Causal effect of population growth on GDP per capita increase I'm wondering if there is a logic for the causal influence of population growth on the increase in GDP per capita.

I guess,


increase in population as a factor of production might move aggregate supply curve to the right, lowering the price.
increase in population as consumers might move the aggregate demand curve to the right, increasing the price.


In both cases, the total amount may increase. But I don't understand how these reasons combine to explain the causal effect (if any!). So, why they are so worried about low birth rate?
Birth rate affects not only total population but also the age structure of the population.  If the birth rate over many years is below the level at which the population replaces itself, the result will be a falling population with an increasing proportion of elderly and often economically inactive people.  With a falling proportion of economically active people, GDP per capita is likely to be less than it would have been with a higher birth rate.  

This effect can to some extent be offset by policies to encourage older people to continue working for longer, such as raising the age at which state pensions become payable.