Introduction:
The theory of production basically
determines how the producer, given the state of technology, combines various
inputs economically to produce a definite amount of output efficiently. In the production process, the firm converts a combination of inputs or
factors of production, into output or finished products.
In economics, by production, we mean the
process by which man utilizes or converts nature's resources, working upon
them to make them satisfy human wants. In other words, production is any
economic activity directed towards satisfying people's wants by converting physical inputs into physical outputs. Whether it is making material goods or providing any service, it is included in production
provided it satisfies some people's wants. For example, if the making of cloth by an
individual worker is production, the retailer's service who delivers it to
consumers is also production. Similarly, the work of doctors, lawyers,
teachers, actors, dancers, etc., is production since the services are provided
by them to satisfy the wants of those who pay for them. The want satisfying
power of goods and services is called utility. Therefore, production can also be defined
as the creation or addition of utility. The money expenses incurred in the production process, i.e., transforming resources into finished products constitute
the cost of production.
Factors of Production:
The factors of production may be defined as
resources that help the firms to produce goods and services. In other words,
the resources required to produce a given product are called the factors of
production. Production is done by combining the various factors of the product.
According to Marshall, the four major factors of production are:
i.
Land
ii.
Labour
iii.
Capital
iv. Entrepreneurship
Production Function:
The functional relationship between input and
output is known as Production Function. The production function states the maximum quantity of output that can be produced from any selected combinations
of inputs. In other words, it states the minimum quantities of input that are
necessary to produce a given quantity of output. It is defined for a given
state of technology. The production function can be expressed in the form of an equation in which the output is the dependent variable and inputs are the
independent variables. The equation is expressed as follows:
Where,
Q à Output
L à Labour
K à Capital
T à Level of technology
n à Other inputs employed in the production
Thus, the production function expresses the relationship between the quantity of output and the quantities of the various inputs used for production. There are two types of a production function, i.e. short-run production and long-run production function.
Total, Average and Marginal Products (2):
Total Product (TP): Total product refers to the total output produced.
Average Product of a factor (AP): Average Product equals total product divided by the total quantity of inputs employed.
Average Product of labour (APL): Average Product of labour equals total product divided by the total quantity of labour employed.
Average Product of capital (APK): Average Product of capital equals total product divided by the total quantity of capital employed.
Marginal Product (MP) of a factor: Marginal product of a factor is the extra output added for each additional unit of input while holding all other inputs constant.
Marginal Product of labour (MPL): Marginal product of labour is the extra output added for each additional unit of labour employed while holding all other inputs such as capital, land, etc., constant.
Marginal Product of capital (MPK): Marginal product of capital is the extra output added for each additional unit of capital employed while holding all other inputs such as labour, land, etc., constant.
The Law of Variable Proportions/Law of Diminishing Returns: Short-Run Analysis of Production:
In the short run, the output may be increased by using more variable factor(s), while capital (and possibly other factors) are kept constant. The marginal product of the variable factor(s) will eventually decline as more quantities of this factor are combined with the other constant factors. The expansion of output with one factor (at least) constant is described by the law of (eventually) diminishing returns of the variable factor, often referred to as the law of variable proportions.
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. The ranges of increasing returns (to a factor) and the range of negative productivity are not equilibrium ranges of output.
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. On the other hand, if 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. Thus, in general, the productivity of a single-variable factor (ceteris paribus) is diminishing.
Laws of Returns to Scale: Long-Run Analysis of Production:
Introduction:
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, the output may be increased by changing all factors by the same proportion or by different proportions. The traditional theory of production concentrates on the first case, that is, the study of output as all inputs change by the same proportion. The term ‘returns to scale’ refers to the changes in output as all factors change by the same proportion. They are of three types:
Constant returns to scale denote a case where a change in all inputs leads to a proportional change in output. For example, if labour, land, capital, and other inputs are doubled, then the output would also double under constant returns to scale. Many handicraft industries (such as haircutting in America or handloom operations in a developing country) show constant returns.
Increasing returns to scale (also called economies of scale) arise when an increase in all inputs leads to a more-than-proportional increase in the level of output. For example, an engineer planning a small-scale chemical plant will generally find that increasing the inputs of labour, capital, and materials by 10 per cent will increase the total output by more than 10 per cent. Engineering studies have determined that many manufacturing processes enjoy modestly increasing returns to scale for plants up to the largest size used today.
Decreasing returns to scale occur when a balanced increase of all inputs leads to a less than proportional increase in total output. In many processes, scaling-up may eventually reach a point beyond which inefficiencies set in. These might arise because the costs of management or control become large. One case had occurred in electricity generation, where firms found that when plants grew too large, risks of plant failure grew too large.
Many productive activities involving natural resources, such as growing wine grapes or providing clean drinking water to a city, show decreasing returns to scale.
Suppose we start from an initial level of inputs and output, and we increase all the factors by the same proportion k. We will clearly obtain a new level of output
, higher than the original level,
,
If X* increases by the same proportion k as the inputs, we say that there are constant returns to scale.
If X* increases less than proportionally with the increase in the factors, we have decreasing returns to scale.
If X* increases more than proportionally with the increase in the factors, we have increasing returns to scale.
Graphical presentation of the returns to scale for a homogeneous production function (3):
The returns to scale may be shown graphically by the distance (on an isocline) between successive ‘multiple-level-of-output’ isoquants, that is, isoquants that show levels of output which are multiples of some base level of output, e.g., X, 2X, 3X, etc.
Constant returns to scale: 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 3.18).
Increasing returns to scale: The distance between consecutive multiple-isoquants decreases. By doubling the inputs, the output is more than doubled. For example, in figure 3.20, doubling K and L leads to point b’, which lies on an isoquant above the one denoting 2X.
Decreasing returns to scale: The distance between consecutive multiple-isoquants increases. By doubling the inputs, output increases by less than twice its original level. In figure 3.19, the point a’, defined by 2K and 2L, lies on an isoquant below the one showing 2X.
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 overall ranges of output, either constant returns everywhere, decreasing returns everywhere, or increasing returns everywhere.
However, the technological conditions of production may be such that returns to scale (6) may vary over different ranges of output. Over some range, we may have constant returns to scale, while we may have increasing or decreasing returns to scale over another range. For example, in figure 3.21, we see that up to the level of output, 4X returns to scale are constant; beyond that output level, returns to scale are decreasing. Production functions with varying returns to scale are difficult to handle,, and economists usually ignore them for the analysis of production.
References
1. Samuelson, P. A., & Nordhuas, W.D (1992), Economics (14th edition). McGraw Hill International edition, U.S.
2. Samuelson, P. A., & Nordhuas, W.D (2013), Microeconomics (19th edition). McGraw Hill Education (India) Pvt. Ltd.
3. Samuelson, P. A., & Nordhuas, W.D (2010), Macroeconomics (19th edition). McGraw Hill Education (India) Pvt. Ltd.
4. Koutsoyiannis, A. (1990), Modern Microeconomics (2nd edition). Macmillan, London.
5. Henderson, J. M. and R. E. Quandt (1980), Microeconomic Theory: A Mathematical Approach (3rd edition). McGraw Hill, New Delhi.
6. Dwivedi, D. N. (2016), Microeconomics: Theory and Applications (3rd edition). Vikas Publication House Pvt. Ltd. Noida (UP), India.
Notes:
1. The relationship between the quantity of output (such as wheat, steel, or automobiles) and the quantity of inputs (labour, land, and capital) is called the production function.
2. Total product is the total output produced. The average product equals total output divided by the total quantity of inputs. Thus, we can calculate the marginal product of a factor as the extra output added for each additional unit of input while holding all other inputs constant.
3. In most empirical studies of the laws of returns, homogeneity is assumed to simplify the statistical work. Homogeneity, however, is a special assumption, in some cases a very restrictive one. For example, when the technology shows increasing or decreasing returns to scale, it may or may not imply a homogeneous production function.
4. Causes of increasing returns to scale: The increasing returns to scale are due to technical and/or managerial indivisibilities. Usually, most processes can be duplicated, but it may not be possible to halve them. One of the basic characteristics of advanced industrial technology is ‘mass-production methods over large sections of the manufacturing industry. ‘Mass-production’ methods (like the assembly line in the motor-car industry) are processes available only when the level of output is large. They are more efficient than the best available processes for producing small levels of output.
5. Causes of decreasing returns to scale: The most common causes are ‘diminishing returns to management’. The ‘management’ is responsible for coordinating the activities of the various sections of the firm. Even when authority is delegated to individual managers (production manager, sales manager, etc.) the final decisions must be taken from the final ‘centre of top management' (Board of Directors). As the output grows, top management becomes eventually overburdened and hence less efficient in its role as coordinator and ultimate decision-maker. Although advances in management science have developed ‘plateaux’ of management techniques, it is still a commonly observed fact that as firms grow beyond the appropriate optimal ‘plateaux’, management diseconomies creep in.
Another cause for decreasing returns may be found in the exhaustible natural resources: doubling the fishing fleet may not lead to a doubling of the catch of fish, or doubling the plant in mining or on an oil-extraction field may not lead to a doubling of output.
6. With a non-homogeneous production function, returns to scale may be increasing, constant or decreasing. Still, their measurement and graphical presentation are not as straightforward as in the case of the homogeneous production function. The isoclines will be curves over the production surface, and along with each one of them, the K/L ratio varies.
7. Returns to a Factor: A return to a factor implies the increase in the output due to the increase in some of the inputs while keeping all other inputs as fixed. It is applicable in the short run. Taking labour, land and capital as the inputs for production, a production function where the quantities of some inputs such as capital and land are kept constant and the quantity of one input such as labour is varied is known as Short-run production function. The study of short-run production is the subject matter of the law of diminishing returns which is also known as the law of variable proportions or returns to a factor. If labour is varied in the production function and all other factors are kept constant, then the resultant increase in output is known as returns to labour.
8. Returns to Scale: Returns to scale are applicable in the long run. The long-run production function is a study of the production function where all inputs are varied in the same proportion. Returns to scale is a study of how output responds when all the factors of production are increase or decrease in the same proportion. An increase in the scale means that all inputs or factors of production are increased in a given proportion. Returns to Scale are of three types:
- Increasing Returns to Scale
- Constant Returns to Scale
- Decreasing Returns to Scale
Increasing Returns to Scale (4): Increasing returns to scale implies that output increases in a greater proportion than the increase in inputs. In other words, if inputs, labour and capital are increased by 100% and the resulting output increases by 250%, then we have a situation of increasing returns to scale. On the other hand, if all inputs are doubled, then the output increases by more than doubles.
Inputs (Units) | Outputs (Units) | |
Labour (L) | Capital (K) | |
10 | 10 | 100 |
20 | 20 | 250 |
Constant Returns to Scale (5): A constant return to scale implies that output increase by the same proportion as the increase in inputs. In other words, if inputs, labour and capital are increased by 100% and the resulting output increases by 200%, then we have a situation of constant returns to scale. If all inputs are doubled, then output also doubles.
Inputs (Units) | Outputs (Units) | |
Labour (L) | Capital (K) | |
10 | 10 | 100 |
20 | 20 | 200 |
Decreasing Returns to Scale: Decreasing returns to scale implies that output increases in a smaller proportion than the increase in inputs. In other words, if inputs, labour and capital are increased by 100% and the resulting output increases by 180%, then we have a situation of decreasing returns to scale. If all inputs are doubled, then the output increases by less than doubles.
Inputs (Units) | Outputs (Units) | |
Labour (L) | Capital (K) | |
10 | 10 | 100 |
20 | 20 | 180 |
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