Increasing population would mean more people are entering the labour work force, more people would demand good and services which would encourage firms to increase their output, and increase the productive potential or the ability to produce goods would rise. The quality of the labour force may increase due to (increased innovation) or if the population growth is a result of the immigration of skilled workers/more young people who receive better education. The higher population would also make better use of resources which would be associated with higher economic growth.
However, the population increase may increase economic growth in terms of output but not GDP per head if the population grows at a greater rate than GDP resulting in negative economic growth. It would also put pressure on resources due to less capital/land per worker. This would reduce productivity and cause the resources to be diverted from increasing productive capacity to coping with more dependents.
But of course, the relationship between the population change and economic growth is influenced according to the sustenance level of each country and their life. population growth in developed (high income) countries with enough sources to sustain the population would result in a positive economic growth while high population growth in low-income countries would have to import more, receive foreign aid or borrow overseas to meet the increased demand due to insufficient resources and would cause an adverse impact on improvement in food supplies, intensifying the constraints on developments of saving, foreign exchange and human resources ultimately slowing their development.
So yes management of population is surely a factor but there are various other factors to consider as well and take into account the economic position of a country (whether its under-developed, developing or developed)
