Nonsense. If you have studied introductory economics, you would know that larger factories in general are more productive and efficient than smaller factories due to economies of scale and division of labor. Similarly large farms are more productive per acre than small farms because of economies of scale.
What you're talking about is the law of diminishing returns on labor due to insufficient investments in capital (under-investment), which happens because of low savings
rate. Reduce your population by half and your capital will be reduce by half as well, ceteris paribus. You must be obtuse if you think savings have a diminishing returns, ie the smaller the population the higher the saving rate.
The onus is on you show that the numerator/denominator is 'not 1-to-1', which I'm sure you simply pulled out of nowhere.