Factor combination in the long run

In the long run it is possible to vary all factors of production. The firm is therefore restricted in its activities by the law of diminishing return to scale.

The law states that successive proportionate increments in all inputs simultaneously will lead eventually to a less than proportionate increase in output.

Returns to scale refers to the rate at which output increases as all inputs are increased simultaneously.  In the illustration below, labour and land are assumed to be the factors of production.

Land (units)                 Labour (units)             Output (units)

30                                             5                                                          41                     Increasing returns

60                                             10                     '                                   100

90                                             15                                                         168                   Constant returns

120                                           20                                                         224

150                                           25                                 '                       275                   Decreasing returns

180                                           30                                                         300

When land increases from 30 units to 60 units and labour from 5 units to 10 units, each has doubled or increased by 100%.  Output increases from 41 units to 100 units i.e. by more than 100.  When land increases from 60 to 90 units, each has increased by 50%.  Output increases from 100 to 168 i.e. by more than 50%.  In each of these cases when the inputs are increased in a certain proportion, output increases in greater proportion.  We say that the firm is in a stage of increasing returns to scale.

This should not be confused with the stage of increasing   returns in the short run.  In the short run.  In the short run the increasing returns  to the variable factor, and the scale of production fixed.

When land is increased from 90 to 120 units and labour from 12 to 16 units, each has increased by 1/3 or 33 1/3% output increases from 168 to 224, i.e. by 1/3 or 33 1/3.  Thus, when the input factors are increased in a certain proportion, output increases in the same proportion.   This is a stage of constant returns to scale.

When land is increased from 120 to 150 units and labour fro 20 to 25 units, each has increased by 25%.  Output increases from 224 to 275 units i.e. by less than 25%.  When land increases from 150 to 180 and labour from 25 to 30 units, each has increased by 20%, output increases from 275 to 300 i.e. by less than 20%.  In both of these cases, when the inputs are increased in a certain proportion output increases in 20%.  The firm is said to be in a stage of decreasing returns to scale  not to be confused with diminishing returns to the variable factor in the short run.