I was reading this paper on non-stable and stable population momentum. There the authors have shown the formula for stable population $Q$ as:

$$Q=\dfrac{\int_0^\beta n(x)v(x)dx}{bA_r},$$

$v(x)$ is Fisher’s reproductive value function, $b$ and $A_r$ are, respectively, the birth rate and the mean age of childbearing in the stable equivalent population, $n(x)dx$ is the number of females between exact ages $x$ and $x + dx$.

As far I have worked out the quantity, $\int_0^\beta n(x)v(x)dx$ seems to me like "average expected number of daughters remaining to be born by initial cohort of women aged $0$ to $\beta$". In that case $\dfrac{\int_0^\beta n(x)v(x)dx}{b}$ should be the size of the initial cohort of women aged $0$ to $\beta$. Then how does $Q$ be the size of the stable population by dividing the quantity by $A_r$? I could be wrong in my interpretation.

Could anyone please clarify?


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