Symbol p_i^H
is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Why this formula appears here
The pricing structure has a feature worth building a mental model around before it costs you money in production: it is not a marginal rate that blends smoothly as a request grows, it is a cliff. Every model’s documented price list carries two tiers — one for requests under 200,000 tokens, and a materially higher one, roughly double across the board, once a request reaches that threshold — and the higher rate applies to the entire request, not just the tokens past the line [ 1 ] . Written as a cost function of input tokens and output tokens against a threshold T = 200{,}000 , with low-tier prices , and high-tier prices , :
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Symbol p_o^H
is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Read this expression with the definitions, units, and assumptions supplied by the article.
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Equation 5 · AI Industry
Actually Building with the Grok API
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
The pricing structure has a feature worth building a mental model around before it costs you money in production: it is not a marginal rate that blends smoothly as a request grows, it is a cliff. Every model’s documented price list carries two tiers — one for requests under 200,000 tokens, and a materially higher one, roughly double across the board, once a request reaches that threshold — and the higher rate applies to the entire request, not just the tokens past the line [ 1 ] . Written as a cost function of input tokens and output tokens against a threshold T = 200{,}000 , with low-tier prices , and high-tier prices , :
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