Computing the margin contribution percent relationship in price setting and the golden ratio in profits structures

Abstract

This work aims to find a formal way to show the margin contribution percent that should be used to set the offer price of a certain product. In order to do this, a function that depends on the margin contribution percent and on the sales profit was constructed, and by algebraic manipulation it was possible to generate a non-dimensional relation between the variables. When the aforementioned function was optimized the result obtained was that the margin contribution is a function of the square root of sales profits.

Likewise, once this result is substituted in the sales expression, it turns out that the sales have a minimum for which profit is 25%, margin contribution percent is 50%, total variable cost equals the equilibrium sales, operative leverage equals the total variable and fixed costs, etc. Also, a more stable fixed point was found, where the equilibrium between profits and sales is the inverse of the squared golden ratio: 0.381966011...As a consequence, and based on results obtained, the author considers that price setting cannot be a subjective process but a mathematically objective and harmonic one.