Final answer:
The production function showing diminishing returns is one where additional inputs result in decreasingly smaller output increases, common in contexts like agriculture and manufacturing once a saturation point with fixed resources is reached.
Step-by-step explanation:
The law of diminishing returns is a concept in economics that describes a situation where, as additional units of a resource are added to a fixed amount of another resource, the resulting increase in output will eventually decrease. This pattern illustrates that there's a point where employing more labor or inputs will result in a smaller increase in production due to the efficiency of using the fixed resources becoming saturated. In the context of agriculture, when water (variable input) is added to land (fixed input), initially, production may increase, but beyond a certain point, more water may lead to less production due to saturation or, in extreme cases, flooding.
For manufacturing, this can mean hiring more workers results in less additional output per worker as the number of employees increases. The production function exhibiting diminishing returns is the one where after a certain number of labor or input units, additional units produce increasingly lesser output. Therefore, a production function with this characteristic typically shows a rise in output with each additional unit up to a point, after which output gains lessen.