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Equation 7 · Part 1 · The Real Economics of Shipping a Model to a Device

Symbol Q^*_distill

Qdistill∗=Cdistillcteacher−cstudent.Q^{*}_{\mathrm{distill}} = \frac{C_{\mathrm{distill}}}{c_{\mathrm{teacher}} - c_{\mathrm{student}}}.
Qdistill∗Q^{*}_{\mathrm{distill}}

What this part means

the break-even query volume.

Its job in the formula

Qd∗Q^*_distill is part of the quantity the equation computes from the expression on the right.

Where the article explains it

The break-even query volume is

The passage around this formula

…consistent with how frontier and compact API tiers are typically priced relative to each other, that a teacher-class model costs $0.002 per query to serve and a well-distilled student costs $0.0002 — a tenfold gap. Then Qdistill∗Q^{*}_{\mathrm{distill}} = 600 / 0.0018 ≈\approx 333{,}000 queries. Any production feature serving that many requests clears the investment in days, sometimes hours. This is the arithmetic reason distillation has become the default route to a deployable small model rather than a research curiosity:…

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