Question: Production function defines the relationship between inputs and the maximum amount that can be produced within a given period of time with a given level of technology. Production functions show how the factors of production are related to output. Given advanced production technology, whatever input or input combinations are included in a particular function, the output from their use will be at the maximum level.

There are many different types of costs and invariably, costs can be too high and the firm will consistently try to lower them. The law of diminishing marginal productivity states that as you add more and more of a single variable, e.g. labor, to production, ultimately the additional output one gets from that additional input is going to fall. As marginal productivity rises, costs fall when more inputs are added. They are mirror images of each other - when one is increasing, the other is decreasing. When one is at a maximum, the other is at a minimum.