CHAPTER 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     EIGHT 
                                                                                                                                                                                                                                                                                                                                                                                             THEORY OF PRODUCTION 
                                                                                              8.1 Definition of Production 
                                                                                              The production function is a purely technical relationship between the quantity of a good 
                                                                                              produced (output)  and  inputs  (resources)  used.  The  inputs  used  for  producing  goods  are 
                                                                                              called factors of production.  
                                                                                              Production function may be written in the following form: 
                                                                                              Q = f (X , X , X - - - - - - - - - - - - - - - - -X ) 
                                                                                                                                         1                   2                  3                                                                                                                                     n
                                                                                              Where, Q is the output and X  and X  ----------------X  are the quantity of various inputs used 
                                                                                                                                                                                                                                                  1                                     2                                                                                  n
                                                                                              in the production of output.  
                                                                                               
                                                                                              8.2   Laws of Returns  
                                                                                              The functional relationship between output and inputs is governed by the laws of returns that 
                                                                                              are categorized into two forms:  
                                                                                              (i)  The law of variable proportions.  
                                                                                                                                    This law explains production in the short run i.e. the time horizon over which at least 
                                                                                                                                    one of the firm’s inputs is fixed in the process of production of output. In short run 
                                                                                                                                    the output is produced by using a variable factor along with fixed factor/factors. 
                                                                                                                                     
                                                                                              (ii) The law of returns to scale.  
                                                                                                                                    This law explains production in the long run i.e. the time horizon over which the firm 
                                                                                                                                    can change all of its inputs in the process of production of output. In the long run 
                                                                                                                                    output  is  produced  by  varying  all  the  factors  of  production  (i.e.  both  labour  and 
                                                                                                                                    capital). Therefore, the responsive change in the output due to proportionate change 
                                                                                                                                    in the factors of production is called returns to scale. 
                                                                            8.3 ISOQUANT  
                                                                            An isoquant represents all the technically efficient methods for producing the same level of 
                                                                            output. An isoquant curve is also called equal product curve. 
                                                                            The concept of isoquant can be understood from the following table as well as graph. It is 
                                                                            showing  that  two  factors  of  production:  labour  (L)  and  Capital  (K)  are  being  employed  to 
                                                                            produce a given level of output (50 units) through different combinations (processes).  
                                                                             
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                   Four  different  combinations  to  produce  a  given  level  of  output  may  be  represented  in  the 
                   following table as well as graph: 
                   Process                        Labour Units (L)              Capital Units (K)              Output (Q) 
                   P                              1                             9                              50 
                     1
                   P                              2                             6                              50 
                     2
                   P                              3                             4                              50 
                     3
                   P                              4                             3                              50 
                     4
                    
                        Y                                                           Y 
                                      P  (1, 9) 
                                       1
                                             P  (2, 6) 
                     K                        2                                 K 
                                                        P  (3, 4)                                                               Q (150) 
                                                         3                                                                       3
                                                                    P  (4, 3) 
                                                                      4                                                         Q (100) 
                                                                                                                                 2
                                                                             Q                                                          X 
                                                                                                                                Q (50) 
                                                                                                                                 1
                     0                                                         X 
                                           L                                                                L                                
                    
                   SLOPE OF ISOQUANT  
                   Production function represented as a function of labour (L) and Capital (K): 
                   Q = f (L, K) 
                                                
                   If the producer is on the same isoquant 
                                                      
                   or          f dL +  f dK=0 
                             L       k 
                   or           f dL = - f dK 
                             L        k 
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                     or                                              = RTS= MRTSLK 
                     Where MRTS             = Marginal rate of technical substitution of the factors. 
                                       L, K
                     Note:  
                           (i)           Shows the rate of at which the producer can substitute one input (L) for another 
                                 input (K) in order to maintain given output level (Q). 
                          (ii)            Shows the slope of the isoquant. This has a negative sign. Therefore, it slopes 
                                    downward from left to right and is convex to the downwards. 
                          (iii)    The  slope  of  the  isoquant  defines  the  degree  of  substitutability  of  the  factors  of 
                                    production. The slop of the isoquant is called the rate of technical substitution (RTS) 
                                    or the Marginal Rate of Technical Substitution (MRTS). 
                     8.4 COBB-DOUGLAS PRODUCTION FUNCTION  
                     One of the most widely estimated production functions is the Cobb-Douglas: 
                     Q = f (L, K) =                    
                     Where A, , and β are positive constants. 
                     8.5 Useful Concepts related to the Cobb-Douglas Production Function  
                          (1) Factors product 
                                
                               (i)       Average product of labour 
                                                                                       
                               (ii)      Average Product of Capital 
                                                                                       
                               (iii)     Marginal Product of Labour 
                                                                                               =                          
                               (iv)      Marginal Product of Capital: 
                                                                                                                               
                                          
                                          
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                                                                                              (2) Marginal rate of technical substitution (MRTS): 
                                                                                                                  
                                                                                                                                                                                                                                                                                                                                                                               
                                                                                                                  
                                                                                              (3) Elasticity of factor Substitution (σ) 
                                                                                                                  
                                                                                                                 It measures the percentage change in the capital labour ratio divided by the percentage 
                                                                                                                 change in the rate of technical substitution. 
                                                                                                                                                                                                                                                                                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                                                           
                                                                                              (4) Factor Intensity  
                                                                                                                 It is measured by the ratio    .The higher this ratio means the more labour intensive 
                                                                                                                 technique and the lower this ratio means more capital intensive technique.  
                                                                                                                  
                                                                                              (5) Efficiency of Production 
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