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Equation 1 · Part 6 · How AI Inference Economics Actually Work

fraction

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

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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.