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Returns to scale for Managerial Economics Mcom Delhi University

Returns to scale for Managerial Economics Mcom Delhi University

Returns to scale for Managerial Economics Mcom Delhi University

In economics, returns to scale and economies of scale are related but different terms that describe what happens as the scale of production increases in the long run, when all input levels including physical capital usage are variable (chosen by the firm). The term returns to scale arises in the context of a firm’s production function. It explains the behavior of the rate of increase in output (production) relative to the associated increase in the inputs (the factors of production) in the long run. In the long run all factors of production are variable and subject to change due to a given increase in size (scale). While economies of scale show the effect of an increased output level on unit costs, returns to scale focus only on the relation between input and output quantities.

The laws of returns to scale are a set of three interrelated and sequential laws: Law of Increasing Returns to Scale, Law of Constant Returns to Scale, and Law of Diminishing returns to Scale. If output increases by that same proportional change as all inputs change then there are constant returns to scale (CRS). If output increases by less than that proportional change in inputs, there are decreasing returns to scale (DRS). If output increases by more than than proportional change in inputs, there are increasing returns to scale (IRS). A firm’s production function could exhibit different types of returns to scale in different ranges of output. Typically, there could be increasing returns at relatively low output levels, decreasing returns at relatively high output levels, and constant returns at one output level between those ranges.

In mainstream microeconomics, the returns to scale faced by a firm are purely technologically imposed and are not influenced by economic decisions or by market conditions (i.e., conclusions about returns to scale are derived from the specific mathematical structure of the production function in isolation).

Returns to scale for Managerial Economics Mcom Delhi University

Law of Returns to Scale : Definition, Explanation and Its Types!

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.

Definition:

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

“Returns to scale relates to the behaviour of total output as all inputs are varied and is a long run concept”. Leibhafsky

Returns to scale are of the following three types:

1. Increasing Returns to scale.

2. Constant Returns to Scale

3. Diminishing Returns to Scale

Explanation:

In the long run, output can be increased by increasing all factors in the same proportion. Generally, laws of returns to scale refer to an increase in output due to increase in all factors in the same proportion. Such an increase is called returns to scale.

Suppose, initially production function is as follows:

P = f (L, K)

Now, if both the factors of production i.e., labour and capital are increased in same proportion i.e., x, product function will be rewritten as.

http://cdn.economicsdiscussion.net/wp-content/uploads/2015/05/clip_image00213.jpg

The above stated table explains the following three stages of returns to scale:

1. Increasing Returns to Scale:

Increasing returns to scale or diminishing cost refers to a situation when all factors of production are increased, output increases at a higher rate. It means if all inputs are doubled, output will also increase at the faster rate than double. Hence, it is said to be increasing returns to scale. This increase is due to many reasons like division external economies of scale. Increasing returns to scale can be illustrated with the help of a diagram 8.

 http://cdn.economicsdiscussion.net/wp-content/uploads/2015/05/clip_image0049.jpg

In figure 8, OX axis represents increase in labour and capital while OY axis shows increase in output. When labour and capital increases from Q to Q1, output also increases from P to P1 which is higher than the factors of production i.e. labour and capital.

2. Diminishing Returns to Scale:

Diminishing returns or increasing costs refer to that production situation, where if all the factors of production are increased in a given proportion, output increases in a smaller proportion. It means, if inputs are doubled, output will be less than doubled. If 20 percent increase in labour and capital is followed by 10 percent increase in output, then it is an instance of diminishing returns to scale.

The main cause of the operation of diminishing returns to scale is that internal and external economies are less than internal and external diseconomies. It is clear from diagram 9.

Returns to scale for Managerial Economics Mcom Delhi University

http://cdn.economicsdiscussion.net/wp-content/uploads/2015/05/clip_image00610.jpg

In this diagram 9, diminishing returns to scale has been shown. On OX axis, labour and capital are given while on OY axis, output. When factors of production increase from Q to Q1 (more quantity) but as a result increase in output, i.e. P to P1 is less. We see that increase in factors of production is more and increase in production is comparatively less, thus diminishing returns to scale apply.

3. Constant Returns to Scale:

Constant returns to scale or constant cost refers to the production situation in which output increases exactly in the same proportion in which factors of production are increased. In simple terms, if factors of production are doubled output will also be doubled.

In this case internal and external economies are exactly equal to internal and external diseconomies. This situation arises when after reaching a certain level of production, economies of scale are balanced by diseconomies of scale. This is known as homogeneous production function. Cobb-Douglas linear homogenous production function is a good example of this kind. This is shown in diagram 10. In figure 10, we see that increase in factors of production i.e. labour and capital are equal to the proportion of output increase. Therefore, the result is constant returns to scale.

Returns to scale for Managerial Economics Mcom Delhi University

http://cdn.economicsdiscussion.net/wp-content/uploads/2015/05/clip_image007.jpg

Returns to scale for Managerial Economics Mcom Delhi University

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Returns to scale for Managerial Economics Mcom Delhi University

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