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Equation 1 · Part 3 · How AI Inference Economics Actually Work

Symbol U

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

What this part means

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

Its job in the formula

U 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

…formula]. Here CfixedC_{\text{fixed}} is the amortized hardware and facility cost per unit time, CenergyC_{\text{energy}} the energy cost per unit time, Tmax⁡T_{\max} the chip’s maximum achievable token throughput under ideal batching, U ∈\in (0,1] the realized utilization fraction, and m a margin term. This is not a model any provider discloses or that this article claims to have measured; it is a bookkeeping identity stated to make one point precisely: U appears in the denominator, so it multiplies with, rather than merely adds…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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