The Production Function
There are several things to be considered when deciding upon methods of production. These include:
- Technical Efficiency – this is related to engineering considerations and labour skills etc.
- Relative Prices of factor inputs.
We will assume that managers wish to minimise costs of production, and thus maximise profit. This is not always possible in reality due to factors such as labour union agreements on the size of workforces etc.
The production function is a mathematical expression to relate the quantity of all inputs to the quantity of outputs, assuming managers employ all inputs efficiently. It may be expresses as follows:
Q = F(I1, I2, I3, I4…..In)
The inputs are usually classified under 3 categories. These are:
The Cost Function
The cost function is important for maximising profit, so that cost of output can be seen next to cost of inputs used.
C = F(Q, p1, p2, p3….pn).
Variable Costs vs Fixed Costs
Fixed Costs are those costs that do not vary as output changes. These might very well include; office rent, machinery (to the point where more machines are required for further increases in production).
Variable Costs are those costs that do alter as output changes, and these will include things such as; fuel, energy consumption, raw materials, staffing levels.
Total Costs of Production = total fixed costs + total variable costs
TCP = TFC + TVC
If we were to average values over TFC and TVC we can derive values for Average Fixed Cost and Average Variable Cost.
Points to note:
- Total fixed costs remain constant for all levels of output.
- Total variable cost, and therefore total costs rise as output increases.
- Average fixed costs decline as output increases, as the fixed costs are distributed over more and more output.
- Average Variable Costs may fall initially, but will level off and even rise after a certain output due to the Law of Diminishing Marginal Returns.
- Average Total Costs (ATC) = AFC + AVC, tend to decline initially and then rise after a certain output level (Q) is reached. ATC is often referred to by accountants as the unit cost, and also the average cost.
TC = TFC + TVC
AVC = TVC/Q
AFC = TFC/Q
TF = AFC + AVC = TC/Q