# Law of Returns to Scale

Law of returns to scale is the long-run concept of production theory. It is known as the long-run production function. This law states that “how the output changes when all factors are changed proportionately in the long-run”. This law involves following three types of returns to scale;

**1. Increasing Returns to Scale:**

When the percentage change in output is more than the percentage change in factor inputs is called increasing returns to scale. For example; if factor inputs are increased by 100% then the output will be increased by more than 100%. It can be further explained with the help of below table and graph;

Units of labor (L) |
Units of Capital (K) | Output (Q) |

1L |
1K |
100 units |

2L |
2k |
200 units |

3L | 3k |
400 units |

In the above figure, initially, the producer produces 100 units of output by using 1 units of labor and 1 units of capital. When the producer doubles the units of labor and capital, the output increased by more than doubles from 100 units to 200 units. When the producer increased the units of labor and capital to 3L and 3K, the output increased from 300 units to 400 units. So, it reflects increasing returns to scale.

**2. Decreasing Returns to Scale:**

When the percentage change in output is less than the percentage change in factor inputs is called constant returns to scale. For example; if factor inputs increased by 100% then the output will be increased by less than 100%. It can be further explained with the help of following figure and table;

Units of labor (L) | Units of Capital (K) | Output (Q) |

1L | 1K | 100 |

2L | 2K | 150 |

3L | 3K | 250 |

Initially, in the above figure, the producer hire 1 units of labor and 1 units of capital to produce 100 units of output. When the producer doubles the units of labor from 1L to to 2L and units of capital from 1K to 2K, then the output increased by less than 100% from 100 units to 150 units. Also, when the producer further increases the units of factor inputs from 2L to 3L and from 2K to 3K, then the output increased by less than 100% from 150 units to 250 units. So, it reflects decreasing returns to scale.

**3) Constant Returns to Scale:**

When the percentage change in output is equal to the percentage change in input then it is called constant returns to scale. For example; if the factor inputs increased by 100% then the output will be increased by 100% too. It can be further explained with the help of following table and graph;

Units of labor (L) | Units of Capital (K) | Output (Q) |

1L | 1K | 100 |

2L | 2K | 200 |

3L | 3K | 300 |

In the above figure, initially, the producer hires 1 units of labor and 1 units of capital to produce 100 units of output. When the producer doubles the units of labor from 1L to 2L and units of capital from 1K to 2K, the output increased by same percentage from 100 units to 200 units. Lastly, when the producer again trebles the units of labor from 2L to 3L and units of capital from 2K to 3K, then the output also increases in the same percentage from 200 units to 300 units which is called constant returns to scale.