$$u^{*} = \frac{P_r}{Q_{\max}\, c_{\mathrm{od}}}$$

Equation 17 · Inference Economics

AI Inference Economics in Practice: An Advanced Technical Guide

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The arithmetic is simple once both prices are in hand, and generalizes across any reserved-capacity product structured this way. Let $P_r$ be the reserved capacity’s price per hour, $Q_{\max}$ the maximum throughput it sustains per hour at full utilization, and $c_{\mathrm{od}}$ the effective on-demand cost of the equivalent work. At actual utilization u , the effective cost per unit under reservation is $P_r$ / (u \, $Q_{\max}$) , and reservation wins exactly when $u^{*} = \frac{P_r}{Q_{\max}\, c_{\mathrm{od}}}$. is cleared. Utilization above $u^*$ favours reservation; below it favours paying as you go. The formula’s value is what it forces a team to measure honestly before signing: not peak throughput or a favourable week’s…

Meanings in this article

• $P_r$: the reserved capacity’s price per hour.
• $Q_{\max}$: the maximum throughput it sustains per hour at full utilization.
• $c_{\mathrm{od}}$: the effective on-demand cost of the equivalent work.

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