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Equation 1 · Part 11 · How AI Inference Economics Actually Work

Denominator: U × T_max

price per token≳Cfixed+CenergyU⋅Tmax⁡+m\text{price per token} \gtrsim \frac{C_{\text{fixed}} + C_{\text{energy}}}{U \cdot T_{\max}} + m
U⋅Tmax⁡U \cdot T_{\max}

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

U × TmT_max occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

This is the reason batching and caching matter for price rather than only for latency: a serving system that keeps a GPU at 80% average utilization across a day divides its fixed hourly cost across roughly twice as many tokens as one running at 40%, and can profitably charge roughly half as much per token for the same margin. Independent benchmarking gives some visibility into what utilization current hardware and software combinations can actually achieve under realistic load. MLCommons’ MLPerf Inference benchmark suite tests submitted systems under both a latency-bounded “server” scenario and an unconstrained “offline” scenario designed to maximize throughput through batching, and recent…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.