## The graph shows that the maximum point of the curve is the point of optimum population where per capita income is maximised

The graph shows that the maximum point of the curve is the point of optimum population where per capita income is maximised. To the left of this point, the per capita income is reduced, implying that the country is under-populated as it can afford to increase population until it reaches the optimum level where resources are fully utilised. Therefore, if an increase in the size of the population is followed by an increase in per capita income, the country is under-populated. When the population is not large enough, there are not enough people to exploit all the resources of the country with maximum efficiency, causing there to be less output and per capita income. To the right of the optimal point, there is also a reduction in per capita income, demonstrating that an increase in population above the maximum point leads to a decline in returns. This is due to there being too many people to work efficiently and produce the maximum goods and the highest per capita income. This is the stage of over population.
The theory of optimum population can be explained by the law of diminishing returns which states that as we add more units of a variable input, labour, to fixed amounts of land and capital, there will initially be an increase in output, but this is followed by a reduction in total output. Diminishing returns to labour occurs when marginal product of labour starts to decline. An increase in the size of the population will cause an increase in the size of the labour force so there will be a larger number of workers. This will increase the output in a country’s economy and will increase per capita income but only up to a certain point. After this maximum point, things such as increasing difficulties in supervising the large work force, more frequent breakdowns by over-utilised capital, or inefficient workers as a result of overcrowding of work spaces begin to take their toll. The marginal returns to each consecutive addition of labour input gets increasingly smaller and eventually turns negative, resulting in lower per capita income in the economy. Therefore, at the stage of over-population, the output from each additional unit of labour will eventually diminish and the output per unit of labour (average product of labour) will also diminish.
However, it is not possible to exactly determine and fix the optimum size of population because the point of optimum population is not a fixed point. For example, if due to inventions in a country there are improvements in the methods and techniques of production, the average product of labour might increase and increase the level of per capita income so that the optimum point rises. In addition, if the capital stock or the stock of natural resources increases, this will also lead to the optimum point being higher than before.