Expected present worth of cost effect of using up an additional unit of spare capacity

Provision of equipment in the telecommunications industry for satisfying demand may be lumpy because it is uneconomical to provide equipment one unit at a time. For example, it is impractical to add one wire pair each time another customer requires telephone service. Wire pairs are therefore bundled in cables. The result of satisfying demand this way is spare capacity. When decisions have to be made regarding alternate courses of action using the methods of engineering economics the effect of using up spare capacity has to be calculated. This paper shows that under certain assumptions the expected incremental present worth of cost due to satisfying the incremental demand for one unit is exactly equal to the average cost per unit in a block used to satisfy demand. While the result has been shown for specific demand functions, this paper proves the result for any nondecreasing demand function.