# The Production Function.

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—

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