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Equation 22 · The Economics of Codex: Tokens, Sandboxes, Review Time, and Software Throughput

What does this equation mean?

AC(N)=FN+c.AC(N)=\frac{F}{N}+c.

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Start withF
Divide byN
This relates toAC(N)
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

AA

Symbol A

A is part of the quantity the equation computes from the expression on the right.

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CC

Symbol C

C is part of the quantity the equation computes from the expression on the right.

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NN

Symbol N

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

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FF

Symbol F

F occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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cc

Symbol c

c is one of the signed contributions combined to compute the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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fraction

fraction

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

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addition

addition

Add the term after the plus sign to the term or group before it.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

If fixed deployment cost is F , variable cost per accepted task is c , and N accepted tasks use the platform, average cost is AC(N)=FN+cAC(N)=\frac{F}{N}+c. Large organizations can amortize F across more work, but they also face heterogeneity: more languages, repositories, regulatory zones, and legacy environments can make fixed cost rise with scope. A small team can achieve high local value precisely because it standardizes one stack and keeps governance informal. Neither scale advantage is universal.

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