Theory of Intelligence
11TH•Mathematics•Theory Of Quadratic Functions•Exercise 3.2

1. The Revenue Invariant

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1. The Revenue Invariant

Let:

  • R=total revenue realizedR = \text{total revenue realized}
  • x=volume of merchandise sold (in standard units / dozens)x = \text{volume of merchandise sold (in standard units / dozens)}
  • p=selling rate per unit (in Rs. per unit)p = \text{selling rate per unit (in Rs. per unit)}

The fundamental economic identity states: R=x⋅p  ⟹  p(x)=RxR = x \cdot p \implies p(x) = \frac{R}{x}

If the merchant had available an additional volume Δx\Delta x sold at a discounted rate (p−Δp)(p - \Delta p) that preserves the identical total revenue: R=(x+Δx)(p−Δp)R = (x + \Delta x)(p - \Delta p)

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