Output per effective worker does not necessarily grow at the rate of population growth.
Instead, output per worker (Y/N) is included by technological progress and capital investment (savings). Mathematically:
Y/N = f(K/N)
Thus, Y (output) per worker (N) is a function of capital (K) per worker (N), with technological progress being an exogenous force that increases labour efficiency (L, maintained in the equation as a constant), or productivity. Beyond technological progress, increasing capital per worker directly increases output per worker.
So, if the population grows without a corresponding increase in technological progress or capital per worker, then output per worker may stagnate or decline.
Thus, capital and technology are critical to prevent diminishing returns from an increasing population and population growth is not a formulaic predictor of output per worker.
Hope that helps, and leave any questions in the comments! Check out my other articles on economics here (useful for studying, or just learning).
