The Production Function

A production function is a purely technical (non-monetary) statement of the MAXIMUM output a firm can obtain from every possible combination of inputs, given the existing state of technology. It answers the question: if a firm uses these quantities of land, labour, capital and organisation, what is the most output it can produce? Symbolically, if output is denoted $Q$ and the factors used are Land ($N$), Labour ($L$), Capital ($K$) and Organisation ($O$), the production function is written:

The production function is always defined for a GIVEN level of technology — if technology improves, the same combination of inputs becomes capable of producing more output than before. This shifts the entire production function upward, rather than representing a movement along it.

For the purpose of analysis, economists distinguish between two time periods, based on how many of the factors above can actually be changed:

• Short run: a period in which AT LEAST ONE factor of production is fixed and cannot be varied — usually capital equipment and the scale of organisation, since expanding these genuinely takes time. The inputs that CAN be varied in the short run, typically labour and raw materials, are called variable factors. Production analysis in the short run is governed by the Law of Variable Proportions (Section 3). …