The demand’s function neperian.

THE DEMAND’s FUNCTION NEPERIAN.

Author: Raul Castañeta.

In the latter of the 1880s, a celebrated English economist said very truly "… our science must be mathematical, simply so that itoperates with quantities…"
And following these words, those who we are economists that we cannot change the nature of the Economic Laws; however, we must generalize them most possible with purpose ofdeveloping instruments to get the requirements not only the Theory but economic practice as well. That is my reason (and also my result), friendly reader, by means of who I display the followingFunction of Demand that I consider fulfills the applicability requirements, pertinence and future value considering the Economic Theory:
Where:

And also:
q = Demanded quantity.
p= Price Variable.
λ = Elasticity parameter concerning ‘q’.
a = Parametric Constant.
e = Numerical Constant (with value 2,718281828459…) natural
Logarithm base.
ln = Naturallogarithm operator.

Notice that such neperian function represents the General Solve of a certain equation differential (procedure and demonstration that it does not contained here because it isa narrow article) the same one that simultaneously is a behavior equation that has the following characteristics:
1. There are no negatives quantities (and also it happens in our real world) for pand q (and it does not happen with a linear function of type q = a - bp)
2. Within a neperian function the different prices are asymptotic to their respective axes. Beside it also:3. That function has its property to get a better fit (than a linear relation) to a certain population of dispersed data for a relation of demand q versus pdue to parameters λ and a.

So, That previous equation takes a new function of demand, which is more natural that a linear one, and that therefore it influences over some foundations of the...