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Equation 11 · Part 4 · Who Builds 2100? The Demographic Engine of Technological Evolution

Symbol phi

gA=gC+gS1−ϕg_A = \frac{g_C + g_S}{1-\phi}
ϕ\phi

What this part means

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

Its job in the formula

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

The passage around this formula

The named argument belongs to Philippe Aghion, Benjamin F. Jones, and Charles I. Jones, whose 2017 National Bureau of Economic Research paper works out formally what happens when artificial intelligence automates tasks inside the idea-production function itself, rather than only inside the production of ordinary goods. Their result, worked through with an idea-production function in which a fraction of research tasks can be automated, is that in the case without automation their model collapses to exactly the semi-endogenous relation from Section 3 above — the growth rate of ideas proportional to the growth rate of the human research population, discounted by diminishing returns — matching…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.