# Cost Function

Costs which a firm incurs in the production of good or service depends on two things:

1. Firmâ€™s production function
2. Marketâ€™s inputs supply functions.

Production function specifies the technical relationship between combination of inputs and the level of output. Given this relationship and input prices (if they are fixed for the firm), one can easily determine the costs associated with different levels of output. The costs would thus vary as output varies, nature of production function varies, or factor prices change. The nature of a production function is tantamount to factor productivities (efficiencies).

Putting all this together, we have the following cost function:

C = f (Q, E1, P1)
f1, f3 > 0> f2

Where

C = Total (production) cost
Q = Total output of inputs
E1= Efficiencies of inputs
P1 = Prices of inputs

The total cost is obviously an increasing function of output, for there is no free lunch, increasing production, ceteris paribus, requires increasing units of inputs and all inputs carry tags. Improvement in factor productivities, other things remaining the same have a depressing effect on input requirements per unit of output, and since inputs have price tags, it leads to a decrease in total cost. It must be noted that factor productivities depends on the level of technology, use of computer, modern plants and equipments, etc., the quality of the work force and management, which are influenced by education training and health conditions, and sincerity and integrity of the labor and management which are reflected in absenteeism, strikes, lock outs and fooling around during working hours. Thus, through factor efficiencies, many factors exercise influence on the cost of production.

Since no output is possible without an input, an increase in input price, other things remaining the same, would lead to an increase in the cost of production. Input price like any other price depends on their demand and supply and on government regulations, if any. Generally in the theory if firm behavior input prices are taken as parameters. This is because, a firm is usually and insignificant part of an economy, its activities have no perceptible bearings on the total demand for and supply of inputs in the economy and so on factor prices. However, if the firm in question happens to be large in this respect, factor prices would be variables like output and factor productivities.

Before the article is closed, it must be emphasized that both factor productivities and factor prices are plural, though they have been argued in singular manner in the foregoing paragraphs. Thus, by an increase in factor productivities we mean, an increase in total factor productivity, or an increase in some productivity with other productivities held constant, or an increase in some productivities and decrease in some other but the effect of the former out-weigh that of the latter on total cost. The arguments with regard to factor prices should be treated in a similar fashion.

Of the three sets of cost determinants, output assumes a special role. This is for two reasons. One, output is the variable which is under the direct control of the firm. Two, the relationship between total cost and output, though is unique in direction, is varying in terms of magnitude That is, total cost increases as output expands, but the rate of increase varies from one set of output levels to the other for the same set of output level from one firm to another firm. For example, for firm A, between output levels 100 to 200, the total cost might increase by just 100 percent but between output levels 200 and 400, the total cost might increase by 150 percent. Similarly, for firm B even between output levels 100 to 200 the total cost might increase by 125 percent. Further firms A and B may or may not belong to the same industry.