A Valid Mathematical Relationship?

[For the following mathematical nomenclature/symbology, read italicized characters/character strings as subscripts. - Ed.]

Given:

Rn = Revenue in period n

Cn = Costs in period n

P = Maximum profit in period n

Ptheoretical = Rn (Cn = 0)

Is the following expression of a proposed mathematical relationship between types of profit valid?

               ?

Ptheoretical > Pfeasible > Psustainable

 

Ptheoretical is the theoretical maximum profit that could be obtained if there were no costs associated with the development, or collection of revenue. Thus revenue, R, would equal profit.

 

Pfeasible represents profit that can be obtained by cutting costs during period n to the absolute minimum in order to maintain operations. Pfeasible acknowledges that a minimum level of cost is unavoidable. Pfeasible is one means of matching analysts's expections (an intellectual fraud of which I shall have more to say at another time) for the current period, but may impose longer-term (beyond period n) impediments to continued profitability.

 

The question mark over the greater-than sign between Pfeasible and Psustainable represents the possibility that a cost structure that allows attainment of a feasible maximum profit may, in fact, be sustainable in the long run. That is to say, Pfeasible may, or may not, be greater than Psustainable. The Skeptical Entrepreneur is, frankly, skeptical that cutting direct costs sufficiently to achieve a short-term profitability metric would allow for continued top-line growth. iPhones, contrary to popular belief, do not actually sell themselves.

 

Your thoughts, as always, will help to inform The Skeptical Entrepreneur's understanding, and decision-making. Thank you!