Signal Analysis and Non-Standard Marginal Cost Curves

We were discussing cost curves in Managerial Economics. Aside from the standard mechanics of cost curves, a great question was asked about non-standard cost curves where examples weren't as simple as they tell us in the textbook.

Our prof used the example of Fed Ex, where the marginal cost for an additional package (assuming additional capacity) are very low, resulting in a flat Total Cost curve. However, once the capacity of individual planes were at maximum, Fed Ex had contracts with other carriers to deliver their packages (at higher marginal costs) resulting in a higher marginal cost (and steeper TC curve) for a portion of the curve.

Yet again, there is another inflection point when there is a certain degree of over capacity at which point Fed Ex decides that it shouldn't pay the exorbident service fees and would rather purchase another plane, resulting in additional capacity, lower marginal costs and flattening out the TC curve. The final cost curve looks like a step ladder, flat in areas where there is additional capacity but steep in areas where over capacity is such that it doesn't justify a new plane.

Note as well, fixed costs in this example also exhibit "step ladder" like characteristics (the purchase of the additional plane).

Besides being a good example of when a standard model doesn't entirely describe what is actually happening, I also thought it was a good example of using a type of signal anaysis methodology to describe what is happening. What do I mean?

Managing the capacity of planes has similar characteristics of frequency analysis of signals and systems. That is to say, the number of packages before maximum capacity is reached and partner carrier contracts are used (as well as the number of packages before a new plane should be purchased) represent a frequency function related to quantity. Assuming uniform capacity of planes (you are buying the same planes to carry your packages, let's say 1000 packages), you can actually predict what the shape of the curve.

Also, imagine that after buying an additional 20 planes, you need to also hire an additional management team to handle them. This would be an example of a low frequency component of the Total Cost "signal" (or more accurately, the marginal cost "signal"). Because planes can be expressed as capacity for 1000 packages, additional management teams can be anticipated at every 20,000 packages which would appear like an infrequently appearing (low frequency) marginal cost signal component.