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Equation 11 · Part 9 · Who Builds 2100? The Demographic Engine of Technological Evolution

Numerator: g_C + g_S

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

What this part means

The complete quantity above the fraction bar.

Its job in the formula

gCg_C + gSg_S occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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 fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

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