origin plan with delivered price ([P.sub.f] + x) and a uniform delivered plan with delivered price [P.sub.u].
We call this a true menu plan because both the F.O.B. origin and the uniform delivered plans are preferred by some customers (Figure 1a).
In this case, no customer will prefer the uniform delivered plan, and the menu plan effectively degenerates into an F.O.B. origin plan (Figure 1b).
Thus, customers with x [is less than or equal to] R will select the uniform delivered plan, while only the F.O.B. origin plan will be available to the customers with x [is greater than] R.
Therefore, the best menu plan is a true menu plan which divides the market it serves into two equally wide cost segments and serves the lower cost segment (x [is less than] [R.sup.*]/2) with an F.O.B. origin plan and the higher cost segment ([R.sup.*]/2 [is less than or equal to] x [is less than or equal to] [R.sup.*]) with a uniform delivered plan.
However, the plot of the best menu plan is a line with slope 1 (the F.O.B. origin plan is selected) over the lower half of the market served (0 [is less than or equal to] x [is less than] [R.sup.*]/2) and is a line with slope zero (the uniform delivered plan is selected) over the upper half ([R.sup.*]/2 [is less than or equal to] x [is less than or equal to] [R.sup.*]).
Comparison With The Best Uniform Delivered & F.O.B. Origin Plans
For the linear demand function, Beckmann and Ingene (1976) have shown that the best F.O.B. origin plan and the best uniform delivered plan generate the same profit, i.e., [[Pi].sub.U] = [[Pi].sub.F].
Thus, if customers are not dispersed widely, the menu plan continues to perform better than the uniform delivered (and hence the F.O.B. origin) plan, but the margin of superiority is small.