The aggregate production function describes how the number of employees in an economy affects its output. In particular, this function shows that an increase in labor input to the economy is associated with an increase in GDP produced by it (8.2 Growth and the long-run, n.s). It is important that in the context of the aggregate production function, all the other factors of production and the economy do not change and remain fixed. Diminishing marginal returns describes the characteristic of a given function when an increasing number of employees gradually brings less and less output. In relation to quantity values, at each stage of economic growth, an increasing amount of labor input is required to achieve the same size of the output.
I think that technology and factors of production need to be fixed when assessing the graphical representation of the aggregate production function because this function illustrates the impact of employment on economic growth. If other variables were introduced, the result would reflect the complex change and influence of all available factors without allowing a separate assessment of the contribution of a particular aspect. Moreover, this graph depicts that employment cannot be a long-term instrument to stimulate growth and needs to be combined with other factors.
The concept of diminishing marginal returns can be illustrated by the example of an express courier service. In the early stages of growth for a delivery company, to meet customer demand, it is enough to hire more couriers who will have time to deliver the packages. However, at a certain point, the company will need to expand delivery to remote areas, which already requires other approaches such as technological renewal. Thus, the output from hiring new employees will be less significant each time. They will not be able to get to remote areas quickly enough, and all closer routes will already be covered by available couriers.
Reference
8.2 Growth and the long-run aggregate supply curve. (n.d). Saylor Academy.