Equation 11 · Part 10 · Who Builds 2100? The Demographic Engine of Technological Evolution
Denominator: 1-phi
What this part means
The complete quantity below the fraction bar; it must be nonzero for this division.
Its job in the formula
1-phi occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Full expression→Denominator: 1-phi→Article meaning
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…
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.