Link between Productivity and Labour Force?
Output per capita is $\dfrac{Y}{N}$. This can be decomposed as:

$$ \frac{Y}{N} \equiv \frac{Y}{h} \times \frac{h}{L} \times \frac{L}{A} \times\frac{A}{N} $$

where $h$ are aggregate hours of work, $L$ is number of employed, and $A$ is active population. $\frac{Y}{h}$ is aggregate labour productivity, $\frac{h}{L}$ is "work intensity", $\frac{L}{A}$ is the employment rate and $\frac{A}{N}$ is the participation rate.

The above equality can be turned into growth rates, which means in approximation, the growth of output per capita is the sum of the growth rates of each of the subcomponents.