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

1. The Fundamental Expenditure Relation

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1. The Fundamental Expenditure Relation

Let:

  • C=total constant budget / expenditureC = \text{total constant budget / expenditure}
  • x=number of items purchased(x∈R+,  x>0)x = \text{number of items purchased} \quad (x \in \mathbb{R}^+, \; x > 0)

The uniform unit price (rate per item) r(x)r(x) is defined by: r(x)=Cxr(x) = \frac{C}{x}

Because ddxr(x)=−Cx2<0\dfrac{d}{dx} r(x) = -\dfrac{C}{x^2} < 0, the rate is a strictly decreasing function of quantity xx.

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