Production - Business Economics

Production theory forms the foundation for the theory of supply. Managerial decision making involves four types of production decisions:

  1. Whether to produce or to shut down?
  2. How much output to produce?
  3. What input combination to use?
  4. What type of technology to use?

Production refers to the transformation of inputs into outputs (or products). It involves transformation of inputs such as capital, equipment, labour, and land into output – goods and services. In economic sense production process may take a variety of forms other than manufacturing eg transporting and all types of services.

An input is a resource that a firm uses in its production process for the purpose of creating a good or service. It is a good or service that goes into the production process.

Output refers to the number of units of the commodity produced. It is a good or service that comes out of the production process.

Factor Inputs

Land: In economics, land as a factor of production does not refer only to the surface of land but to all gifts of nature, such as rivers, oceans, climate, mountains, fisheries, mines, forests, etc. In the words of Dr Marshall. By land is meant…..materials and forces which nature gives freely for man’s aid, in land, water, in air, light and heat.

Labour: Labour refers to all mental and physical work undertaken for some monetary reward. It includes the services of a factory worker, a doctor, a teacher, a lawyer, an engineer, an officer, etc. But labour does not include any work done for leisure or which does not carry any monetary reward.

A person painting for leisure, singing a song to entertain his friends, or attending to his garden would not be considered to have done any labour in the sense of economics.

On the other hand, if a person sells his paintings, a singer sings a song for a film and a gardener looks after a garden in payment for money, their services are regarded as labour. Thus labour is essential for production.

Capital: Capital means all man-made resources. It comprises all wealth other than land which is used for further production of wealth. It includes tools, implements, machinery, seeds, raw materials and means of transport such as roads, railways, canals, etc.

In modern usage, capital not only refers to physical capital but also to human capital which is the process of increasing knowledge, the skills and capacities of all people of the country.

It is this human capital which is regarded more important than physical capital in production these days. As pointed out by Professor Galbraith, We now get the larger part of our industrial growth not from more capital investment but from investment in men and improvements brought about by improved men.

Entrepreneur: Factors of production viz. land, labour and capital are scattered at different places. All these factors have to be assembled together. This work is done by enterprise through entrepreneur.

This is an ‘Organization Function’. Organization function is the work of bringing the required factors together and making them work harmoniously.

The term ‘Entrepreneur’ has been derived from a French word ‘Entreprendre’ meaning to undertake certain activities. Entrepreneur has to bear risks and uncertainties. For facing uncertainties he may get profit or may incur loss. This is the ‘Risk Bearing Function’ and entrepreneur is the risk bearer

In short run these inputs can be classified into Fixed Inputs & Variable Inputs.

  • Fixed inputs remain fixed (constant) up to certain level of output. Their supply is inelastic in the short run. A Fixed input is defined as one whose quantity cannot be changed instantaneously in response to changes in market conditions requiring an immediate change in output. Example- Buildings, major capital equipment and managerial personnel.
  • Variable inputs change with the change in output. Their supply is elastic in the short run. Variable input is one whose quantity can be changed readily when market conditions suggest that an immediate change in output is beneficial to the producer. Example- Raw materials and labour services.

The distinction between fixed and variable inputs exists only in the short run but in the long run all inputs become variable.

Short Run Vs Long Run

 Short run refers to a period of time in which supply of certain inputs i.e., plant, building and machinery etc. is fixed or inelastic. The Short Run is a period so brief that the amount of at least one input is fixed.

Therefore, production of a commodity can be increased by increasing use of only variable inputs like labour and raw materials.

Very short run- all factors of production are inelastic in supply.

Long run refers to a time period in which the supply of all the inputs is elastic or variable. The Long Run is distinguished from the short run by being a period of time long enough for all inputs, or factors of production, to be variable as far as an individual firm is concerned.

Very long run refers to a time period in which the technology of production is also subject to change. Thus the production function changes.

Short run and long run are economists jargon. They do not refer to any specific time period. The length of time necessary for all inputs to be variable may differ according to the nature of the industry and the structure of a firm.

While for some firms short run may be 3-5 years eg shipping, aircrafts, construction etc. but for others it can be few days, weeks and months.

Production Function

Production theory can be divided into short run theory or long run theory.

Hence, a production function is defined as the maximum amount of output that can be produced (through the use of a given production technology) with a given amount of input.

A production function indicates the highest output (Q) that a firm can produce for every specified combinations of inputs (physical relationship between inputs and output), while holding technology constant at some predetermined state.

In other words, Production Function is a mathematical expression which defines the various combination between the input that help in producing optimum output.

Mathematically, we represent a firm’s production function as: Q = f (L, N,K,T, t)

Where,

Q= Production function

L= Land, K= Capital, N= Labour, T= Technology and t= Time

The production function is based on the assumptions:

Technology is invariant– It means that it won’t change as per the production.

Firm’s utilise their input at maximum level of efficiency.

We assume that all units of L and K are homogeneous or identical

The Production Function in the Short Run

The short run is a time period in which the quantity of some inputs, called fixed factors, cannot be increased. So, it does not correspond to a specific number of months or years. A fixed factor is usually an element of capital (such as plant and equipment).

Therefore, in our production function capital is taken to be the fixed factor and labor the variable one. This aspect of Production function is known as Law of Variable Proportion.

The Production Function in the Long Run

The long run is a time period in which all inputs may be varied but in which the basic technology of production cannot be changed. This aspect of Production function is known as Law of Returns to scale.

 The long run corresponds to a situation that the firm faces when is planning to go into business (to expand the scale of its operations) Like the short run, the long run does not correspond to a specific length of time

Law of Variable Proportions

The law of variable proportion is one of the fundamental laws of economics. The law of variable proportion is the study of short run production function with some factors fixed and some factors variable.

As the quantity of different units of only one factor input is increased to a given quantity of fixed factors, beyond a particular point, the marginal, average and total output eventually decline.

The law of variable proportions is the new name for the famous “Law of Diminishing Returns” of classical economists. This law is stated by various economists in the following manner –

According to Prof. Benham, “As the proportion of one factor in a combination of factors is increased, after a point, first the marginal and then the average product of that factor will diminish”.

In the words of Prof. Marshall “An increase in the quantity of a variable factor added to fixed factors, at the end results in a less than proportionate increase in the amount of product, given technical conditions.”

The change in factor proportion and its effect on output forms the subject- matter of the law of variable proportions.

With disproportionate combination of factors, the returns may initially increase then remain constant for sometime and ultimately diminishes. Therefore, the law of variable proportion is called non-proportional returns.

Assumptions of the Law:

  • The state of technology is assumed be given and unchanged.
  • The law specially operates in the short run because some factors are fixed and the proportion between factors is disturbed.
  • Variable factor units are homogeneous or identical in amount and quality.
  • The law is based on the possibility of varying the proportions in which the various factors can be combined to produce a product.
  • The law will hold good for short and given period.
  • Input prices remain unchanged.
  • Output is measured in physical units.
  • Factors are indivisible in nature.

Explanation of the law: The law can be explained with an example. Supposing there are two factors-land and labor. 

It can be seen from the table that upto the use of 3 units of labour, total product increases at an increasing rate and beyond the third unit total product increases at a diminishing rate.

It can be seen from the table that the marginal product of labour initially rises and beyond the use of three units of labour, it starts diminishing. The use of six units of labour does not add anything to the total production of wheat. Hence, the marginal product of labour has fallen to zero.

Beyond the use of six units of labour, total product diminishes and therefore marginal product of labour becomes negative. Regarding the average product of labour, it rises up to the use of third unit of labour and beyond that it is falling throughout.

Three Stages of the Law of Variable Proportions: These stages are illustrated in the following figure where labour is measured on the X-axis and output on the Y-axis.

Stage 1. Stage of Increasing Returns: In this stage, total product increases at an increasing rate up to a point. This is because the efficiency of the fixed factors increases as additional units of the variable factors are added to it.

In the figure, from the origin to the point F, slope of the total product curve TP is increasing at increasing rate. In this stage MP is increasing and reaches its maximum point and same is the case with AP, It is also increasing and reaches the point of maximum.

Stage 2. Stage of Diminishing Returns: In this stage, total product continues to increase but at a diminishing rate until it reaches its maximum point H where the second stage ends. In this stage both the marginal product and average product of labour are diminishing but are positive.

This is because the fixed factor becomes inadequate relative to the quantity of the variable factor. At the end of the second stage, i.e., at point M marginal product of labour is zero which corresponds to the maximum point H of the total product curve TP. This stage is important because the firm will seek to produce in this range.

Stage 3. Stage of Negative Returns: In stage 3, total product declines and therefore the TP curve slopes downward. As a result, marginal product of labour is negative and the MP curve falls below the X-axis. As MP is negative this stage is also known as the stage of negative return.

In this stage the proportion of variable factor (labour) is  very much relative higher  to the fixed factor. Which leads to inappropriate proportion between both the factors of production.

Causes of Operation of Law of Variable Proportion/ Why does this law operate?

The various reasons for 3 phases of law of variable proportions are:

Reasons for Increasing Returns to a Factor (Phase 1):

There are three important reasons for the operation of increasing returns to a factor:

  1. Better Utilization of the Fixed Factor:

In the first phase, the supply of the fixed factor (say, land) is too large, whereas variable factors are too few.

So, the fixed factor is not fully utilised. When variable factors are increased and combined with fixed factor, then fixed factor is better utilised and output increases at an increasing rate.

  1. Increased Efficiency of Variable Factor:

When variable factors are increased and combined with the fixed factor, then former is utilised in a more efficient manner.

At the same time, there is greater cooperation and high degree of specialization between different units of the variable factor.

  1. Indivisibility of Fixed Factor:

Generally, the fixed factors which are combined with variable factors are indivisible. Such factors cannot be divided into smaller units.

Once an investment is made in an indivisible fixed factor, then addition of more and more units of variable factor, improves the utilisation of fixed factor. The increasing returns apply as long as optimum level of combination between variable and fixed factor is achieved.

Reasons for Diminishing Returns to a Factor (Phase 2):

The main reasons for occurrence of diminishing returns to a factor are:

  1. Optimum Combination of Factors:

Among the different combinations between variable and fixed factor, there is one optimum combination, at which total product (TP) is maximum. After making the optimum use of fixed factor, the marginal return of variable factor begins to diminish.

For example, if a machinery (fixed factor) is at its optimum use, when 4 labours are employed, then addition of one more labour will increase TP by very less amount and MP will start diminishing.

  1. Imperfect Substitutes:

Diminishing returns to a factor occurs because fixed and variable factors are imperfect substitutes of one another. There is a limit to the extent of which one factor of production can be substituted for another.

For example, labour can be substituted in place of capital or capital can be substituted in place of labour till a particular limit. But, beyond the optimum limit, they become imperfect substitutes of one another, which leads to diminishing returns.

Reasons for Negative Returns to a Factor (Phase 3):

The main reasons for occurrence of negative returns to a factor are:

  1. Limitation of Fixed Factor:

The negative returns to a factor apply because some factors of production are of fixed nature, which cannot be increased with increase in variable factor in the short run.

  1. Poor Coordination between Variable and Fixed Factor:

When variable factor becomes too excessive in relation to fixed factor, then they obstruct each other. It leads to poor coordination between variable and fixed factor. As a result, total output falls instead of rising and marginal product becomes negative.

  1. Decrease in Efficiency of Variable Factor:

With continuous increase in variable factor, the advantages of specialization and division of labour start diminishing. It results in inefficiencies of variable factor, which is another reason for the negative returns to eventually set in.

Importance of the Law of Variable Proportion:

The law of variable proportions has vast general applicability. Briefly:

  • It is helpful in understanding clearly the process of production. It explains the input output relations. We can find out by-how much the total product will increase as a result of an increase in the inputs.
  • It help the producer to work most ideal combination of input factors at reasonable prices.
  • It is useful for short run production planning at micro level.
  • The law tells us that the tendency of diminishing returns is found in all sectors of the economy which may be agriculture or industry.
  • The law tells us that any increase in the units of variable factor will lead to increase in the total product at a diminishing rate. The elasticity of the substitution of the variable factor for the fixed factor is not infinite.

From the law of variable proportions, it may not be understood that there is no hope for raising the standard of living of mankind.

The fact, however, is that we can suspend the operation of diminishing returns by continually improving the technique of production through the progress in science and technology

Law of Returns To Scale

The law of returns to scale is concerned with the scale of production. The scale of production of a firm is determined by the amount of factors units.

In the long run all factors are variable. The firm therefore can expand its production by using more of all inputs. When there is increase in the quantity of all factors in the long period, keeping the factor proportion constant, there is increase in the scale of production.

The concept of returns to scale explains the behavior of output when changes are made in the scale of production.

Thus, the relationship between quantities of output and the scale of production in the long run when all inputs are increased in the same proportion, is called law of returns to scale.

When inputs are increased proportionately i.e., scale is increased, there are three possibilities

  • Total output may increase more than proportionately as the inputs,
  • Total output may increase at same proportion as the inputs
  • Total output may increase less than proportionately as the inputs

Thus it indicates that there are three possible cases of returns to scale:

  • Increasing returns to scale,
  • Constant returns to scale and
  • Decreasing returns to scale.

 (1) Increasing Returns to Scale: If the output of a firm increases more than in proportion to an equal percentage increase in all inputs, the production is said to exhibit increasing returns to scale.

For example, if the amount of inputs are doubled and the output increases by more than double, it is said to be an increasing returns to scale. When there is an increase in the scale of production, it leads to lower average cost per unit produced as the firm enjoys economies of scale.

(2) Constant Returns to Scale: When all inputs are increased by a certain percentage, the output increases by the same percentage, the production function is said to exhibit constant returns to scale.

For example, if a firm doubles inputs, it doubles output. In case, it triples output. The constant scale of production has no effect on average cost per unit produced.

(3) Diminishing Returns to Scale:

The term ‘diminishing’ returns to scale refers to scale where output increases in a smaller proportion than the increase in all inputs.

For example, if a firm increases inputs by 100% but the output decreases by less than 100%, the firm is said to exhibit decreasing returns to scale. In case of decreasing returns to scale, the firm faces diseconomies of scale. The firm’s scale of production leads to higher average cost per unit produced.

The Laws of Returns to Scale

The laws of returns to scale can also be explained in terms of the isoquant approach. The laws of returns to scale refer to the effects of a change in the scale of factors (inputs) upon output in the long-run when the combinations of factors are changed in some proportion.

The returns to scale can be shown diagrammatically on an expansion path “by the distance 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., 100, 200, 300, etc.”

Increasing Returns to Scale:

Figure 24.11 shows the case of increasing returns to scale where to get equal increases in output, lesser proportionate increases in both factors, labour and capital, are required.

It follows that in the figure:

100 units of output require 3C +3L

200 units of output require 5C + 5L

300 units of output require 6C + 6L

So that along the expansion path OR, OA > AB > BC.

Causes of increasing returns to scale

  1. Indivisibilities in machines, management, labour, finance, etc: Some items of equipment or some activities have a minimum size and cannot be divided into smaller units. When a business unit expands, the returns to scale increase because the indivisible factors are employed to their full capacity.
  2. Specialisation and division of labour: When the scale of the firm expands there is wide scope for specialisation and division of labour. Work can be divided into small tasks and workers can be concentrated to narrower range of processes. For this, specialized equipment can be installed. Thus with specialization, efficiency increases and increasing returns to scale follow.
  3. Internal economies of production: It may be able to install better machines, sell its products more easily, borrow money cheaply, procure the services of more efficient manager and workers, etc. All these economies help in increasing the returns to scale more than proportionately.
  4. External economies: When the industry itself expands to meet the increased ‘long-run demand for its product, external economies appear which are shared by all the firms in the industry. When a large number of firms are concentrated at one place, skilled labour, credit and transport facilities are easily available. Subsidiary industries crop up to help the main industry. Trade journals, research and training centres appear which help in increasing the productive efficiency of the firms. Thus these external economies are also the cause of increasing returns to scale.

Decreasing Returns to Scale:

Figure 24.12 shows the case of decreasing returns where to get equal increases in output, larger proportionate increases in both labour and capital are required.

It follows that:

100 units of output require 2C + 2L

200 units of output require 5C + 5L

300 units of output require 9C + 9L

So that along the expansion path OR, OG < GH < HK.

Causes of decreasing returns to scale : All these factors tend to raise costs and the expansion of the firms leads to diminishing returns to scale so that doubling the scale would not lead to doubling the output.

  1. Indivisible factors may become inefficient and less productive.
  2. Internal and External diseconomies. Business may become unwieldy and produce problems of supervision and coordination. Large management creates difficulties of control and rigidities. To these internal diseconomies are added external diseconomies of scale. These arise from higher factor prices or from diminishing productivities of the factors. As the industry continues to expand the demand for skilled labour, land, capital, etc. rises. There being perfect competition, intensive bidding raises wages, rent and interest. Prices of raw materials also go up. Transport and marketing difficulties emerge.
  3. Increase in business risk: Due to increase in inflation level, changes in the economy and many other factors can lead to the risk in the business that can reduce the efficiency of the businessman and employees and thus result in the decrease in efficiency of employees and then they will produce less and leads to dimishing return to scale.
  4. Lack of entrepreneurial efficiency: If the entrepreneur is not a good leader, motivator and coordinator then he wont be able to manage the things properly which will give rise to decreasing return to scale.
  5. Unhealthy management and organization
  6. Imperfect factor substitutability
  7. Transport bottlenecks and Marketing difficulties.

Constant Returns to Scale:

Figure 24.13 shows the case of constant returns to scale. Where the distance between the isoquants 100, 200 and 300 along the expansion path OR is the same, i.e., OD = DE = EF. It means that if units of both factors, labour and capital, are doubled, the output is doubled. To treble output, units of both factors are trebled.

It follows that:

100 units of output require 1 (2C + 2L) = 2C + 2L

200 units of output require 2(2C + 2L) = 4C + 4L

300 units of output require 3(2C + 2L) = 6C + 6L

Causes of constant returns to scale:

  1. The returns to scale are constant when internal economies enjoyed by a firm are neutralised by internal diseconomies so that output increases in the same proportion.
  2. Another reason is the balancing of external economies and external diseconomies. Constant returns to scale also result when factors of production are perfectly divisible, substitutable, homogeneous and their supplies are perfectly elastic at given prices.

5 Major Differences between Returns to Scale and Returns to a factor Proportions

Law of Returns

1) Only one factor varies while all the rest are fixed.

2) The factor-proportion varies as more and more of the units of the variable factor are employed to increase output.

3) Returns to a factor or to variable proportions end up in negative returns.

Law of Return to Scale

  1. All or at least two factors vary.
  2. Factor proportion called scale does not vary. Factors are increased in same proportion to increase output.
  3. Returns to scale end up in decreasing returns

Isoquants – Production

An isoquant (isoproduct) is a curve on which the various combinations of labour and capital show the same output. According to Cohen and Cyert, “An iso-product curve is a curve along which the maximum achievable rate of production is constant.” It is also known as a production indifference curve or a constant product curve.

Just as indifference curve shows the various combinations of any two commodities that give the consumer the same amount of satisfaction (iso-utility), similarly an isoquant indicates the various combinations of two factors of production which give the producer the same level of output per unit of time.

Table 24.1 shows a hypothetical isoquant schedule of a firm producing 100 units of a good.

This Table 24.1 is illustrated on Figure 24.1 where labour units are measured along the X-axis and capital units on the K-axis. The first, second, third and the fourth combinations are shown as A, S, С and D respectively. Connect all these points and we have a curve IQ.

This is an isoquant. The firm can produce 100 units of output at point A on this curve by having a combination of 9 units of capital and 5 units of labour.

Similarly, point В shows a combination of 6 units of capital and 10 units of labour; point C,4 units of capital and’ 15 units of labour; and point D, a combination of 3 units of capital and 20 units of labour to yield the same output of 100 units.

An isoquant map shows a number of isoquants representing different amounts of output.

In Figure 24.1, curves IQ, IQ1 and IQ2 show an isoquant map. Starting from the curve IQ which yields 100 units of product, the curve IQ1, shows 200 units and the IQ2 curve 300 units of the product which can be produced with altogether different combinations of the two factors.

Properties of Isoquants

Isoquants possess certain properties which are similar to those of indifference curves.

(1) Isoquants are negatively inclined: Isoquant must slope downward to the right.

(2) An Isoquant lying above and to the right of another represents a higher output level. In Figure 24.3 combination В on IQ1 curve shows larger output than point A on the curve IQ.

The combination of ОС of capital and OL of labour yields 100 units of product while OC1 of capital and OL1 of labour produce 200 units.

Therefore, the isoquant IQ1 which lies above and to the right of the isoquant IQ, represents a larger output level.

(3) No two isoquants can intersect each other. The absurd conclusion that follows when two isoquants cut each other is explained with the aid of Figure 24.4. On the isoquant IQ, combination A =B. And on the isoquant IQ1 combination R=S. But combination S is preferred to combination B, being on the higher portion of isoquant IQ1.

On the other hand, combination A is preferred to R, the former being on the higher portion of the isoquant IQ.

To put it algebraically, it means that S> В and R< A. But this is logically absurd because S combination is as productive as R and A combination produces as much as B. Therefore, the same combination cannot both be less and more productive at the same time. Hence two isoquants cannot intersect each other.

(4) Isoquants need not be parallel because the rate of substitution between two factors is not necessarily the same in all the isoquant schedules.

(5) In between two isoquants there can be a number of isoquants showing various levels of output which the combinations of the two factors can yield. In fact, in between the units of output 100, 200, 300, etc. represented on isoquants there can be innumerable isoquants showing 120, 150, 175,235, or any other higher or lower unit.

(6)  No isoquant can touch either axis. If an isoquant touches X-axis, it would mean that the product is being produced with the help of labour alone without using capital at all. This is a logical absurdity for OL units of labour alone are incapable of producing anything.

Similarly, ОС units of capital alone cannot produce anything without the use of labour. Therefore IQ and lQ1 cannot be isoquants, as shown in Figure 24.5.

(7) Each isoquant is convex to the origin:

As more units of labour are employed to produce 100 units of the product, lesser and lesser units of capital are used. This is because the marginal rate of substitution between two factors diminishes.

In Figure 24.6, in order to produce 100 units of the product, as the producer moves along the isoquant from combination A to В and to С and D, he gives up smaller and smaller units of capital for additional units of labour.

To maintain the same output of 100 units, BR less of capital and relatively RC more of labour is used.

Choice of Optimal Factor Combination or Least Cost Combination of Factors or Producer’s Equilibrium:

A profit maximisation firm faces two choices of optimal combination of factors (inputs): First, to minimise its cost for a given output; and second, to maximise its output for a given cost.

Thus the least cost combination of factors refers to a firm producing the largest volume of output from a given cost and producing a given level of output with the minimum cost when the factors are combined in an optimum manner.

Assumptions:

This analysis is based on the following assumptions:

  1. There are two factors, labour and capital.
  2. All units of labour and capital are homogeneous.
  3. The prices of units of labour (w) and that of capital (r) are given and constant.
  4. The cost outlay is given.
  5. The firm produces a single product.
  6. The price of the product is given and constant.
  7. The firm aims at profit maximisation.
  8. There is perfect competition in the factor market.

Producer’s equilibrium: The point of tangency between the isocost line and the isoquant is an important first order condition but not a necessary condition for the producer’s equilibrium. There are two essential or second order conditions for the equilibrium of the firm.

  1. The first condition is that the slope of the isocost line must equal the slope of the isoquant curve.
  2. The second condition is that at the point of tangency, the isoquant curve must he convex to the origin.

The point where the isocost line is tangent to an isoquant represents the least cost combination of the two factors for producing a given output. If all points of tangency like LMN are joined by a line, it is known as an output- factor curve or least-outlay curve or the expansion path of a firm.

Salvatore defines expansion path as “the locus of points of producer’s equilibrium resulting from changes in total outlays while keeping factor prices constant.” It shows how the proportions of the two factors used might be changed as the firm expands.

For example, in Figure 24.8 (A) the proportions of capital and labour used to produce 200 (IQ1) units of the product are different from the proportions of these factors used to produce 300 (IQ2) units or 100 (OQ) units at the lowest cost.

Like the price-income line in the indifference curve analysis, a relative cheapening of one of the factors to that of another will extend the isocost line to the right. If one of the factors becomes relatively dearer, the isocost line will contract inward to the left.

Given the price of capital, if the price of labour falls, the isocost line EF in Panel (B) will extend to the right as EG and if the price of labour rises, the isocost line EF will contract inward to the left as EH. if the equilibrium points L, M, and N are joined by a line, it is called the price-factor curve.

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