The production function expresses a functional relationship between quantities of inputs and outputs . It shows how and to what extend output changes with variations in inputs during a specified period of time . Basically the production function is a schedule or table showing the amount of output obtained from various combinations of inputs , given the state of technology . Algebraically , it may be expressed in the form of an equation as –
P = f[ A, B , C ,D]
where P stands for the output of goods per unit of time and A ,B ,C, D are the various inputs of resources land , Labor , Capital and organisation used in making the output .
The production function as determined by technical conditions of production is of two types : it may be rigid or variable. In the short run , the technical conditions of production are rigid so that the various input resources used to produce a given output are in fixed productions . This is however , rare phenomenon in production because it is possible to change inputs in different proportions .
Even in the short run , it is possible to increase the quantities of one input while keeping the quantities of other inputs constant in order to have more output . This aspect of the production function is known as the law of variable proportions.
In the long run , it is possible for a firm to change all inputs up or down in accordance with its scale . This is known as returns to scale . The returns to scale are constant when output increases in the same proportion as the increase in the quantities of inputs . The returns to scale are increasing when the increase in output is more than proportional to the increase in inputs and they are decreasing if the increase in output is less than proportional to the increase in inputs.
Let us illustrate the case of constant returns to scale with the help of our production function.
P= f[ A , B ,C ,D]
If the quantities of all inputs A,B,C,D are increased n fold , the output P also increase n fold . Then the production function becomes –
nP = f [ nA , nB , nC , nD].
This is known as the Linear and homogenous production function , or a homogenous function of the first degree. If the homogenous function is of the kth degree , the production function is
nk.p = f[ nA , nB , nC ,nD]
If k is equal to 1 , it is a case of increasing returns to scale , and if it is less than 1 , it is a case of decreasing returns to scale .
TYPES OF PRODUCTION FUNCTION. :- Thus a production function is of two types : [i] Linear homogenous of the first degree in which the output would change in exactly the same proportion as the change in inputs . Doubling the inputs would exactly double the output , and vice versa . Such a production expresses constant returns to scale .
[ii] Non – homogenous production of a first degree is greater or less than one . The former relates to increasing returns to scale and the latter to decreasing returns to scale .
One of the important production function based on empirical hypothesis is the” Cobb- Douglas” production function. Originally it was applied to the whole manufacturing industry in America, though it can be applied to the whole economy or to any of its sectors .The cobb-Douglas production theory is also related to production function process. Later I shall explain you in detail. Now production function exhibits technological relationships between physical inputs and output and is thus said to belong to the domain of engineering. Prof. Stigler does not agree with this commonly held view . The function of an entrepreneur is to sort out the right type of combination of inputs for the quantity of output he desires . For this he was to know the prices of this inputs and the technique to be used for producing a specified output within a specified period of time . All these technical possibilities are derived from applied sciences , but cannot be worked out by engineers alone. ———-#—END—