Equation 10 · Part 4 · Comparing Frontier Model Pricing Without Comparing Apples to Oranges

Symbol p^in_i

C_i \;=\; \kappa_i\Big[(1-h_i)\,p^{\text{in}}_i + h_i\, p^{\text{in}}_i\,\gamma_i\Big] \;+\; \rho_i\, p^{\text{out}}_i .

p^{\text{in}}_i

What this part means

the reading.

Its job in the formula

$p^i$ $n_i$ is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol p^in_iArticle meaning

Where the article explains it

Reading $p^{\text{in}}_i$ and $p^{\text{out}}_i$ off a rate card and comparing them directly across vendors is equivalent to assuming $\kappa_i$ , $\gamma_i$ , and $\rho_i$ are all equal to each other and to 1 across every vendor in the comparison.

The passage around this formula

Collecting every distinction above into one expression makes explicit what a bare price comparison assumes without saying so. For vendor i , let $p^{\text{in}}_i$ and $p^{\text{out}}_i$ be the published input and output rates; let $\kappa_i$ be a tokenizer expansion factor, the number of tokens vendor i ’s own tokenizer needs to encode one fixed reference passage, normalised so $\kappa_i$ = 1 for whichever vendor is used as the baseline; let $h_i$ be…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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