# Law Of Variable Proportions And Returns To Scale Pdf

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- Diminishing returns
- Production – CBSE Notes for Class 12 Micro Economics
- Diminishing Marginal Returns vs. Returns to Scale: What's the difference?
- Theory of Production

*The functional relationship between physical inputs and physical output of a firm is called production function. Production is also defined as 'transformation of physical inputs into physical output.*

Diminishing returns , also called law of diminishing returns or principle of diminishing marginal productivity , economic law stating that if one input in the production of a commodity is increased while all other inputs are held fixed, a point will eventually be reached at which additions of the input yield progressively smaller, or diminishing, increases in output. In the classic example of the law, a farmer who owns a given acreage of land will find that a certain number of labourers will yield the maximum output per worker. If he should hire more workers, the combination of land and labour would be less efficient because the proportional increase in the overall output would be less than the expansion of the labour force. The output per worker would therefore fall.

## Diminishing returns

The laws of production describe the technically possible ways of increasing the level of production. Output may increase in various ways. Output can be increased by changing all factors of production. Clearly this is possible only in the long run. Thus the laws of returns to scale refer to the long-run analysis of production. In the short run output may be increased by using more of the variable factor s , while capital and possibly other factors as well are kept constant.

The marginal product of the variable factors will decline eventually as more and more quantities of this factor are combined with the other constant factors. In the long run expansion of output may be achieved by varying all factors. In the long run all factors are variable. The laws of returns to scale refer to the effects of scale relationships.

In the long run output may be increased by changing all factors by the same proportion, or by different proportions. Traditional theory of production concentrates on the first case, that is, the study of output as all inputs change by the same proportion.

If k cannot be factored out, the production function is non-homogeneous. Thus A homogeneous function is a function such that if each of the inputs is multiplied by k, then k can be completely factored out of the function. The power v of k is called the degree of homogeneity of the function and is a measure of the returns to scale. This production function is sometimes called linear homogeneous. Returns to scale are measured mathematically by the coefficients of the production function.

For example, in a Cobb-Douglas function. For a homogeneous production function the returns to scale may be represented graphically in an easy way. Before explaining the graphical presentation of the returns to scale it is useful to introduce the concepts of product line and isocline. To analyze the expansion of output we need a third dimension, since along the two- dimensional diagram we can depict only the isoquant along which the level of output is constant.

Instead of introducing a third dimension it is easier to show the change of output by shifts of the isoquant and use the concept of product lines to describe the expansion of output. A product line shows the physical movement from one isoquant to another as we change both factors or a single factor.

A product curve is drawn independently of the prices of factors of production. It does not imply any actual choice of expansion, which is based on the prices of factors and is shown by the expansion path. The product line describes the technically possible alternative paths of expanding output. What path will actually be chosen by the firm will depend on the prices of factors.

The product curve passes through the origin if all factors are variable. If only one factor is variable the other being kept constant the product line is a straight line parallel to the axis of the variable factor figure 3. Among all possible product lines of particular interest are the so-called isoclines. An isocline is the locus of points of different isoquants at which the MRS of factors is constant. If the production function is homogeneous the isoclines are straight lines through the origin.

If the production function is non-homogeneous the isoclines will not be straight lines, but their shape will be twiddly.

Along any isocline the distance between successive multiple- isoquants is constant. Doubling the factor inputs achieves double the level of the initial output; trebling inputs achieves treble output, and so on figure 3.

The distance between consecutive multiple-isoquants increases. By doubling the inputs, output increases by less than twice its original level. In figure 3. The distance between consecutive multiple-isoquants decreases. By doubling the inputs, output is more than doubled. Returns to scale are usually assumed to be the same everywhere on the production surface, that is, the same along all the expansion-product lines.

All processes are assumed to show the same returns over all ranges of output either constant returns everywhere, decreasing returns everywhere, or increasing returns everywhere. Over some range we may have constant returns to scale, while over another range we may have increasing or decreasing returns to scale.

Production functions with varying returns to scale are difficult to handle and economists usually ignore them for the analysis of production. With a non-homogeneous production function returns to scale may be increasing, constant or decreasing, but their measurement and graphical presentation is not as straightforward as in the case of the homogeneous production function.

In most empirical studies of the laws of returns homogeneity is assumed in order to simplify the statistical work. Homogeneity, however, is a special assumption, in some cases a very restrictive one. When the technology shows increasing or decreasing returns to scale it may or may not imply a homogeneous production function. Usually most processes can be duplicated, but it may not be possible to halve them. They are more efficient than the best available processes for producing small levels of output.

The larger-scale processes are technically more productive than the smaller-scale processes. Clearly if the larger-scale processes were equally productive as the smaller-scale methods, no firm would use them: the firm would prefer to duplicate the smaller scale already used, with which it is already familiar.

Although each process shows, taken by itself, constant returns to scale, the indivisibilities will tend to lead to increasing returns to scale. The switch from the smaller scale to the medium-scale process gives a discontinuous increase in output from 49 tons produced with 49 units of L and 49 units of K, to tons produced with 50 men and 50 machines.

If the demand in the market required only 80 tons, the firm would still use the medium-scale process, producing units of X, selling 80 units, and throwing away 20 units assuming zero disposal costs. This is one of the cases in which a process might be used inefficiently, because this process operated inefficiently is still relatively efficient compared with the small-scale process.

Similarly, the switch from the medium-scale to the large-scale process gives a discontinuous increase in output from 99 tons produced with 99 men and 99 machines to tons produced with men and machines. This is because the large-scale process, even though inefficiently used, is still more productive relatively efficient compared with the medium-scale process.

Even when authority is delegated to individual managers production manager, sales manager, etc. As the output grows, top management becomes eventually overburdened and hence less efficient in its role as coordinator and ultimate decision-maker. If one factor is variable while the other s is kept constant, the product line will be a straight line parallel to the axis of the variable factor.

In general if one of the factors of production usually capital K is fixed, the marginal product of the variable factor labour will diminish after a certain range of production.

We said that the traditional theory of production concentrates on the ranges of output over which the marginal products of the factors are positive but diminishing. If the production function is homogeneous with constant or decreasing returns to scale everywhere on the production surface, the productivity of the variable factor will necessarily be diminishing.

If, however, the production function exhibits increasing returns to scale, the diminishing returns arising from the decreasing marginal product of the variable factor labour may be offset, if the returns to scale are considerable.

This, however, is rare. In general the productivity of a single-variable factor ceteris paribus is diminishing. Let us examine the law of variable proportions or the law of diminishing productivity returns in some detail. If the production function is homogeneous with constant returns to scale everywhere, the returns to a single-variable factor will be diminishing.

This is implied by the negative slope and the convexity of the isoquants. With constant returns to scale everywhere on the production surface, doubling both factors 2K, 2L leads to a doubling of output. However, if we keep K constant at the level K and we double only the amount of L, we reach point c, which clearly lies on a lower isoquant than 2X. If we wanted to double output with the initial capital K, we would require L units of labour. Hence doubling L, with K constant, less than doubles output.

The variable factor L exhibits diminishing productivity diminishing returns. If the production function is homogeneous with decreasing returns to scale, the returns to a single-variable factor will be, a fortiori, diminishing. Since returns to scale are decreasing, doubling both factors will less than double output. If we double only labour while keeping capital constant, output reaches the level c, which lies on a still lower isoquant.

If the production function shows increasing returns to scale, the returns to the single- variable factor L will in general be diminishing figure 3.

Figure 3. Article Shared by Trisha. Related Articles. Theory of Costs Short Notes.

## Production – CBSE Notes for Class 12 Micro Economics

In traditional production theory resources used for the production of a product are known as factors of production. Factors of production are now termed as inputs which may mean the use of the services of land, labour, capital and organization in the process of production. The term output refers to the commodity produced by the various inputs. Production theory concerns itself with the problems of combining various inputs, given the state of technology, in order to produce a stipulated output. The technological relationships between inputs and outputs are known as production functions. The inputs are what the firm buys, namely productive resources, and outputs are what it sells.

Principles and Theories of Micro Economics. Definition and Explanation of Economics. Theory of Consumer Behavior. Indifference Curve Analysis of Consumer's Equilibrium. Theory of Demand. Theory of Supply.

## Diminishing Marginal Returns vs. Returns to Scale: What's the difference?

In order to produce goods and services which can be sold, and generate revenue and profits , a firm must purchase or hire scarce inputs, which are its factors of production. These factors can be fixed or variable. Fixed factors are those that do not change as output is increased or decreased, and typically include premises such as its offices and factories, and capital equipment such as machinery and computer systems.

This chapter gives a clear account of terms like Production function, short period, long period, fixed factors, variable factors, concepts like total product, average product, marginal product and their interrelationships. Law of variable proportion and its phases are studied with reasoning. The relationship between physical input and physical output of a firm is generally referred to as production function. Variable factors refer to those factors, which can be changed in the short run.

The laws of production describe the technically possible ways of increasing the level of production. Output may increase in various ways. Output can be increased by changing all factors of production. Clearly this is possible only in the long run. Thus the laws of returns to scale refer to the long-run analysis of production.

### Theory of Production

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In economics, production theory explains the principles in which the business has to take decisions on how much of each commodity it sells and how much it produces and also how much of raw material ie. It defines the relationships between the prices of the commodities and productive factors on one hand and the quantities of these commodities and productive factors that are produced on the other hand. Production is a process of combining various inputs to produce an output for consumption.

Production can be increased by changing one or more of the inputs. The returns to scale are constant when output increases in the same proportion as the increase in the quantities of inputs. The returns to scale are increasing when the increase in output is more than proportional to the increase in inputs.

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Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy. See our Privacy Policy and User Agreement for details. Published on Jul 16, This presentation puts emphasis on Law of Variable proportion and Law of Returns to Scale It also puts light on production function, cost function, etc. SlideShare Explore Search You.

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Joseph L.A. Laws of Returns to Scale: Long-Run Analysis of Production: · B. The Law of Variable Proportions: Short-Run Analysis of Production.

Ogier M.THE LAW OF VARIABLE PROPORTIONS. THE LAW OF RETURNS TO SCALE. Dr. D. K. More. Asso. Professor. Dept. of Business Economics. Arts & Commerce.

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