Aporte Teórico

¡Que estafa!

La matemática no estafa pero sus aplicaciones en manos de ciertos personajes puede que sí.

Pensemos por un momento que lo que a continuación relatamos ocurriera en el lugar que cada uno de los lectores habita. A esta altura debo rectificarme y decir que tal vez haya ocurrido o esté ocurriendo.

Veamos, entonces.

En una ciudad, el comercio La Perla, que se dedica a la venta de adornos sacros, pone el siguiente aviso:

"El Cristo tallado en madera que está en vidriera cuesta $ 500  pero usted puede adquirirlo pagando tan solo $ 100 de contado".

Es de suponer que quienes leen el cartel se entusiasman y le trasmiten la oferta a otras personas e inmediatamente el local comienza a recibir algunos compradores.

Cuando el comprador llega con sus $ 100 se le informa que por el momento no recibirá el Cristo tallado sino tan sólo 4 billetes, promocionando la oferta y que tendrá que vender a $ 100  cada uno de ellos, entre personas de su conocimiento. Cuando venda esos billetes entregará en La Perla los $ 400 y se hará acreedor del Cristo tallado que tanto le gustó. Con esto el aviso se hace realidad porque ese comprador adquirió el Cristo tallado invirtiendo de sí, solamente,
$ 100 y el resto fue simplemente un poco de su trabajo personal.

A su vez, cada uno de los tenedores de billetes adquiridos a los compradores que mencionamos anteriormente, con la entrega de ese billete en La Perla  reciben cinco billetes para difundir la oferta y cuando se hacen del dinero vienen a retirar el Cristo tallado, y así sucesivamente.

De modo que la oferta se cumple y nadie gasta más de los $ 100 por un Cristo tallado cuyo valor real es de $ 500.

Todo parece absolutamente legal, sin embargo la estafa está en camino. Analicemos.

El primer comprador es A, quien pagó tan sólo $ 100 y recibió su Cristo tallado, de éste salieron cuatro compradores que también, pagaron $ 100 y cad uno recibió su Cristo tallado.

Por lo tanto la sucesión de tenedores de billetes podrá ser la siguiente:

1, 4, 20, 100, que suman un total de 125 personas de las cuales reciben su Cristo tallado apenas 25 porque los últimos 100 aún no vendieron sus billetes. Esos 25 representan tan sólo 1/5 del total de compradores de billetes en circulación.

Si seguimos con la sucesión tal vez nos sorprendamos porque si la circulación de la promoción se da para los siguientes compradores de billetes:

1,4,20,100,500,2500,12500,62500 estaríamos hablando de una población de 78125 habitantes capaces de gastar $100 cada uno. Observemos que, si exceptuamos a niños sin poder adquisitivo propio, no son muchas las ciudades con esa población, por lo tanto los últimos 62500 consideramos que no tendrán a quien venderle los billetes y por consiguiente, sobre un total de 78125 compradores de billetes de $100 que hacen una recaudación de $ 7812500 tan sólo 1/5 de ellos, o sea 15625 recibirán el famoso Cristo tallado cuyo valor real es de $ 500 con lo cual La Perla recaudará sus $ 7812500 sin necesidad de personal de venta para llevar a cabo la misma.

Esta metodología, basada en las progresiones geométricas, puede diferir en montos y en cantidad de billetes por persona, pero el crecimiento de la demanda por la tentación misma la hace muy real.

Tomemos en cuenta que la progresión geométrica aumenta rápidamente con lo cual podría llegar fácilmente a cubrir toda la población de un Pais dejando a 4/5 de ellos sin el ansiado Cristo tallado.

Una aplicación social de esto fue, en la década del 60, en la República Argentina la cadena de cartas con billetes de $2 que con la promesa de bienestar todos aportaban para  los primeros de la cadena y sólo se hicieron de esos dividendos 1/5 de la población participante.

La historia le dio nombres a esta "matemática aplicada" y trascendió cómo la "avalancha" o "la bola de nieve".

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