# Estimation of Cost Function

Decision making requires forward planning. Thus, a firm, be it a new one or an existing one, would like to know the cost function facing it. Of course, the exact function may not be available until the firm really goes for expansion of its output there are methods through which the firm could get approximate information of its future cost output relationship. As is usual with regard to methods, there are alternative methods available for this purpose. The three well-known are the following:

1. Engineering method
2. Survivorship method
3. Statistical method

Discussion on each of these follows.
The engineering method of cost estimation is based directly on the physical relationship expressed in the production function for a particular product. On the basis of the production function, and input prices, the optimum input combination for producing any given quantity of a given product is determined. The cost curve is then formulated by multiplying each input in the so obtained least cost combinations by its price and summing, to develop the cost function. Since the estimates on the least cost estimates are provided by engineers, it is called the engineering method.

The method is based on the currently available technology and the existing factor prices. The users must have a through knowledge of the production technology as well as of factor prices. Nevertheless, since technology as well as factor prices are highly volatile over time, the method may not yield accurate estimates.

The survivorship technique was developed by George Stigler in 1958. Under this technique, the various firms of an industry are first classified into certain size groups, and then the growth of firms over time in each size group is examined. The size group whose share in the industry grows the most is then considered as the most efficient (the least average cost) size group, and vice versa. To explain this approach, let us consider a hypothetical example. Let the firms be divided into three classes on the basis of their current outputs. Let the share of each groups in the industry output in the base year and the current year be as follows:

Size Group Industry share in (%)

Base year Current year

Small 10 12
Medium 30 50
Large 60 38

On the basis of the above data, the method would conclude that the medium size class is the most efficient one and the large size class the most inefficient. The rationale for this approach is that competition will tend to eliminate those firms whose size is relatively inefficient, leaving only those size firms with lower average cost to survive over time.

The survivor method is quite simple. However, it suffers from a major limitation. The method gives the optimum size of a firm only and that too in terms of output range or the size class. It does not yield the cost function.

Statistical Method: Under this method, the cost function is estimated through the application through the application of some statistical method (e.g. least square method) to the historical data on the cost and its determinants. The data could be a time series data of a firm in the industry or of all firms in the industry or a cross section data for a particular year from various firms in the industry. However, depending on the kind of data used, we would get a short-run or a long run cost function. For example, if time series data of a firm is used and the output capacity of the firm has not changed much during the sample period, the cost function would be the short run one. In contrast, if cross section data of many firms, whose size vary substantially or the time series data of the industry as a whole whose output has expanded enormously during the sample periods were used, the estimated cost function would be the long run one.