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Law of Return to Scale

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In the long run all factors of production are variable. No factor is fixed. Accordingly, the scale of production can be changed by changing the quantity of all factors of production. The law of returns to scale explains the proportional change in output with respect to proportional change in inputs. In other words, the law of returns to scale states when there are a proportionate change in the amounts of inputs, the behavior of output also changes. The degree of change in output varies with change in the amount of inputs. For example, an output may change by a large proportion, same proportion, or small proportion with respect to change in input. 

There are three stages or types of law of returns to scale. They are:
1. Increasing Returns to scale
2. Constant Returns to scale
3. Decreasing Returns to scale 

Increasing Returns to scale:

 If the proportional change in the output of an organization is greater than the proportional change in inputs, the production is said to reflect increasing returns to scale. For example, to produce a particular product, if the quantity of inputs is doubled and the increase in output is more than double, it is said to be an increasing returns to scale.
 

Units of Labor (L)

Units of Capital (K)

Total Units of Inputs(L+K)

TP

MP

1L

1K

1L+1K

500

500

2L

2K

2L+2K

1200

700

3L

3K

3L+3K

2500

1300


From the above table, we can see one unit of labor and capital produce 500 units of output. When both inputs are increased by 100% i.e. 2L and 2K the level of output is 1200 units which is more than 100% change. Here, a percentage change in output is more than the percentage change in input which shows increasing return to scale.


Constant Returns to scale:

The production is said to generate constant returns to scale when the proportionate change in input is equal to the proportionate change in output. For example, when inputs are doubled, so output should also be doubled, then it is a case of constant returns to scale.

Units of Labor(L)

Units of Capital (K)

Total Units of Inputs(L+K)

TP

MP

1L

1K

1L+1K

500

500

2L

2K

2L+2K

1000

500

3L

3K

3L+3K

1500

500


From the above table, we can see one unit of labor and capital produces 500 units of output. When both inputs are increased by 100% i.e. 2L and 2K,the level of output increases to 1000 units which are exactly 100% change. Here, a percentage change in output is equal to the percentage in input which shows constant returns to scale.

Decreasing Returns to Scale:

Decreasing returns to scale refers to a situation when the proportionate change in output is less than the proportionate change in input. For example, when capital and labor is doubled but the output generated is less than doubled, the returns to scale would be termed as diminishing returns to scale.

Units of Labor (L)

Units of capital(K)

Total Units of Inputs(L+K)

TP

MP

1L

1K

1L+1K

500

500

2L

2K

2L+2K

900

400

3L

3K

3L+3K

1100

200


From the above table, we can see one unit of labor and capital produces 500 units of output. When both inputs are increased by 100% i.e. 2L and 2K,the level of output is 900 units which are less than 100% change. Here, a percentage change in output is less than the percentage change in input which shows decreasing returns to scale.  

The concept of law of returns to scale can be explained with the help of figure given below:
 

In the figure above X-axis represents combination of inputs and Y-axis represents marginal product. The upward slopping segment of the curve represents the increasing returns to scale because it shows increasing marginal productivity of inputs. The horizontal segments of the curve represents constant returns to scale because its shows constant marginal productivity of inputs. Finally, the downward slopping segment of the curve represents the decreasing returns to scale because it shows decreasing marginal productivity of inputs.