Cost function is the representation of the relationship between the cost and its determinants such, as the size of plant, level of output, input prices, technology, managerial efficiency, etc. The cost function of a firm may be expressed as follows:
C = (S, O, P, T, E…)
- C = cost (it can be unit cost or total cost)
- S = represents the plant size
- O = stands for the output level
- P = represents the prices of inputs used in production
- T = stands for nature of technology
- E = represents the managerial efficiency
Though there is no standard fixed with regards to the factors, as they tend to vary from one firm to another in the same industry or from one industry to another industry. However, the main determinants of a cost function would include:
Plant Size: This is considered as an important variable in the process of determination of cost. As the scale of operations or the plant size, and the unit cost have an inverse relation. In other words, it can be said that with an increase in the plant size the unit cost decreases and vice versa. This further causes the cost function to be a downward sloping curve, which provides for only engineering estimates of cost.
Output Level: Unlike plant size, the output level and the total cost depict positive relationship with each other. As the total cost increases with an increase in the output and with a decrease in the total cost the output also decreases. This is based on the fact that increased production is based on an increase in the use of raw materials, labour, etc. This may also lead to an increase in the fixed input costs.
Price of Inputs: The cost also gets affected with any change in the prices of inputs, which is dependent on the relative usage of the inputs and relative changes in their prices. That is because of the fact that with an increase in the cost of the inputs more money needs to be paid, with no reduction in the cost from other sources. Hence, it can be said that there exists a direct relation between the cost of production and the prices of production.
Technology: It is regarded an important factor in the determination of cost. As with any improvement in technology provides for an increase in the productivity of the firm, which further leads to a decrease in the cost of production. Therefore, there exists an inverse relation between cost and the technological progress of the firm. Also the fact that improved technology provides for a higher capital-output ratio.
Managerial Efficiency: A higher managerial efficiency leads to less cost of production. However, it is very difficult to measure the managerial efficiency in quantitative terms.
Thus, it can be said on the basis of the above factors that cost is a part of many factors, which have a bearing on it and its relation with these factors.