Note on Laws of Return to Scale

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 LAW OF RETURN TO SCALE

It is based on long run productioin function. It shows change in the scale of production when all factor are changed simulatoneously.

“The term returns to scale refers to the changes in output as all factors change by the same proportion.” Koutsoyiannis

Assumption:
1. All factors are variable but enterprise is fixed.
2. Input ( labour & capital ) are used in fixed proportion.
3. No change in state of technology.
4. There is perfect competition.
5. The product is measured in quantities.

The law of return to scale states that if both factors of inputs are to be varied in a fixed proportion, then the production function shows 3 types of relationship in long run. They are:

  • Increase returns to scale
  • Decreasing returns to scale
  • Constant returns to scale

 

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  • Increasing Returns to Scale (IRS)

If quantity output increases in higher proportion then the increase in quantity input. This type of situation will be called incerasing return to scale. For eg. if all factor are increased by 20% then the final output also increases by more than 20%.

It can be explained by the following table:

Unit of labour Unit of capital Total unit of input TP MP
1L 1K 1L+1K 500 500
2L 2K 2L+2K 1200 7000
3L 3K 3L+3K 2500 1300

From the above table, we can see one unit of labour 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.

It can be represented diagrammatically as:

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In the given figure, capital and labour are shown in X-axis and TP of returns is shown in Y-axis. As shown in the graph, TP is increasing returns to scale in units of labour and capital. The positive curve sloping upwards shows the increasing returns to scale. The combination points a, b, c are the increasing trend of TP.

The reason for increasing returns to scale are as follows:

  1. Internal and external economics
  2. Discount in price of raw materials
  3. Specialisation of labour

 

  • Decreasing Returns to Scale (DRS)

If quantity output increases in less proportion then the increase in input . This type of situation is called decreasing return to scale.  For eg, If all factors increases by 25% then the final output increases by less than 25%.

Unit of labour Unit of capital Total unit of input 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 labour 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 increasing returns to scale.

It can be represented diagrammatically as:


 

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In the given figure, capital and labour are shown in X-axis and TP of returns is shown in Y-axis. As shown in the graph, TP continuously increases with the decrease rate with the increase in the variable factors inputs. The combination point a, b, c shows the decreasing trend of MP.

The main reason for the decreasing returns to scale are as follow:

  1. Entrepreneurship is a fixed
  2. Lack of natural factors
  3. Internal and external diseconomies of scale

 

 

  • Constant Returns to Scale (CRS)

If quantity input & output both are changed in same proportion the situation is called constant return to scale. In other words, if the ratio change in quantity input is equal to ratio change in quantity output then the situation is called constant return scale. For eg, if all factor increases by 25% then the final output also increases by same 25%.

Unit of labour Unit of Capital Total unit of Input TP MP
1L 1K 1L+1K 500 500
2L 2K 2L+2k 1000 500
3L 3K 3L+3k 1500 500
4L 4K 4L+4K 2000 500

From the above table, we can see one unit of labour 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.

This can be shown in the following figure:


 

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In the given figure, capital and labour are shown in X-axis and TP of returns is shown in Y-axis. We can see that marginal production rises with the increasing returns to scale remain constant with constant returns to scale and declines with decreasing returns to scale. The combination of points a, b, c shows the constant returns to scale.

 

 

 

(Karna, Khanal, and Chaulagain)(Khanal, Khatiwada, and Thapa)(Jha, Bhusal, and Bista)

Bibliography

Jha, P.K., et al. Economics II. Kalimati, Kathmandu: Dreamland Publication, 2011.

Karna, Dr.Surendra Labh, Bhawani Prasad Khanal and Neelam Prasad Chaulagain. Economics. Kathmandu: Jupiter Publisher and Distributors Pvt. Ltd, 2070.

Khanal, Dr. Rajesh Keshar, et al. Economics II. Kathmandu: Januka Publication Pvt. Ltd., 2013.

  1. Laws of return to scale is a long-run concept. It is also called long run production function.

The production function shows 3 types of relationship in long run they are:

  1. Increase returns to scale
  2. Decreasing returns to scale
  3. Constant returns to scale
.

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