A firm’s production function defines the relationship between the quantity of inputs the firm uses and the quantity of output it produces. A firm’s production function underlies its cost structure.
More particularly, in the short run, because at least one input is fixed (usually capital), the production function shows the relationship between the variable input (usually labour) and the quantity of output.
What’s really important here is the marginal product of labour (MPL) – the additional quantity of output that would result from using one more unit of labour. There are usually always diminishing returns to using more of the variable input – as each additional unit of the variable input gets less of the fixed input to work with, the marginal product of that input declines.
Since variable costs (the cost of the variable input) depend upon the quantity of output produced, an economically efficient production system would always minimize the amount of variable input needed to produce the desired input quantity. Another way of saying this is that each unit of the variable input employed must have as much of the fixed input to work with as possible. Simply put, the MPL is higher when any given unit of labour has more of the fixed input to work with.
Because total costs are the sum of fixed and variable costs, the slope of a firm’s total cost curve gets steeper as output rises. Why? Because of diminishing returns to the variable output – more labour (and hence more cost) is being incurred, but the marginal product of that labour is decreasing.
When we talk about waste and non-value adding activity, we are really talking about those activities which prevent a unit of variable input from maximizing its use of the fixed input. For example, when workers have to set up machines, those workers cannot work with the fixed input to produce output. As a result, variable costs are increased and the MPL is decreased.
A production function can be looked at in two ways. One way is to consider, from the total set of all technically feasible combinations of inputs and output, which combination produces the maximum output for a specified set of inputs. A second way is to view the production function as the specification of the minimum input requirements that are needed to produce designated quantities of output, given the available technology.
As I noted in the previous blog, because firms are profit-maximizing entities, for any given quantity of output a firm must strive to implement an economically efficient production technology where costs are minimized. If costs are not minimized, then profit is not being maximized. This is the whole rationale for the continuous improvement of a firm’s production technology.