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Equation 1 · Part 8 · The Unit Economics of a Token

Symbol p_out

c=pinn+pcww+pcrr+pout(y+z)c = p_{\mathrm{in}} n + p_{\mathrm{cw}} w + p_{\mathrm{cr}} r + p_{\mathrm{out}} \left( y + z \right)
poutp_{\mathrm{out}}

What this part means

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

Its job in the formula

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

The passage around this formula

Instrument each request to record five quantities: new input tokens, cache-write tokens, cache-read tokens, visible output tokens, and reasoning tokens. The cost of a single request is then c=pinn+pcww+pcrr+pout(y+z)c = p_{\mathrm{in}} n + p_{\mathrm{cw}} w + p_{\mathrm{cr}} r + p_{\mathrm{out}} \left( y + z \right). where n , w , r , y and z are the five counts in that order and each p is the corresponding published rate. The important feature is the last term: visible output and reasoning share one price, and the reasoning count is the only one of the five you cannot recover by inspecting what came back.

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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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