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Cost which a firm incurs in the production of goods or services depend on two things
a) Firm's production function
b) Market's inputs supply function
The cost would vary
* Output level varies
* Nature of production function varies or factor prices change.
Putting all this together we have the following cost function
C= f( Q1,E1,P1)
f1,f3>0>f2
Where, C= Total Production cost
Q= Total output
E1= Efficiency of inputs
P1= prices of inputs
Factor productivities depends on the levels of technology, the quality of the work force and management. Which are influenced by education, training and health condition and sincerity and integrity of the labour and mis management which are reflected in absentism, strikes, lockouts etc. Thus through factor efficiencies many factors exercise influence on the cost of production.
An increase in input price and if other things remaining the same would lead to an increase in the cost of production. Input prices depend on their demand and supply and on government regulations.
Costfunction & Cost function:
The shape of the cost curve depends on the nature of the cost functions.Cost functions are derivedfrom actual cost data of the firms. Cost function may take a variety of forms yielding different kinds of cost curves. It includes
a) Linear cost function
b) Quadratic cost function
c) Cubic cost function
a) Linear cost function:
It takes the following form
TC= a+bQ
TC = Total cost
Q = output
a= fixed cost
b is a constant.
b) Quadratic Cost function:
A quadratic cost function is of the following form
TC= a+bQ+Q^2
Where a&b are constants and TC and Q are total cost and total output.
c) Cubic cost function:
A cubic cost function is of the following form
TC= a+bQ-cQ^2+Q^3
Where a,b and c are the parametric constants.
Estimation of cost:
A firm be it a new or an existing one would like to know the cost function. The exact function may not be available until the firm really goes for expansion of it's output. There are methods through which the firm could get information of it's future cost output relation. The three methods available for this purpose are as follows
a) Engineering method
b) Survivorship method
c) Statistical method.
a) Engineering method:
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 quality of a given product is determined.
Since the estimates on the least cost estimates are provided by engineers it is called engineering method.
The method is based on the currently available technology and the existing factor prices.
b) Survivorship Method:
The government technique was developed by George stigler in 1958. Under this Technique the various firms of an industry are first classified into certain size groups 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 size group.
c) Statistical method:
Under this method the cost function is estimated through the application of some statistical method. Eg: least square method to the historical data on the cost and it's 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 firm in the industry.
Depending on the kind of data used we would get a short run or a long run cost function.