The concept of a production function
The production function is a mathematical expression which relates the quantity of factor inputs to the quantity of outputs that result. Three measures of production / productivity are:
- Total product -the total output that is generated from the factors of production employed by a business such asvehicles, freezers and DVD players, it is straightforward to measure the volume of production from labour and capital inputs that are used. But in many serviceindustries, where much of the output is “intangible” its harder to measure productivity
- Average product is the total output divided by the number of units of the variable factor of production employed (e.g. output per worker employed or output per unit of capital employed)
- Marginal product is the change in total product when an additional unit of the variable factor of production is employed. For example marginal product would measure the change in output that comes from increasing the employment of labour by one person, or by adding one more machine to the production process in the short run.
The Short Run Production Function
The short run is a period of time where at least one factor of production is assumed to be in fixed supply. Usually the quantity of capital inputsis fixed andproduction can be altered by suppliers through changing the demand for variable inputs such as labour, components, raw materials and energy inputs. Often the amount of land available for production is also fixed.
In the short run, the law of diminishing returns states that as more units of a variable input (i.e. labour or raw materials) are added to fixed amounts of land and capital, the change in total output will at first rise and then fall. Diminishing returns to labour occurs when marginal product of labour starts to fall. This means that total output will still be rising – but increasing at a decreasing rate as more workers are employed eventually a decline in marginal product leads to a fall in average product.
What happens to marginal product is linked directly to the productivity of each extra worker employed. At low levels of labour input, the fixed factors of production - land and capital, tend to be under-utilised which means that each additional worker will have plenty of capital to use and, as a result, marginal product may rise.
Beyond a certain point however, the fixed factors of production become scarcer and new workers will not have as much capital to work with so that the capital input becomes diluted among a larger workforce.
As a result, the marginal productivity of each worker tends to fall – this is known as the principle of diminishing returns.