Let us study about Cost Function. After reading this article you will learn about: 1. Concept of Cost Function 2. Importance of Cost Function.

Concept of Cost Function:

The relationship between output and costs is expressed in terms of cost function. By incorporating prices of inputs into the production function, one obtains the cost function since cost function is derived from production function. However, the nature of cost function depends on the time horizon. In microeconomic theory, we deal with short run and long run time.

A cost function may be written as:

Cq = f(Qf Pf)


Where Cq is the total production cost, Qf is the quantities of inputs employed by the firm, and Pf is the prices of relevant inputs. This cost equation says that cost of production depends on prices of inputs and quantities of inputs used by the firm.

Importance of Cost Function:

The study of business behaviour concentrates on the production process—the conversion of inputs into outputs—and the relationship between output and costs of production.

We have already studied a firm’s production technology and how inputs are combined to produce output. The production function is just a starting point for the supply decisions of a firm. For any business decision, cost considerations play a great role.

Cost function is a derived function. It is derived from the production function which captures the technology of a firm. The theory of cost is a concern of managerial economics. Cost analysis helps allocation of resources among various alternatives. In fact, knowledge of cost theory is essential for making decisions relating to price and output.


Whether production of a new product is a wiser one on the part of a firm greatly depends on the evaluation of costs associated with it and the possibility of earning revenue from it. Decisions on capital investment (e.g., new machines) are made by comparing the rate of return from such investment with the opportunity cost of the funds used.

The relevance of cost analysis in decision-making is usually couched in terms of short and long periods of time by economists. In all market structures, short run costs are crucial in the determination of price and output. This is due to the fact that the basis for cost function is production and the prices of inputs that a firm pays.

On the other hand, long run cost analysis is used for planning the optimal scale of plant size. In other words, long run cost functions provide useful information for planning the growth as well as the investment policies of a firm. Growth of a firm largely depends on cost considerations.

The position of the U-shaped long run AC of a firm is suggestive of the direction of the growth of a firm. That is to say, a firm can take a decision whether to build up a new plant or to look for diversification in other markets by studying its existence on the long run AC curve. Further, it is the cost that decides the merger and takeover of a sick firm.


Non-profit sector or the government sector must also have a knowledge of cost function for decision-making. Whether the Narmada Dam is to be built or not, it should evaluate the costs and benefits ‘flowing’ from the dam.