unit - 3 mg 2452

Unit – 3

3.2 Engineering Economics and Financial Accounting

3.1.1 Introduction

A business firm is an economic unit. It is also called as a production unit. Production is one of the most important activities of a firm in the circle of economic activity. The main objective of production is to satisfy the demand for different kinds of goods and services of the community.

3.1.2 Meaning of Production

The concept of production can be represented in the following manner.

The term “Production” means transformation of physical “Inputs” into physical “Outputs”.

The term “Inputs” refers to all those things or items which are required by the firm to produce a particular product. Four factors of production are land, labor, capital and organization. In addition to four factors of production, inputs also include other items like raw materials of all kinds, power, fuel, water, technology, time and services like transport and communications, warehousing, marketing, banking, shipping and Insurance etc. It also includes the ability, talents, capacities, inputs.

Production always results in either creation of new utilities or addition of values. It is an activity that increases consumer satiability of goods and services. Production is undertaken by producers and basically it depends on cost of production. Production analysis is always made in physical terms and it shows the relationship between physical inputs and physical outputs.

It is to be noted that higher levels of production is an index of progress and growth of an organization and that of a society. It leads to higher income, employment and economic prosperity. Production of different types of goods and services in different nations indicates the nature of economic inter dependence between different nations.

The primary and the ultimate aim of the economic activity is the satisfaction of human wants. In order to satisfy these wants individuals have to put in efforts to produce goods & services. Without production there cannot be satisfaction of wants.

Commonly understood, production refers to creation of something tangible which can be used to satisfy human want.

3.1 PRODUCTION COST ANALYSIS

Engineering Economics 3.3

However, matter already exists. We cannot create a matter. We can only add utilities to the existing matter by either changing its form, place or keeping it over time & create values. For example: We can transform a log of wood into a piece of furniture, thereby adding utility. This process of addition of utilities to the existing matter by changing its form, place and keeping it over time is referred to as Production in Economics. We can therefore add form utility, time utility, place utility or personnel utility. Addition of all such utilities to the existing matter is referred to as Production in Economics. However technologically production is referred to as the process of transforming inputs into output. In order to undertake production we require certain factors of production such as land, labour, capital & organization. These factors are the inputs & the product that emerges at the end of the process of production is referred to as the output.

3.1.3 Agents of production

The agents of production are broadly classified into four categories, viz.

Land

Labour

Capital and

Organisation.

(i) Land in economics has a much wider connotation than being understood merely as a portion of the surface of the earth. In economics, land refers to all the natural resources found on, above and under the surface of the earth and which essentially free gifts of Nature are.

(ii) Labour essentially refers to the human factor in the process of production. Labour in economics may be defined as human efforts, mental or manual, undertaken in order to add utilities and create values.

(iii) Capital is a man-made factor of production. When labour works on land, it produces two types of goods, consumers’ goods which directly satisfy human wants and capital goods which satisfy human wants only indirectly. Capital goods are those goods which are used to produce other goods. Thus Capital is often defined as the “produced means for further production”.

(iv)Organization refers to that factor of production which coordinates the various other factors (Land, Labour, and Capital) in a manner so as to minimize the cost of production and maximize the output.


Production, as such has two dimensions

(i) Technical or Physical and

(ii) (ii) Financial.

In Technical sense production is concerned with conversion of inputs into output. However it should be noted here that production does not necessarily imply merely a physical conversion of inputs into a physically new unit of output.; but processes like transportation and storage should also be incorporated in the definition of production for they too are involved in addition of utilities to goods. An input refers to any good or service which enters the process of production and an output is the resulting good which emerges as the consequence of production process.

There is also the financial dimension to the process of production. In fact, production involves cost. Certain amount of expenditure is to be incurred to initiate and continue production.

The entire theory of production centre round the concept of production function. “A production Function” expresses the technological or engineering relationship between physical quantity of inputs employed and physical quantity of outputs obtained by a firm. It specifies a flow of output resulting from a flow of inputs during a specified period of time. It may be in the form of a table, a graph or an equation specifying maximum output rate from a given amount of inputs used. Since it relates inputs to outputs, it is also called as “Input output relation.” The production is purely physical in nature and is determined by the quantum of technology, availability of equipments, labor, and raw materials, and so on employed by a firm.

A production function can be represented in the form of a mathematical model or equation as Q = f(L, N, K….etc) where Q stands for quantity of output per unit of time and L N K etc are the various factor inputs like land, capital labor etc which are used in the production of output. The rate of output Q is thus, a function of the factor inputs L N K etc, employed by the firm per unit of time.

In microeconomics and macroeconomics, a production function is a function that specifies the output of a firm, an industry, or an entire economy for all combinations of inputs. This function is an assumed technological relationship, based on the current state of

3.2 PRODUCTION FUNCTION


engineering knowledge; it does not represent the result of economic choices, but rather is an externally given entity that influences economic decision-making. Almost all economic theories presuppose a production function, either on the firm level or the aggregate level. In this sense, the production function is one of the key concepts of mainstream neoclassical theories. Some non-mainstream economists, however, reject the very concept of an aggregate production function.

Figure (a) Figure (b)

The technological relationship between inputs and output of a firm is generally referred to as the production function. The production function shows the functional relationship between the physical inputs and the physical output of a firm in the process of production.

“The production function is the Technical relationship telling the maximum amount of output capable of being produced by each and every set of specified inputs. It is defined for a given set of technical knowledge.” – Samuelson.

According to Stigler, “the production function is the name given to the relationship between the rates of input of productive services and the rate of output of product. It is the economist’s summary of technical knowledge.

In fact the production function shows the maximum quantity of output. Q, that can be produced as a function of the quantities of inputs X1, X2, X3...Xn.

In equation form the production function can be presented as :

Q =f(X1, X2, X3…Xn, T)

L0 L1 L2 L1 L2 L3O


Where:

Q: Stands for the physical quantity of output produced.

f: represents the functional relationship.

X1, X2, X3…Xn: indicate the quantities used of factors X1, X2, X3…Xn

T (read T bar ;) stands for a given State of Technology; Technology held constant.

Production function, thus expresses the technological functional relationship between inputs and output. It shows that output is the function of several inputs. Besides, the Production function must be considered with reference to a particular period of time and for a given state of technology.

It may be remembered that the Production function shows only the physical relationship between inputs and the output. It is basically an engineering concept; whereas selecting an optimal input combination is an economic decision which requires additional information with respect to prices of the factor inputs and the market demand for the output.

3.2.1 What is Production Function?

Production of goods requires resources or inputs. These inputs are called factors of production named as land, labor, capital and organization. A rational producer is always interested that he should get the maximum output from the set of resources or inputs available to him. He would like to combine these inputs in a technical efficient manner so that he obtains maximum desired output of goods. The relationship between the inputs and the resulting output is described as production function. A production function shows the relationship between the amounts of factors used and the amount of output generated per period of time.

It can be expressed in algebraic form as under:

X = f (a1, a2 ,........, an)

This equation tells us the quantity of the product X which can be produced by the given quantities of inputs (lands labor, capital) that are used in the process of production. Here it may be noted that production function shows only the maximum amount of output which can be produced from given inputs. It is because production function includes only efficient production process.

The analysis of production function is generally carried with reference to time period which is called short period and long period. In the short run, production function is explained


with one variable factor and other factors of productions are held constant. We have called this production function as the Law of Variable Proportions or the Law of Diminishing returns.

In the long run, production function is explained by assuming all the factors of production as variable. There are no fixed inputs in the long run. Here the production function is called the Law of Returns according to the scale of production. As it is difficult to handle more than two variables in graph, we therefore, explain the Law of Returns according to scale of production by assuming only two inputs i.e., capital and labor and study how output responds to their use. We first of all explain the concept of isoquants and their properties.

3.2.2 Factor inputs are of two types

1. Fixed Inputs

Fixed inputs are those factors the quantity of which remains constant irrespective of the level of output produced by a firm. For example, land, buildings, machines, tools, equipments, superior types of labor, top management etc.

2. Variable inputs

Variable inputs are those factors the quantity of which varies with variations in the levels of output produced by a firm For example, raw materials, power, fuel, water, transport and communication etc. The distinction between the two will hold good only in the short run. In the long run, all factor inputs will become variable in nature.

Short run is a period of time in which only the variable factors can be varied while fixed factors like plants, machineries, top management etc would remain constant. Time available at the disposal of a producer to make changes in the quantum of factor inputs is very much limited in the short run.

Long run is a period of time where in the producer will have adequate time to make any sort of changes in the factor combinations. It is necessary to note that production function is assumed to be a continuous function, i.e. it is assumed that a change in any of the variable factors produces corresponding changes in the out put. Generally speaking, there are two types of production functions.

They are as follows;

a. Short Period Analysis of Production

The short run is a period of time in which only one input (say labor) is allowed to vary while other inputs land and capital are held fixed. In the short run, therefore, production can be increased with one variable factor and other factors remaining constant. In the short run, the law of variable proportion governs the production behavior of a firm. The law of variable


proportion shows the direction and rate of change in the output of firm when the amount of only one factor of production is varied while other factor of production are held constant. The law of variable proportion passes mainly through two phases,

1. Increasing Returns and

2. Diminishing Returns.

In this case, the producer will keep all fixed factors as constant and change only a few variable factor inputs. In the short run, we come across two kinds of production functions.

1. Quantities of all inputs both fixed and variable will be kept constant and only one variable input will be varied.

For example, Law of Variable Proportions.

2. Quantities of all factor inputs are kept constant and only two variable factor inputs are varied.

For example, IsoQuants and IsoCost curves.

b. Technical Efficient Combination:

Production function establishes a physical relationship between output and inputs. It describes what is technical feasible when the firm uses each combination of input. The firm can obtain a given level of output by using more labor and less capital or more capital and less labor. Production function describes the maximum output feasible for a given set of inputs in technical efficient manner.

3.2.3 Production Function takes Quantities of Inputs

It is imperative to note that production function does not take unto account the prices of input or of the output. It simply takes into account the quantities of inputs which are employed to produce certain quantities of output.

3.2.4 Long Run Production With Variable Inputs

The long run is the lengthy period of time during with all inputs can be varied. There are no fixed output in the long run. All factors of production are variable inputs.

We now analyze production function by allowing two factors say labor and capital to very while all others are held constant. With both factors are variable, a firm can produce a given level of output by using more labor and less capital or a greater amount of capital and


less labor or moderate amounts of both. A firm continues to substitute one input for another while continuing to produce the same level of output.

If two inputs say labor and capital are allowed to vary, the resulting production function can be illustrated in the figure 12(a).

In this figure each curve (called an isoquant) represents a different level of output. The curves which lie higher and to the right represent greater output levels than curves which are lower and to the left.

For example, point D represents a higher output level of 250 units than point A or B which shows output level of 150 units.

The curve isoquant which represents 150 units of output illustrate that the same level of output (150 units) can be produced with different combinations of labor and capital. Combination of labor and capital represented by A, can employ OL1 quantity of labor and OC1 units of capital to produce 150 units of output. The combination of labor and capital represented by point B will use only OL2 units of labor and OC1 of capital to produce the same level of output. Thus, if a country has surplus labor and less capital, it may use the combination of labor and capital represented by point A. In case the country has abundant capital and less labor, it might produce at point B. The isoquants through points A and B shows all the different combinations of labor and capita that can be used to produce 150 units of output.

In this case, the producer will vary the quantities of all factor inputs, both fixed as well as variable in the same proportion.

For Example, The laws of returns to scale.

Each firm has its own production function which is determined by the state of technology, managerial ability, organizational skills etc of a firm. If there are any improvements in them, the old production function is disturbed and a new one takes its place. It may be in the following manner:

1. The quantity of inputs may be reduced while the quantity of output may remain same.

2. The quantity of output may increase while the quantity of inputs may remain same.

3. The quantity of output may increase and quantity of inputs may decrease.

3.2.5 Uses of Production Function

Though production function may appear as highly abstract and unrealistic, in reality, it is both logical and useful. It is of immense utility to the managers and executives in the decision making process at the firm level.


There are several possible combinations of inputs and decision makers have to choose the most appropriate among them. The following are some of the important uses of production function.

1. It can be used to calculate or work out the least cost input combination for a given output or the maximum output input combination for a given cost.

2. It is useful in working out an optimum, and economic combination of inputs for getting a certain level of output. The utility of employing a unit of variable factor input in the production process can be better judged with the help of production function. Additional employment of a variable factor input is desirable only when the marginal revenue productivity of that variable factor input is greater than or equal to cost of employing it in an organization.

3. Production function also helps in making long run decisions. If returns to scale are increasing, it is wise to employ more factor units and increase production. If returns to scale are diminishing, it is unwise to employ more factor inputs & increase production. Managers will be indifferent whether to increase or decrease production, if production is subject to constant returns to scale.

Thus, production function helps both in the short run and long run decision making process.

a. Production function

The technological physical relationship between inputs and outputs per unit of time, is referred to as production function.

The relationship between the inputs to the production process and the resulting output is described by a production function.

“The production function is the name given to the relationship between rates of input of productive services and the rate of output of the product. It is the economist’s summary of technical knowledge.”-Stigler. Explanation of the meaning of Production Function: The theory of production begins with some prior knowledge of the technical and/or engineering information.

3.3 PRODUCTION ANALYSIS


For instance, if a firm has a given quantity of labour, land and machinery, the level of production will be determined by the technical and engineering conditions and cannot be predicted by the economist. The level of production depends on technical conditions. If there is improvement in the technique of production, increased output can be obtained even with the same (fixed) quantity of factors. However, at a given point of time, there is only one maximum level of output that can be obtained with a given combination of factors of production. This technical law which expresses the relationship between factor inputs and output is termed as production function.

b. Fixed Inputs

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.

E.g., Buildings, major capital equipments and managerial personnel. Variable Inputs

A variable input is one whose quantity can be changed readily when market condition suggests that an immediate change in output is beneficial to the producer.

E.g. raw materials and labour services. Short Run

The short run is that period of time in which quantity of one or more inputs remains fixed irrespective of the volume of output.

Therefore, if output is to be increased or decreased in the short run, change exclusively in the quantity of variable inputs is to be made. Long Run

Long run refers to that period of time in which all inputs are variable.

Thus, the producer does not feel constrained in any way while changing the output.

In the long run it is possible for the producer to make output changes in the most advantageous way. Production process or method of production is a combination of factor inputs for producing one unit of output

3.3.1 Production Function With One Variable Input Case

a. The Law of Variable Proportions

This law is one of the most fundamental laws of production. It gives us one of the key insights to the working out of the most ideal combination of factor inputs. All factor inputs are not available in plenty. Hence, in order to expand the output, scarce factors must be kept constant and variable factors are to increased in greater quantities. Additional units of a variable factor on the fixed factors will certainly mean a variation in output. The law of


variable proportions or the law of non-proportional output will explain how variation in one factor input give place for variations in outputs.

The law can be stated as the following.

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”.

The same idea has been expressed by Prof.Marshall in the following words. 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.

b. Assumptions of The Law

Only one variable factor unit is to be varied while all other factors should be kept constant.

Different units of a variable factor are homogeneous.

Techniques of production remain constant.

The law will hold good only for a short and a given period.

There are possibilities for varying the proportion of factor inputs.

Illustration

A hypothetical production schedule is worked out to explain the operation of the law. Fixed factors = 1 Acre of land + Rs 5000-00 capital. Variable factor = labor.

Units of TP in units AP in units MP in units


Variable inputs (Labor)

0 0 0 0

1 10 10 10

2 24 12 14

3 39 13 15

4 52 13 13

5 60 12 8

6 66 11 6

7 70 10 4

8 72 9 2

9 72 8 0

10 70 7 -2

Total Product or Output : (TP) It is the output derived from all factors units, both fixed & variable employed by the producer. It is also a sum of marginal output.

Average Product or Output : (AP). It can be obtained by dividing total output by the number of variable factors employed.

Marginal Product or Output : (MP) It is the output derived from the employment of an additional unit of variable factor unit

Trends in output : From the table, one can observe the following tendencies in the TP, AP, & MP.

1. Total output goes on increasing as long as MP is positive. It is the highest when MP is zero and TP declines when MP becomes negative.

2. MP increases in the beginning, reaches the highest point and diminishes at the end.


3. AP will also have the same tendencies as the MP. In the beginning MP will be higher than AP but at the end AP will be higher than MP.

Figure

In the above diagram along with OX axis, we measure the amount of variable factors employed and along OY axis, we measure TP, AP & MP. From the diagram it is clear that there are III stages.

Stage Number I : The Law Of Increasing Returns

The total output increases at an increasing rate (More than proportionately) up to the point P because corresponding to this point P the MP is rising and reaches its highest point. After the point P, MP decline and as such TP increases gradually.

The first stage comes to an end at the point where MP curve cuts the AP curve when the AP is maximum at N.

The Ist stage is called as the law of increasing returns on account of the following reasons.

1. The proportion of fixed factors is greater than the quantity of variable factors. When the producer increases the quantity of variable factor, intensive and effective utilization of fixed factors become possible leading to higher output.

1 2 3 4 5 6 7 8 9 10

9080

7060

5040

3020

10

Stage – 1

Stage – 2

Stage – 3

TP

E

P

0x

y


2. When the producer increases the quantity of variable factor, output increases due to the complete utilization. of the “Indivisible Factors”

3. As more units of the variable factor is employed, the efficiency of variable factors will go up because it creates more opportunity for the introduction of division of labor and specialization resulting in higher output.

Stage Number II : The Law Of Diminishing Returns

In this case as the quantity of variable inputs is increased to a given quantity of fixed factors, output increases less than proportionately. In this stage, the T.P increases at a diminishing rate since both AP & MP are declining but they are positive. The II stage comes to an end at the point where TP is the highest at the point E and MP is zero at the point B. It is known as the stage of “Diminishing Returns” because both the AP & MP of the variable factor continuously fall during this stage. It is only in this stage, the firm is maximizing its total output.

Diminishing returns arise due to the following reasons:

1. The proportion of variable factors are greater than the quantity of fixed factors. Hence, both AP & MP decline.

2. Total output diminishes because there is a limit to the full utilization of indivisible factors and introduction of specialization. Hence, output declines.

3. Diseconomies of scale will operate beyond the stage of optimum production.

4. Imperfect substitutability of factor inputs is another cause. Up to certain point substitution is beneficial. Once optimum point is reached, the fixed factors cannot be compensated by the variable factor. Diminishing returns are bound to appear as long as one or more factors are fixed and cannot be substituted by the others.

Stage Number III : The Stage Of Negative Returns.

In this case, as the quantity of variable input is increased to a given quantity of fixed factors, output becomes negative. During this stage, TP starts diminishing, AP continues to diminish and MP becomes negative. The negative returns are the result of excessive quantity of variable factors to a constant quantity of fixed factors. Hence, output declines. The proverb “Too many cooks spoil the broth” and “ Too much is too bad” aptly applies to this stage. Generally, the III stage is a theoretical possibility because no producer would like to come to this stage.


The producer being rational will not select either the stage I (because there is opportunity for him to increase output by employing more units of variable factor) or the III stage (because the MP is negative). The stage I & III is described as Non economic Region or Uneconomic Region.

Hence, the producer will select the II stage (which is described as the most economic region) where he can maximize the output. The II stage represents the range of rational production decision.

It is clear that in the above example, the most ideal or optimum combination of factor units = 1 Acre of land+ Rs. 5000-00 capital and 9 laborers.

All the 3 stages together constitute the law of variable proportions. Since the second stage is the most important, in practice we normally refer this law as the law of Diminishing Returns.

3.3.2 Practical application of the law

1. It helps a producer to work out the most ideal combination of factor inputs or the least cost combination of factor inputs.

2. It is useful to a businessman in the short run production planning at the micro-level.

3. The law gives guidance that by making continuous improvements in science and technology, the producer can postpone the occurrence of diminishing returns.

3.3.3 Concept of Production functions

The Main concepts of Production Functions are:

1. The marginal productivity of factors of production.

2. The marginal rate of technical substitution.

3. Elasticity of substitution

4. Factor intensity

5. The returns to scale.

Marginal Product of Factors The marginal product of a factor of production is defined as a change in output due to a very small change in the quantity of this factor while quantities of all other factors of production remain constant.


3.3.4 Marginal rate of technical substitution

The marginal rate of technical substitution of labour for capital is that quantity of capital which has to be reduced on an increase in the use of labour by one unit to keep the level of production constant. Table showing Marginal Rate of Technical Substitution Elasticity of Technical Substitution

The elasticity of technical substitution is defined as the percentage change in the ratio of the two factors of production (say, capital – labour ratio), divided by the percentage change in the marginal rate of technical substitution. percentage change in K/L •Es = percentage change in MRTSLK Factor Intensity In any process, if only two factors (e.g., capital and labour) are used, the factor intensity refers to capital-labour ratio. If K1/L1 > K2/L2 it shows that the former process is more capital intensive than the latter.

3.3.5 Returns to Scale

Commonly used General Production Function: X = f (L, K, v, u ) Law of Diminishing Marginal Returns Marshall stated this law as follows: “An increase in capital and labour applied in the cultivation of land causes in general a less than proportionate increase in the amount of produce raised, unless it happens to coincide with an improvement in the arts of agriculture.” In the initial stages of cultivation of a given piece of land, perhaps due to under-cultivation of land, when additional units of capital and labour are invested, additional output may be more than proportionate. But after a certain extent when the land is cultivated with some more investment, the additional output will be less than proportionate under all normal circumstances, unless some improvements take place in the methods of techniques of cultivation. The law is applicable to all fields of production such as industry, mining, house construction, besides agriculture.

Assumptions of the Law of Diminishing Marginal Returns

The law of diminishing marginal returns holds good subject the following two conditions:-

1. Same technology is used throughout the process of production. Whatever change takes place in the proportion of factor inputs is within the scope of available methods and techniques.

2. Units of different factor inputs are perfectly homogeneous; every unit is of equal efficiency and therefore, are interchangeable with any other factor input in the production function.

a. Law of Variable Proportions


Prof. Benham states the law as follows:

“As the proportion of one factor in a combination of factors is increased after a point, the average and marginal production of that factor will diminish”.

G. J. Stigler: •“As equal increments of one input are added, the inputs of other productive services being held constant, beyond a certain point the resulting increments of product will decrease, i.e. the marginal product will diminish.”

The law is summarised thus:•In the short run, as the amount of variable factors increases, other things remaining equal, output (or the returns to the factors varied) will increase more than proportionately to the amount of variable inputs in the beginning, then it may increase in the same proportion and ultimately it will increase less proportionately”.

b. Law of Variable Proportions

The conditions underlying the law are :

Only one factor is varied; all other factors remain constant.

The scale of output is unchanged and production capacity remains constant.

Technique of production is unchanged.

All units of factor input varied, are homogeneous – all units have identical efficiencies and characteristics.

All factors of production cannot be substituted for one another. Measurements of the Product

c. Total Product

Total number of units produced per unit of time by all factor inputs in referred to as total product. In the short run, since Total Product (output)(TP) increases with an increase in the Quantity of Variable Factor (QVF), TP = f(QVF). •Average Product: Average Product refers to the total product per unit of the given variable factor. AP = TP/QVF •Marginal Product: Owing to the addition of a unit to a variable factor, all other factors being held constant, the additional realised in the total product is technically called marginal product. MPn = TPn – TPn-1

1. Stage I – The law of diminishing returns becomes evident in the marginal product line. Initially the marginal product of the variable input (labour) rises. The total product rises at


an increasing rate (=marginal product). Average product also rises. This is the stage of increasing returns.

2. Stage II – Reaching a certain point, the marginal product begins to diminish. Thus, the rate of increase in the total output slows down. This is the stage of diminishing returns. When the average product is maximum, the average product is equal to the marginal product.

3. Stage III – As the marginal product tends to diminish, it ultimately becomes zero and negative thereafter. •When the marginal product becomes zero, the total product is the maximum. Thus when marginal product becomes negative, the total product begins to decline in the same proportion. Even though AP is decreasing, it does not become negative immediately.

3.3.6 Short-run Versus Long-run Production function

The short run and the long run have no calendrical specificity. These are only functional and analytical period-wise classification. The Short-run is that period of time in which at least one of the factors of production remains fixed. Whereas, the Long-run is that period of time in which all factors are variable. The major determinant of the short-run or long-run time periods is the existence or non-existence of fixed input. When one or more inputs remain constant we consider that period of time as short period; whereas when all inputs are capable of being varied that period is regarded as the long-period.

If we consider a simple production function with two inputs

labour (l) and

capital (k) and

only one output (Q)

Then we can summarize the short-run production function as :

Q = f (l,k )

Or

Q = f (l , k)

When the bar above k or l shows that the amount of that input is fixed.

The long-run production function may be summarized as


Q = f (l, k)

Where both labour and capital are variable inputs. Since in short-run, not all inputs can be varied simultaneously, the proportions in which inputs are combined go on varying. There fore the analysis of input-output relation depicted by the short-run production function is called the Returns to Variable Proportions. It takes shape in the Laws of Returns. Whereas the long-run production function gives the input-output relationship when all inputs are varied. In fact economists are particularly interested in finding out as to what happens to the output when all inputs are varied proportionately. This analysis of relationship between proportionate change in inputs and the resulting output gives rise to proportionate change in inputs and the resulting output gives rise to Returns to Scale.

3.3.7 Laws of returns and returns to scale

Returns to scale, returns to scale, in economics, the quantitative change in output of a firm or industry resulting from a proportionate increase in all inputs. If the quantity of output rises by a greater proportion—e.g., if output increases by 2.5 times in response to a doubling of all inputs—the production process is said to exhibit increasing returns to scale. Such economies of scale may occur because greater efficiency is obtained as the firm moves from small- to large-scale operations. Decreasing returns to scale occur if the production process becomes less efficient as production is expanded, as when a firm becomes too large to be managed effectively as a single unit.

In economics, returns to scale and economies of scale are related 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). They are different terms and should not be used interchangeably.

The term returns to scale arises in the context of a firm's production function. It refers to changes in output resulting from a proportional change in all inputs (where all inputs increase by a constant factor). If output increases by that same proportional change then there are constant returns to scale (CRS). If output increases by less than that proportional change, there are decreasing returns to scale (DRS). If output increases by more than that proportional change, there are increasing returns to scale (IRS). Thus the returns to scale faced by a firm are purely technologically imposed and are not influenced by economic decisions or by market conditions.

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.


An economic concept referring to a situation in which economies of scale no longer function for a firm. Rather than experiencing continued decreasing costs per increase in output, firms see an increase in marginal cost when output is increased.

Example

When all inputs increase by a factor of 2, new values for output will be:

Twice the previous output if there are constant returns to scale (CRS)

Less than twice the previous output if there are decreasing returns to scale (DRS)

More than twice the previous output if there are increasing returns to scale (IRS)

Assuming that the factor costs are constant (that is, that the firm is a perfect competitor in all input markets), a firm experiencing constant returns will have constant long-run average costs, a firm experiencing decreasing returns will have increasing long-run average costs, and a firm experiencing increasing returns will have decreasing long-run average costs. However, this relationship breaks down if the firm is not a perfect competitor in the input markets.

For example, if there are increasing returns to scale in some range of output levels, but the firm is so big in one or more input markets that increasing its purchases of an input drives up the input's per-unit cost, then the firm could have diseconomies of scale in that range of output levels. Conversely, if the firm is able to get bulk discounts of an input, then it could have economies of scale in some range of output levels even if it has decreasing returns in production in that output range.

Network effect

Network externalities resemble economies of scale, but they are not considered such because they are a function of the number of users of a good or service in an industry, not of the production efficiency within a business. Economies of scale external to the firm (or industry wide scale economies) are only considered examples of network externalities if they are driven by demand side economies.

Formal definitions

Formally, a production function is defined to have:

constant returns to scale if (for any constant a greater than or equal to 1)

increasing returns to scale if (for any constant a greater than 1)


decreasing returns to scale if (for any constant a greater than 1)

where K and L are factors of production, capital and labor, respectively.

Formal example

The Cobb-Douglas functional form has constant returns to scale when the sum of the exponents adds up to one. The function is: where A > 0 and 0 < b < 1. Thus But if the Cobb-Douglas production function has its general form with 0 < c < 1, then there are increasing returns if b + c > 1 but decreasing returns if b + c < 1, since which is greater than or less than aF(K,L) as b+c is greater or less than one.

The relationship between the inputs and the output in the process of production is clearly explained by the Laws of Returns or the Law of Variable Proportions. This law examines the production function with only one factor variable, keeping the quantities of other factors constant. The laws of returns comprise of three phases:

(a) The Law of Increasing Returns.

(b) The Law of Constant Returns.

(c) The Law of Diminishing Returns.

The Laws of Returns may be stated as follows:

“If in any process of production, the factors of production are so combined that if the varying quantity of one factor is combined with the fixed quantity of other factor (or factors), then there will be three tendencies about the additional output or marginal returns:

(i) Firstly, in the beginning, as more and more units of a variable factor are added to the units of a fixed factor, the additional output or Marginal Returns will go on increasing. Here we have the Law of Increasing Returns operating.

(ii) Secondly, if still more units of variable factor inputs are added to the units of a fixed factor, the additional output or marginal returns will remain constant. The Law of Constant Returns begins to operate; and

3.4 LAWS OF RETURNS


(iii) Finally, if still more units of variable factors are fed into the process of production, then the additional output or marginal returns begins to decline. Thus, eventually, we have the operation of the Law of Diminishing Returns. We can best illustrate these three stages of Law of Returns with the help of a model. Let us assume that a farmer has a fixed size of land, say one

3.4.1 Economies of Scale

The study of economies of scale is associated with large scale production. Today there is a general tendency to organize production on a large scale basis. Mass production of standardized goods has become the order of the day. Large scale production is beneficial and economical in nature. “The advantages or benefits that accrue to a firm as a result of increase in its scale of production are called ‘Economies of scale’. They have close relationship with the size of the firm. They influence the average cost over different ranges of output. They are gain to a firm. They help in reducing production cost and establishing an optimum size of a firm. Thus, they help a lot and go a long way in the development and growth of a firm.

According to Prof. Marshall these economies are of two types, viz Internal Economies and External Economics.

I. Internal Economies or Real Economies

Internal Economies are those economies which arise because of the actions of an individual firm to economize its cost. They arise due to increased division of labor or specialization and complete utilization of indivisible factor inputs. Prof. Cairncross points out that internal economies are open to a single factory or a single firm independently of the actions of other firms. They arise on account of an increase in the scale of output of a firm and cannot be achieved unless output increases.

The following are some of the important aspects of internal economies.

1. They arise “with in” or “inside” a firm.

2. They arise due to improvements in internal factors.

3. They arise due to specific efforts of one firm.

4. They are particular to a firm and enjoyed by only one firm.

5. They arise due to increase in the scale of production.

6. They are dependent on the size of the firm.


7. They can be effectively controlled by the management of a firm.

8. They are called as “Business Secrets “of a firm.

3.4.2 Kinds of Internal Economies

1. Technical Economies

These economies arise on account of technological improvements and its practical application in the field of business. Economies of techniques or technical economies are further subdivided into five heads.

a. Economies of superior techniques

These economies are the result of the application of the most modern techniques of production. When the size of the firm grows, it becomes possible to employ bigger and better types of machinery. The latest and improved techniques give place for specialized production. It is bound to be cost reducing in nature.

For example, cultivating the land with modern tractors instead of using age old wooden ploughs and bullock carts, use of computers instead of human labor etc.

b. Economies of increased dimension

It is found that a firm enjoys the reduction in cost when it increases its dimension. A large firm avoids wastage of time and economizes its expenditure. Thus, an increase in dimension of a firm will reduce the cost of production.

For example, operation of a double decker instead of two separate buses.

c. Economies of linked process

It is quite possible that a firm may not have various processes of production with in its own premises. Also it is possible that different firms through mutual agreement may decide to work together and derive the benefits of linked processes.

For example, in diary farming, printing press, nursing homes etc.

d. Economies arising out of research and by products

A firm can invest adequate funds for research and the benefits of research and its costs can be shared by all other firms. Similarly, a large firm can make use of its wastes and byproducts in the most economical manner by producing other products.


For example, cane pulp, molasses, and abases of sugar factory can be used for the production of paper, varnish distilleries etc.

e. Inventory Economies

Inventory management is a part of better materials management. A big firm can save a lot of money by adopting latest inventory management techniques.

For example, Just-In-Time or zero level inventory techniques. The rationale of the Just-in-Time technique is that instead of having huge stocks worth of lakhs and Crores of rupees, it can ask the seller of the inputs to supply them just before the commencement of work in the production department each day.

2. Managerial Economies

They arise because of better, efficient, and scientific management of a firm. Such economies arise in two different ways.

a. Delegation of details

The general manager of a firm cannot look after the working of all processes of production. In order to keep an eye on each production process he has to delegate some of his powers or functions to trained or specialized personnel and thus relieve himself for coordination, planning and executing the plans. This will enable him to bring about improvements in production process and in bringing down the cost of production.

b. Functional Specialization

It is possible to secure economies of large scale production by dividing the work of management into several separate departments. Each department is placed under an expert and the rest of the work is left into the hands of specialists. This will ensure better and more efficient productive management with scientific business administration. This would lead to higher efficiency and reduction in the cost of production.

3. Marketing or Commercial economies

These economies will arise on account of buying and selling goods on large scale basis at favorable terms. A large firm can buy raw materials and other inputs in bulk at concessional rates.

As the bargaining capacity of a big firm is much greater than that of small firms, it can get quantity discounts and rebates. In this way economies may be secured in the purchase of different inputs.


A firm can reduce its selling costs also. A large firm can have its own sales agency and channel. The firm can have a separate selling organization, marketing department manned by experts who are well versed in the art of pushing the products in the market. It can follow an aggressive sales promotion policy to influence the decisions of the consumers

4. Financial Economies

They arise because of the advantages secured by a firm in mobilizing huge financial resources. A large firm on account of its reputation, name and fame can mobilize huge funds from money market, capital market, and other private financial institutions at concessional interest rates. It can borrow from banks at relatively cheaper rates. It is also possible to have large overdrafts from banks. A large firm can float debentures and issue shares and get subscribed by the general public.

Another advantage will be that the raw material suppliers, machine suppliers etc., are willing to supply material and components at comparatively low rates, because they are likely to get bulk orders. Thus, a big firm has an edge over small firms in securing sufficient funds more easily and cheaply.

5. Labor Economies

These economies will arise as a result of employing skilled, trained, qualified and highly experienced persons by offering higher wages and salaries. As a firm expands, it can employ a large number of highly talented persons and get the benefits of specialization and division of labor. It can also impart training to existing labor force in order to raise skills, efficiency and productivity of workers.

New schemes may be chalked out to speed up the work, conserve the scarce resources, economize the expenditure and save labor time. It can provide better working conditions promotional opportunities, rest rooms, sports rooms etc, and create facilities like subsidized canteen, crèches for infants, recreations. All these measures will definitely raise the average productivity of a worker and reduce the cost per unit output.

6. Transport and Storage Economies

They arise on account of the provision of better, highly organized and cheap transport and storage facilities and their complete utilization. A large company can have its own fleet of vehicles or means of transport which are more economical than hired ones. Similarly, a firm can also have its own storage facilities which reduce cost of operations.

7. Over Head Economies


These economies will arise on account of large scale operations. The expenses on establishment, administration, bookkeeping, etc, are more or less the same whether production is carried on small or large scale. Hence, cost per unit will be low if production is organized on large scale.

8. Economies of Vertical integration

A firm can also reap this benefit when it succeeds in integrating a number of stages of production. It secures the advantages that the flow of goods through various stages in production processes is more readily controlled. Because of vertical integration, most of the costs become controllable costs which help an enterprise to reduce cost of production.

9. Risk bearing or survival economies

These economies will arise as a result of avoiding or minimizing several kinds of risks and uncertainties in a business. A manufacturing unit has to face a number of risks in the business.

Unless these risks are effectively tackled, the survival of the firm may become, difficult. Hence many steps are taken by a firm to eliminate or to avoid or to minimize various kinds of risks.

Generally speaking, the risk-bearing capacity of a big firm will be much greater than that of a small firm. Risk is avoided when few firms amalgamate or join together or when competition between different firms is either eliminated or reduced to the minimum or expanding the size of the firm. A large firm secures risk-spreading advantages in either of the four ways or through all of them.

Diversification of output Instead of producing only one particular variety, a firm has to produce multiple products if there is loss in one item it can be made good in other items.

Diversification of market: Instead of selling the goods in only one market, a firm has to sell its products in different markets. If consumers in one market desert a product, it can cover the losses in other markets.

Diversification of source of supply: Instead of buying raw materials and other inputs from only one source, it is better to purchase them from different sources. If one person fails to supply, a firm can buy from several sources.

Diversification of the process of manufacture: Instead adopting only one process of production to manufacture a commodity, it is better to use different processes or


methods to produce the same commodity so as to avoid the loss arising out of the failure of any one process.

II. External Economies or Pecuniary Economies

External economies are those economies which accrue to the firms as a result of the expansion in the output of whole industry and they are not dependent on the output level of individual firms. These economies or gains will arise on account of the overall growth of an industry or a region or a particular area. They arise due to benefit of localization and specialized progress in the industry or region.

Prof. Stonier & Hague points out that external economies are those economies in production which depend on increase in the output of the whole industry rather than increase in the output of the individual firm The following are some of the important aspect of external economies.

1. They arise ‘outside’ the firm.

2. They arise due to improvement in external factors.

3. They arise due to collective efforts of an industry.

4. They are general, common & enjoyed by all firms.

5. They arise due to overall development, expansion & growth of an industry or a region.

6. They are dependent on the size of industry.

7. They are beyond the control of management of a firm.

8. They are called as “open secrets “of a firm.

3.4.3 Kinds of External Economies

1. Economies of concentration or Agglomeration

They arise because in a particular area a very large number of firms which produce the same commodity are established. In other words, this is an advantage which arises from what is called ‘Localization of Industry’.

The following benefits of localization of industry is enjoyed by all the firms provision of better and cheap labor at low or reasonable rates, trained educated and skilled labor, transport and communication, water, power, raw materials financial assistance through private and public institutions at low interest rates, marketing facilities, benefits of common repairs, maintenance and service shops, services of specialists or outside experts, better use of byproducts and other such benefits. Thus, it helps in reducing the cost of operation of a firm.


2. Economies of Information

These economies will arise as a result of getting quick, latest and up to date information from various sources. Another form of benefit that arises due to localization of industry is economies of information. Since a large number of firms are located in a region, it becomes possible for them to exchange their views frequently, to have discussions with others, to organize lectures, symposiums, seminars, workshops, training camps, demonstrations on topics of mutual interest.

Revolution in the field of information technology, expansion in inter net facilities, mobile phones, emails, video conferences, etc has helped in the free flow of latest information from all parts of the globe in a very short span of time. Similarly, publication of journals, magazines, information papers etc have helped a lot in the dissemination of quick information. Statistical, technical and other market information becomes more readily available to all firms. This will help in developing contacts between different firms. When inter-firm relationship strengthens, it helps a lot to economize the expenditure of a single firm.

3. Economies of Disintegration

These economies will arise as a result of dividing one big unit in to different small units for the sake of convenience of management and administration. When an industry grows beyond a limit, in that case, it becomes necessary to split it in to small units. New subsidiary units may grow up to serve the needs of the main industry. For example, in cotton textiles industry, some firms may specialize in manufacturing threads, a few others in printing, and some others in dyeing and coloring etc. This will certainly enhance the efficiency in the working of a firm and cut down unit costs considerably.

4. Economies of Government Action

These economies will arise as a result of active support and assistance given by the government to stimulate production in the private sector units. In recent years the government, in order to encourage the development of private industries have come up with several kinds of assistance. It is granting tax concessions, tax holidays, tax exemptions, subsidies, development rebates financial assistance at low interest rates, etc.

It is quite clear from the above detailed description that both internal and external economies arise on account of large scale production and they are benefits to a firm and cost reducing in nature.

4. Economies of Physical Factors

These economies will arise due to the availability of favorable physical factors and environment. As the size of an industry expands, positive physical environment may to reduce


the costs of all firms working in the industry. For example, Climate, weather conditions, fertility of the soil, physical environment in a particular place may help all firms to enjoy certain physical benefits.

5. Economies of Welfare

These economies will arise on account of various welfare programs under taken by an industry to help its own staff. A big industry is in a better position to provide welfare facilities to the workers. It may get land at concessional rates and procure special facilities from the local governments for setting up housing colonies for the workers. It may also establish health care units, training centers, computer centers and educational institutions of all types. It may grant concessions to its workers. All these measures would help in raising the overall efficiency and productivity of workers.

3.4.4 Diseconomies of Scale

When a firm expands beyond the optimum limit, economies of scale will be converted in to diseconomies of scale. Over growth becomes a burden. Hence, one should not cross the limit. On account of diseconomies of scale, more output is obtained at higher cost of production. The following are some of the main diseconomies of scale

1. Financial diseconomies

As there is over growth, the required amount of fiancée may not be available to a firm. Consequently, higher interest rates are to be paid for additional funds.

2. Managerial diseconomies

Excess growth leads to loss of effective supervision, control management, coordination of factors of production leading to all kinds of wastages, indiscipline and rise in production and operating costs.

3. Marketing diseconomies

Unplanned excess production may lead to mismatch between demand and supply of goods leading to fall in prices. Stocks may pile up, sales may decline leading to fall in revenue and profits.

4. Technical diseconomies

When output is carried beyond the plant capacity, per unit cost will certainly go up. There is a limit for division of labor and specialization. Beyond a point, they become negative. Hence, operation costs would go up.

5. Diseconomies of risk and uncertainty bearing


If output expends beyond a limit, investment increases. The level of inventory goes up. Sales do not go up correspondingly. Business risks appear in all fields of activities. Supply of factor inputs become inelastic leading to high prices.

6. Labor diseconomies

An unwieldy firm may become impersonal. Contact between labor and management may disappear. Workers may demand higher wages and salaries, bonus and other such benefits etc. Industrial disputes may arise. Labor unions may not cooperate with the management. All of them may contribute for higher operation costs.

II External diseconomies

When several business units are concentrated in only place or locality, it may lead to congestion,, environmental pollution, scarcity of factor inputs like, raw materials, water, power, fuel, transport and communications etc leading to higher production and operational costs.

Thus, it is very clear that a firm can enjoy benefits of large scale production only up to a limit.

Beyond the optimum limit, it is bound to experience diseconomies of scale. Hence, there should be proper check on the growth and expansion of a firm.

3.4.5 Internalisation of External Economies

It implies that a firm will convert certain external benefits created by the government or the entire society to its own favor with out making any additional investments. A firm may start a new unit in between two big railway stations or near the air port or near the national high ways or a port so that it can enjoy all the infrastructure benefits. Similarly, a new computer firm can commence its operations where there is 24 hours supply of electricity. Hence, they are also called as privatization of public benefits. Such type of efforts is to be encouraged by the government.

3.4.6 Externalisation of Internal Diseconomies

In this case, a particular firm on account of its regular operations will pass on certain costs on the entire society. A firm instead of taking certain precautionary measures by spending some amount of money will escape and pass on this burden to the government or the society.


For example, a firm may throw chemical or industrial wastes, dirt and filth either to open air or rivers leading to environmental pollution. In that case, the government is forced to spend more money to clean river water or prevent environmental pollution. This is a clear case of externalized internal diseconomies. It is to be avoided at all costs.

Benefits

1. An accurate forecast of future cash flows and associated risks

2. Cost savings by avoiding unnecessary attention to areas that are non-critical, and improved focus on areas of higher value

3. Discovery of enhancement opportunities during the conceptual and design phase, rather than later in the project’s life-cycle, when the cost of change is considerably higher

4. Systematic identification of key technological risks for a specific concept, and setting of priorities for further technology development, qualification and testing (to reduce and manage these risks)

5. Improved insight into technical and managerial issues that may cause critical failures and production losses

6. A road map on how to improve production capacities and production availability based on risk and cost-benefit assessments.

Important parameters include

a. Production capacity profiles

b. Demand profiles and product prices

c. Physical asset layout and design

d. Equipment reliability performance

e. Maintenance and repair activities including spare part strategies

f. Operation and mobilisation activities.

3.5 PRODUCTION OPTIMIZATION


In economics, an isoquant (derived from quantity and the Greek word iso, meaning equal) is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs. While an indifference curve mapping helps to solve the utility-maximizing problem of consumers, the isoquant mapping deals with the cost-minimization problem of producers.

Isoquants are typically drawn on capital-labor graphs, showing the technological tradeoff between capital and labor in the production function, and the decreasing marginal returns of both inputs. Adding one input while holding the other constant eventually leads to decreasing marginal output, and this is reflected in the shape of the isoquant. A family of isoquants can be represented by an isoquant map, a graph combining a number of isoquants, each representing a different quantity of output. Isoquants are also called equal product curves.

3.8.1 Isoquants and Isocosts

The prime concern of a firm is to workout the cheapest factor combinations to produce a given quantity of output. There are a large number of alternative combinations of factor inputs which can produce a given quantity of output for a given amount of investment. Hence, a producer has to select the most economical combination out of them. Isoproduct curve is a technique developed in recent years to show the equilibrium of a producer with two variable factor inputs. It is a parallel concept to the indifference curve in the theory of consumption.

3.8.2 Meaning and Definitions

The term “Iso –Quant” has been derived from ‘Iso’ meaning equal and ‘Quant’ meaning quantity. Hence, Iso – Quant is also called as Equal Product Curve or Product Indifference Curve or Constant Product Curve. An Iso – product curve represents all the possible combinations of two factor inputs which are capable of producing the same level of output. It may be defined as – “ a curve which shows the different combinations of the two inputs producing the same level of output .”

Each Iso – Quant curve represents only one particular level of output. If there are different

Iso–Quant curves, they represent different levels of output. Any point on an Iso–Quant curve

represents same level of output. Since each point indicates equal level of output, the producer

becomes indifferent with respect to any one of the combinations.

3.8 ISOQUANT


What are Isoquants?

ISO – means equal, QUANT – means quantity.

Isoquant literally means Equal Quantity.

Isoquant curve can also be called Isoproduct curve. This curve represents equal quantity of output produced using various combinations of inputs. An Isoquant is the locus of all the combinations of two factors of production that yield the same level of output. .

Assumptions of Isoquants

1. It is generally assumed that there are only two factors or inputs of production.

2. The factors of production are divisible into small units and can be used in any proportion.

3. Technical conditions of production are given and cannot be changed.

4. Given the technical conditions of production, different factors are used in the most efficient manner.

5. Properties of Isoquants

a. Isoquants are negatively sloped i.e. slope downward from left to right.

b. A higher Isoquant represents a larger output.

c. No two Isoquants intersect each other.

d. Isoquants are convex to the origin. - because the marginal rate of technical substitution tends to fall. Types of Isoquants

An isoquant shows the extent to which the firm in question has the ability to substitute between the two different inputs at will in order to produce the same level of output. An isoquant map can also indicate decreasing or increasing returns to scale based on increasing or decreasing distances between the isoquant pairs of fixed output increment, as output increases. If the distance between those isoquants increases as output increases, the firm's production function is exhibiting decreasing returns to scale; doubling both inputs will result in placement on an isoquant with less than double the output of the previous isoquant. Conversely, if the distance is decreasing as output increases, the firm is experiencing increasing returns to scale; doubling both inputs results in placement on an isoquant with more than twice the output of the original isoquant.


As with indifference curves, two isoquants can never cross. Also, every possible combination of inputs is on an isoquant.

Finally, any combination of inputs above or to the right of an isoquant results in more output than any point on the isoquant. Although the marginal product of an input decreases as you increase the quantity of the input while holding all other inputs constant, the marginal product is never negative in the empirically observed range since a rational firm would never increase an input to decrease output.

An isoquant map where Q3 > Q2 > Q1. A typical choice of inputs would be labor for input X and capital for input Y. More of input X, input Y, or both is required to move from isoquant Q1 to Q2, or from Q2 to Q3.

3.8.3 Production Isoquant/Isocost Curve

1) Example of an isoquant map with two inputs that are perfect substitutes.

Input xO

Inpu

t y

Q1

Q2

Q3

y

x

Q3 > Q2 > Q1

O

Inpu

t y

Q1 Q2 Q3

y

x


2) Example of an isoquant map with two inputs that are perfect complements.

3.8.4 Shapes of Isoquants

If the two inputs are perfect substitutes, the resulting isoquant map generated is represented in fig. A; with a given level of production Q3, input X can be replaced by input Y at an unchanging rate. The perfect substitute inputs do not experience decreasing marginal rates of return when they are substituted for each other in the production function.

If the two inputs are perfect complements, the isoquant map takes the form of fig. B; with a level of production Q3, input X and input Y can only be combined efficiently in the certain ratio occurring at the kink in the isoquant. The firm will combine the two inputs in the required ratio to maximize profit.

Isoquants are typically combined with isocost lines in order to solve a cost-minimization problem for given level of output. In the typical case shown in the top figure, with smoothly curved isoquants, a firm with fixed unit costs of the inputs will have isocost curves that are linear and downward sloped; any point of tangency between an isoquant and an

Input xO

Inpu

t y

Q1

Q2

Q3

y

x

Q4

Labour O

y

x

Q4

K0

K


isocost curve represents the cost-minimizing input combination for producing the output level associated with that isoquant.

The only relevant portion of the iso quant is the one that is convex to the origin, part of the curve which is not convex to the origin implies negative marginal product for factors of production. Higher ISO-Quant higher the production

Isoquants:

The word 'ISO' is of Greek origin and means equal or same and 'quant' means quantity. An isoquant may be defined as a curve showing all the various combinations of two factors that can produce a given level of output. The isoquant shows the whole range of alternative ways of producing the same level of output.

The modern economists are using isoquant, or "ISO" product curves for determining the optimum factor combination to produce certain units of a commodity at the least cost. The concept of isoquant or equal product curve can be better explained with the help of .schedule given below:

Isoquant Schedule

Combinations Factor X Factor Y Total Output

A 1 14 100 METER

B 2 10 100 METER

C 3 7 100 METER

D 4 5 100 METER

E 5 4 100 METER

In the table given above, it is shown that a producer employs two factors of production X and Y for producing an output of 100 meters of cloth. There are five combinations which produce the same level of output (100 meters of cloth). The factor combination A using 1 unit of factor X and 14 units of factor Y produces 100 meters of cloth. The combination B using 2 units of factor X and 10 units of factor Y produces 100 meters of cloth. Similarly combinations C, U and E, employing 3 units of X and 7 units of Y, 4 units of X and 5 units of Y, 5 units of X and 4 units of Y produce 100 units of output, each. The producer, here., is indifferent as to which combination of inputs he uses for producing the same amount of


output. The alternative techniques for producing a given level of output can be plotted on a graph.

The figure shows y the 100 units isoquant plotted to ISO product schedule. The five factor combinations of X and Y are plotted and are shown by points a, b, c, d and e. if we join these points, it forms an 'isoquant'. An isoquant therefore, is the graphic representation of an iso-product schedule. It may here be noted that all the factor combinations of X and Y on an iso product curve are technically efficient combinations. The producer is indifferent as to which combination he uses for producing the same level of output. It is in this way that an iso product curve is also called 'production indifference curve'. In the figure 12.1, ISO product IP curve represents the various combinations of the two inputs which produce the same level of output (100 meters of cloth).

Isoquant Map

An isoquant map shows a set of iso product curves. Each isoquant represents a different level of output. A higher isoquant shows a higher level of output and a lower isoquant represents a lower level of output.

1 2 3 4 5 6 7 89

87

65

43

21

0 x

y

P


In the figure, a family of three Iso product curves which produce various level of output is shown. The iso product IQ1 yields 100 units of output by using quantities of inputs X and Y. So is also the case with isoquant IQ3 yielding 300 units of output. We conclude that an isoquant map includes a series, of jso-product curves. Each isoquant represents a different level of output. The higher the isoquant output, the further right will be the isoquant.

Properties of Isoquants

The main properties of the isoquants are similar to those of indifference curves. These properties are now discussed in brief.

i) An Isoquant slopes downward from left to right

This implies that the Isoquant is a negatively sloped curve. This is because when the quantify of factor K (capital) is increased, the quantity of L (labor) must be reduced so as to

1 2 3 4 5

76

54

32

1

0x

y

Q1

Q2

Q3

1 2 3 4

2012

84

0x

y


keep the same level of output. The figure depicts that an isoquant IP is negatively sloped curve. This curve shows that as the amount of factor K is increased from one unit to 2 units, the units of factor L are decreased from 20 to 15 only so that output of 100 units remains constant.

(ii) An Isoquant that lies above and to the right of another represents a higher output level

It means a higher isoquant represents higher level of output. The figure represents this property. It shows that greater output can be secured by increasing the quantity combinations of both the factors X and Y. The producer increases the output from 100 units to 200 units by increasing the quantity combination of both the X and Y. The combination of OC of capital and OL of labor yield 100 units of production. The production can be increased to 200 units by increasing the capital from OC to OC1 and labor from OL to OL1.

(iii) Isoquants cannot cut each other

The two isoquants can not intersect each other. If two isoquant are drawn to intersect each other as is shown in this figure, then it is a negation of the property that higher Isoquant represents higher level of output to a lower Isoquant. The intersection at point E shows that the same factor combination can produce 100 units as well as 200 units. But this is quite

C1

C

0x

y

Q2

Q1

B

0x

y

Capital

E

A

Labo

ur


absurd. How can the same level of factor combination produce two different levels of output, when the technique of production remains unchanged. Hence two isoquants cannot intersect each other.

(iv) The isoquants are convex to the origin

This property implies that the marginal significance of one factor in terms of another factor diminishes along an ISO product curve. In other words, the isoquants are convex to the origin due to diminishing marginal rate of substitution, In this figure MRSKL diminishes from 5:1 to 4:1 and further to 3:1. This shows that as more and more units of capital (K) are employed to produce 100 units of the product, lesser and lesser units of labor (L) are used. Hence diminishing marginal rate of technical substitution is the reason for the convexity of an isoquant.

(v) Each isoquant is oval shaped

The iso product curve, is elliptical. This means that the firm produces only those segments of the iso-product curves which are convex to the origin and lie between the ridge lines. This is the economic region of production.

3.8.5 Isocost Lines

Definition of Isocost Lines

A firm can produce a given level of output using efficiently different combinations of two inputs. For choosing efficient combination of the inputs, the producer selects that combination of factors which has the lower cost of production. The information about the cost can be obtained from the isocost lines.

Labour

O

Cap

ital

A

B

C

y

x


Explanation of Isocost Lines

An isocost line is also called outlay line or price line or factor cost line. An isocost line shows all the combinations of labor and capital that are available for a given total cost to-the producer. Just as there are infinite number of isoquants, there are infinite number of isocost lines, one for every possible level of a given total cost. The greater the total cost, the further from origin is the isocost line. The isocost line can be explained easily by taking a simple example.

Let us examine a firm which wishes to spend $100 on a combination of two factors labor and capital for producing a given level of output. We suppose further that the price of one unit of labor is $5 per day. This means that the firm can hire 20 units of labor. On the other hand if the price of capital is $10 per unit, the firm will purchase 10 units of capital. In the fig. 12.7, the point A shows 10 units of capital used whereas point T shows 20 units of labor are hired at the given price. If we join points A and T, we get a line AT. This AT line is called isocost line or outlay line. The isocost line is obtained with an outlay of $100.

Let us assume now that there is no change in the market prices of the two factors labor and capita! but the firm increases the total outlay to $150. The new price line BK shows that with an outlay of $150, the producer can purchase 15 units of capital or 30 units of labor. The new price line BK Shifts upward to the right. In case the firm reduces the outlay to $50 only, the isocost line CD shifts downward to the left of original isocost line and remains parallel to the original price line.

The isocost line plays a similar role in the firm's decision making as the budget line does in consumer's decision making. The only difference between the two is that the consumer has a single budget line which is determined by the income of the consumer. Whereas the firm faces many isocost lines depending upon the different level of expenditure the firm might make. A firm may incur low cost by producing relatively lesser output or it may incur relatively high cost by producing a relatively large quantity.

3.8.6 Types of Isoquants

(1) Linear Isoquant

(2) There is perfect substitutability of inputs.

(3) Right angle Isoquant

(4) Convex Isoquant

(5) Equal Product curves


1. Linear isoquant

Given output – say 100 units – can be produced by using only capital or only labour or by a number of combinations of labour and capital. – both are perfectly substitutable.

2. Perfect suitability of inputs

Given a power plant, equipped to use either oil or gas, various units of electric power can be produced by burning gas only, oil only or in varying combinations of each. Both gas and oil are perfect substitutes. Linear Isoquants Oil

3. Right angle Isoquant

Here there is complete non-substitutability between the inputs (strictly complimentary).

For example, exactly two wheels and one frame are required to produce a bicycle and wheels cannot be substituted for frames.

Similarly, two wheels and one chassis are required for a scooter.

This is also known as Leontief Isoquant. Right angle Isoquant Chassis

4. Convex Isoquant

This form assumes imperfect substitutability of inputs.

E.g. A shirt can be made with more wastage of cloth when less care (less labour) is used. (C1)

If more is spent on labour, the shirt can be made with less cloth, wastage being less. (C2)

If still more care is taken by spending more on labour, minimum wastage is done, by using still lesser amount of cloth.(C3) Convex Isoquant Cloth.

Economic Region of an Isoquant When relatively small amount of a factor is combined with relatively large amount of another factor in an iso-quant, in such a manner that the marginal productivity of this abundant factor tends to be negative, resulting in decline in total output. In such cases, the end portions of the curves are regarded as uneconomical. Thus when extended on either side, the iso-quants are oval shaped.


Economic region of the iso-quant is determined by drawing tangents to the curves parallel to the two axes, and the points of tangency indicate zero marginal productivity of the abundant factor. Economic Region Difference between Equal Product Curve (Isoquant) and Indifference Curve Indifference Curves

Indifference curves indicate level of satisfaction.

Indifference curves relate to combinations between two commodities.

Indifference curves cannot be labelled easily as there is no numerical measurement of the satisfaction involved.

On indifference map, between higher and lower indifference curve, the extent of difference in the satisfaction is not quantifiable.

5. Equal Product curves

Equal product curves indicate quantity of output.

Equal product curves relate to combinations between two factors of production.

Equal product curves can be labelled easily as physical units of output represented by it are measurable.

On equal product map, we can measure the exact difference between output represented by one iso-quant and another iso-quant. Cobb-Douglas Production Function Cobb-Douglas production function relates output in American Manufacturing industries to labour and capital inputs, taking the form P = a(LbC1-b) …a and b are +ve constants. P = total output (production) L = index of labour employed in manufacturing C = index of fixed capital in manufacturing b and 1-b are elasticities of production representing percentage response of output to percentage changes in labour and capital. The above stated production function is a linear and homogeneous function of degree, one which establishes constant returns to scale.

Managerial uses of production function

In microeconomics, a production function asserts that the maximum output of a technologically-determined production process is a mathematical production of input factors of production. Considering the set of all technically feasible combinations of output and inputs, only the combinations encompassing a maximum output for a specified set of inputs would constitute the production function.


Alternatively, a production function can be defined as the specification of the minimum input requirements needed to produce designated quantities of output, given available technology. It is usually presumed that unique production functions can be constructed for every production technology.

By assuming that the maximum output technologically possible from a given set of inputs is achieved, economists using a production function in analysis are abstracting away from the engineering and managerial problems inherently associated with a particular production process. The engineering and managerial problems of technical efficiency are assumed to be solved, so that analysis can focus on the problems of allocative efficiency.

The firm is assumed to be making allocative choices concerning how much of each input factor to use, given the price of the factor and the technological determinants represented by the production function. A decision frame, in which one or more inputs are held constant, may be used;

For example, capital may be assumed to be fixed or constant in the short run, and only labour variable, while in the long run, both capital and labour factors are variable, but the production function itself remains fixed, while in the very long run, the firm may face even a choice of technologies, represented by various, possible production functions.

The relationship of output to inputs is non-monetary, that is, a production function relates physical inputs to physical outputs, and prices and costs are not considered. But, the production function is not a full model of the production process: it deliberately abstracts away from essential and inherent aspects of physical production processes, including error, entropy or waste.

Moreover, production functions do not ordinarily model the business processes, either, ignoring the role of management, of sunk cost investments and the relation of fixed overhead to variable costs. (For a primer on the fundamental elements of microeconomic production theory, see production theory basics).

The primary purpose of the production function is to address allocative efficiency in the use of factor inputs in production and the resulting distribution of income to those factors. Under certain assumptions, the production function can be used to derive a marginal product for each factor, which implies an ideal division of the income generated from output into an income due to each input factor of production.


Meaning

Cost is analyzed from the producer’s point of view. Cost estimates are made in terms of money.

Cost calculations are indispensable for management decisions.

In the production process, a producer employs different factor inputs. These factor inputs are to be compensated by the producer for the services in the production of a commodity. The compensation is the cost. The value of inputs required in the production of a commodity determines its cost of output.

Cost of production refers to the total money expenses (Both explicit and implicit) incurred by the producer in the process of transforming inputs into outputs.

In short, it refers total money expenses incurred to produce a particular quantity of output by the producer. The knowledge of various concepts of costs, cost output relationship etc. occupies a prominent place in cost analysis.

3.6.1 Managerial Uses of Cost Analysis

A detailed study of cost analysis is very useful for managerial decisions. It helps the management

1. To find the most profitable rate of operation of the firm.

2. To determine the optimum quantity of output to be produced and supplied.

3. To determine in advance the cost of business operations.

4. To locate weak points in production management to minimize costs.

5. To fix the price of the product.

6. To decide what sales channel to use.

7. To have a clear understanding of alternative plans and the right costs involved in them.

8. To have clarity about the various cost concepts.

9. To decide and determine the very existence of a firm in the production field.

3.6 COST CONCEPTS


10. To regulate the number of firms engaged in production.

11. To decide about the method of cost estimation or calculations.

12. To find out decision making costs by reclassifications of elements, reprising of input factors etc, so as to fit the relevant costs into management planning, choice etc.

3.6.2 Different Kinds of Cost Concepts.

1. Money Cost and Real Cost

When cost is expressed in terms of money, it is called as money cost. It relates to money outlays by a firm on various factor inputs to produce a commodity. In a monetary economy, all kinds of cost estimations and calculations are made in terms of money only. .Hence, the knowledge of money cost is of great importance in economics. Exact measurement of money cost is possible.

When cost is expressed in terms of physical or mental efforts put in by a person in the making of a product, it is called as real cost. It refers to the physical, mental or psychological efforts, the exertions, sacrifices, the pains, the discomforts, displeasures and inconveniences which various members of the society have to undergo to produce a commodity. It is a subjective and relative concept and hence exact measurement is not possible.

2. Implicit or Imputed Costs and Explicit Costs

Explicit costs are those costs which are in the nature of contractual payments and are paid by an entrepreneur to the factors of production [excluding himself] in the form of rent, wages, interest and profits, utility expenses, and payments for raw materials etc. They can be estimated and calculated exactly and recorded in the books of accounts. Implicit or imputed costs are implied costs. They do not take the form of cash outlays and as such do not appear in the books of accounts. They are the earnings of owner employed resources.

For example, the factor inputs owned by the entrepreneur himself like capital can be utilized by himself or can be supplied to others for a contractual sum if he himself does not utilize them in the business. It is to be remembered that the total cost is a sum of both implicit and explicit costs.

3. Actual costs and Opportunity Costs

Actual costs are also called as outlay costs, absolute costs and acquisition costs. They are those costs that involve financial expenditures at some time and hence are recorded in the books of accounts. They are the actual expenses incurred for producing or acquiring a commodity or service by a firm. For example, wages paid to workers, expenses on raw materials, power, fuel and other types of inputs. They can be exactly calculated and accounted without any difficulty.


Opportunity cost of a good or service is measured in terms of revenue which could have been earned by employing that good or service in some other alternative uses.

In other words, opportunity cost of anything is the cost of displaced alternatives or costs of sacrificed alternatives. It implies that opportunity cost of anything is the alternative that has been foregone. Hence, they are also called as alternative costs. Opportunity cost represents only sacrificed alternatives. Hence, they can never be exactly measured and recorded in the books of accounts.

The knowledge of opportunity cost is of great importance to management decision. They help in taking a decision among alternatives. While taking a decision among several alternatives, a manager selects the best one which is more profitable or beneficial by sacrificing other alternatives.

For example, a firm may decide to buy a computer which can do the work of 10 laborers. If the cost of buying a computer is much lower than that of the total wages to be paid to the workers over a period of time, it will be a wise decision. On the other hand, if the total wage bill is much lower than that of the cost of computer, it is better to employ workers instead of buying a computer. Thus, a firm has to take a number of decisions almost daily.

4. Direct costs and indirect costs

Direct costs are those costs which can be specifically attributed to a particular product, a department, or a process of production. For example, expenses on raw materials, fuel, wages to workers, salary to a divisional manager etc are direct costs. On the other hand, indirect costs are those costs, which are not traceable to any one unit of operation. They cannot be attributed to a product, a department or a process.

For example, expenses incurred on electricity bill, water bill, telephone bill, administrative expenses etc.

5. Past and future costs.

Past costs are those costs which are spent in the previous periods. On the other hand, future costs are those which are to be spent. in the future. Past helps in taking decisions for future.

6. Marginal and Incremental costs

Marginal cost refers to the cost incurred on the production of another or one more unit. It implies additional cost incurred to produce an additional unit of output It has nothing to do with fixed cost and is always associated with variable cost. Incremental cost on the other hand refers to the costs involved in the production of a batch or group of output. They are the added costs due to a change in the level or nature of business activity.


For example, cost involved in the setting up of a new sales depot in another city or cost involved in the production of another 100 extra units.

7. Fixed costs and variable costs.

Fixed costs are those costs which do not vary with either expansion or contraction in output. They remain constant irrespective of the level of output. They are positive even if there is no production. They are also called as supplementary or over head costs.

On the other hand, variable costs are those costs which directly and proportionately increase or decrease with the level of output produced. They are also called as prime costs or direct costs.

8. Accounting costs and economic costs.

Accounting costs are those costs which are already incurred on the production of a particular commodity. It includes only the acquisition costs. They are the actual costs involved in the making of a commodity. On the other hand, economic costs are those costs that are to be incurred by an entrepreneur on various alternative programs. It involves the application of opportunity costs in decision making.

3.6.3 Determinants of Costs

Cost behavior is the result of many factors and forces. But it is very difficult to determine in general the factors influencing the cost as they widely differ from firm to firm and even industry to industry. However, economists have given some factors considering them as general determinants of costs. They have enough importance in modern business set up and decision making process.

The following factors deserve our attention in this connection.

1. Technology

Modern technology leads to optimum utilization of resources, avoid all kinds of wastages, saving of time, reduction in production costs and resulting in higher output. On the other hand, primitive technology would lead to higher production costs.

2. Rate of output: (the degree of utilization of the plant and machinery)

Complete and effective utilization of all kinds of plants and equipments would reduce production costs and under utilization of existing plants and equipments would lead to higher production costs.

3. Size of Plant and scale of production


Generally speaking big companies with huge plants and machineries organize production on large scale basis and enjoy the economies of scale which reduce the cost per unit.

4. Prices of input factors

Higher market prices of various factor inputs result in higher cost of production and vice-versa.

5. Efficiency of factors of production and the management

Higher productivity and efficiency of factors of production would lead to lower production costs and vice versa.

6. Stability of output

Stability in production would lead to optimum utilization of the existing capacity of plants and equipments. It also brings savings of various kinds of hidden costs of interruption and learning leading to higher output and reduction in production costs.

7. Law of returns

Increasing returns would reduce cost of production and diminishing returns increase cost.

8. Time period

In the short run, cost will be relatively high and in the long run, it will be low as it is possible to make all kinds of adjustments and readjustments in production process. Thus, many factors influence cost of production of a firm.

Relationship: Cost Function

Cost and output are correlated. Cost output relations play an important role in almost all business decisions. It throws light on cost minimization or profit maximization and optimization of output. The relation between the cost and output is technically described as the “COST FUNCTION”. The significance of cost output relationship is so great that in economic analysis the cost function usually refers to the relationship between cost and rate of

3.7 COST OUTPUT


output alone and we assume that all other independent variables are kept constant. Mathematically speaking TC = f (Q) where TC = Total cost and Q stands for output produced.

However, cost function depends on three important variables.

1. Production function

If a firm is able to produce higher output with a little quantity of inputs, in that case, the cost function becomes cheaper and vice-versa.

2. The market prices of inputs

If market prices of different factor inputs are high in that case, cost function becomes higher and vice-versa.

3. Period of time

Cost function becomes cheaper in the long run and it would be relatively costlier in the short run.

Types of cost function.

Generally speaking there are two types of cost functions.

1. Short run cost function.

2. Long run cost function.

Relationship and Cost curves in the Short-Run.

It is interesting to note that the relationship between the cost and output is different at two different periods of time i.e. short run and long run. Generally speaking, cost of production will be relatively higher in the short run when compared to the long run. This is because a producer will get enough time to make all kinds of adjustments in the productive process in the long run than in the short run.

When cost and output relationship is represented with the help of diagrams, we get short run and long run cost curves of the firm. Now we shall make a detailed study of cost out put relations both in the short-run as well as in the long run.

3.7.1 Meaning of Short Run

Short-run is a period of time in which only the variable factors can be varied while fixed factors like plant, machinery etc remains constant.


Hence, the plant capacity is fixed in the short run. The total number of firms in an industry will remain the same. Time is insufficient either for the entry of new firms or exit of the old firms. If a firm wants to produce greater quantities of output, it can do so only by employing more units of variable factors or by having additional shifts, or by having over time work for the existing labor force or by intensive utilization of existing stock of capital assets etc. Hence, short run is defined as a period where adjustments to changed conditions are only partial.

The short run cost function relates to the short run production function. It implies two sets of input components – (a) fixed inputs and (b) variable inputs. Fixed inputs are unalterable. They remain unchanged over a period of time. On the other hand, variable factors are changed to vary the output in the short run.

Thus, in the short period some inputs are fixed in amount and a firm can expand or contract its output only by changing the amounts of other variable inputs. The cost output relationship in the short run refers to a particular set of conditions where the scale of operation is limited by the fixed plant and equipment. Hence, the costs of the firm in the short run are divided into fixed cost and variable costs. We shall study these two concepts of costs in some detail

1. Fixed costs

These costs are incurred on fixed factors like land, buildings, equipments, plants, superior type of labor, top management etc. Fixed costs in the short run remain constant because the firm does not change the size of plant and the amount of fixed factors employed.

Fixed costs do not vary with either expansion or contraction in output. These costs are to be incurred by a firm even output is zero. Even if the firm close down its operation for some time temporarily in the short run, but remains in business, these costs have to be borne by it. Hence, these costs are independent of output and are referred to as unavoidable contractual cost.

Prof. Marshall called fixed costs as supplementary costs. They include such items as contractual rent payment, interest on capital borrowed, insurance premiums, depreciation and maintenance allowances, administrative expenses like manager’s salary or salary of the permanent staff, property and business taxes, license fees, etc. They are called as overhead costs because these costs are to be incurred whether there is production or not. These costs are to be distributed on each unit of output produced by a firm. Hence, they are called as indirect costs.


2. Variable costs

The cost corresponding to variable factors are discussed as variable costs. These costs are incurred on raw materials, ordinary labor, transport, power, fuel, water etc, which directly vary in the short run.

Variable costs directly and proportionately increase or decrease with the level of output. If a firm shuts down for some time in the short run; then it will not use the variable factors of production and will not therefore incur any variable costs. Variable costs are incurred only when some amount of output is produced. Total variable costs increase with increase in the level of production and vice-versa.

Prof. Marshall called variable costs as prime costs or direct costs because the volume of output produced by a firm depends directly upon them. It is clear from the above description that production costs consist of both fixed as well as variable costs. The difference between the two is meaningful and relevant only in the short run. In the long run all costs become variable because all factors of production become adjustable and variable in the long run.

However, the distinction between fixed and variable costs is very significant in the short run because it influences the average cost behavior of the firm. In the short run, even if a firm wants to close down its operation but wants to remain in business, it will have to incur fixed costs but it must cover at least its variable costs.

Cost output relationship and nature and behavior of cost curves in the short run In order to study the relationship between the level of output and corresponding cost of production, we have to prepare the cost schedule of the firm.

A cost schedule is a statement of a variation in costs resulting from variations in the levels of output. It shows the response of cost to changes in output. A hypothetical cost schedule of a firm has been represented in the following table.

Output in Units

FC TVC TC AFC AVC AC MC

0 360 - 360 - - - -

1 360 180 540 360 180 540 180

2 360 240 600 180 120 300 60

3 360 270 630 120 90 210 30


4 360 315 675 90 78 168 45

5 360 420 780 72 84 156 105

6 360 630 900 60 105 165 210

On the basis of the above cost schedule, we can analyse the relationship between changes in the level of output and cost of production. If we represent the relationship between the two in a geometrical manner, we get different types of cost curves in the short run. In the short run, generally we study the following kinds of cost concepts and cost curves.

1. Total fixed cost (TFC)

TFC refers to total money expenses incurred on fixed inputs like plant, machinery, tools & equipments in the short run. Total fixed cost corresponds to the fixed inputs in the short run production function. TFC remains the same at all levels of output in the short run. It is the same when output is nil. It indicates that whatever may be the quantity of output, whether 1 to 6 units, TFC remain constant. The TFC curve is horizontal and parallel to OX axis, showing that it is constant regardless of out put per unit of time. TFC starts from a point on Y axis indicating that the total fixed cost will be incurred even if the output is zero. In our example, Rs 30000 is TFC. It is obtained by summing up the product or quantities of the fixed factors multiplied by their respective unit price.

TFC = TC – TFC

2. Total variable cost (TVC)

TVC refers to total money expenses incurred on the variable factors inputs like raw materials, power, fuel, water, transport and communication etc, in the short run. Total variable cost corresponds to variable inputs in the short run production function. It is obtained

Output O

Cos

t of p

lan

300 TFC

y

x


by summing up the production of quantities of variable inputs multiplied by their prices. The formula to calculate TVC is as follows. TVC = TCTFC.

TVC = f (Q) i.e. TVC is an increasing function of out put. In other words TVC varies with output. It is nil, if there is no production. Thus, it is a direct cost of output. TVC rises sharply in the beginning, gradually in the middle and sharply at the end in accordance with the law of variable proportion. The law of variable proportion explains that in the beginning to obtain a given quantity of output, relative variation in factors needed are in less proportion, but after a point when the diminishing returns operate, variable factors are to be employed in a larger proportion to increase the same level of output. TVC curve slope upwards from left to right.

TVC curve rises as output is expanded. When out put is Zero, TVC also will be zero. Hence, the TVC curve starts from the origin.

TVC = TC – TFC

3. Total cost (TC)

The total cost refers to the aggregate money expenditure incurred by a firm to produce a given quantity of output. The total cost is measured in relation to the production function by multiplying the factor prices with their quantities. TC = f (Q) which means that the T.C. varies with the output. Theoretically speaking TC includes all kinds of money costs, both explicit and implicit cost. Normal profit is included in the total cost as it is an implicit cost. It includes fixed as well as variable costs.

Hence, TC = TFC +TVC.

TC varies in the same proportion as TVC. In other words, a variation in TC is the result of variation in TVC since TFC is always constant in the short run.

Output O

Cos

t of p

lan

TVC

y

x


The total cost curve is rising upwards from left to right. In our example the TC curve starts form Rs. 300-00 because even if there is no output, TFC is a positive amount. TC and TVC have same shape TC = TFC + TVC TC because an increase in output increases them both by the same amount since TFC is constant. TC curve is derived by adding up vertically the TVC and TFC curves. The vertical distance between TVC curve and TC curve is equal to TFC and is constant throughout because TFC is constant.

4. Average fixed cost (AFC)

Average fixed cost is the fixed cost per unit of output. When TFC is divided by total units of out put AFC is obtained, Thus, AFC = TFC/Q

AFC and output have inverse relationship. It is higher at smaller level and lower at the higher levels of output in a given plant. The reason is simple to understand. Since AFC = TFC/Q, it is a pure mathematical result that the numerator remaining unchanged, the increasing denominator causes diminishing product. Hence, TFC spreads over each unit of out put with the increase in output. Consequently, AFC diminishes continuously. This relationship between output and fixed cost is universal for all types of business concerns.

Output O

Cos

t of p

lan

TC

y

x

TFC

Output O

Cos

t of p

lan

y

x

AFC


The AFC curve has a negative slope. The curve slopes downwards throughout the length. The AFC curve goes very nearer to X axis, but never touches axis. Graphically it will fall steeply in the beginning, gently in middle and tend to become parallel to OX axis. Mathematically speaking as output increases, AFC diminishes. But AFC will never become zero because the TFC is a positive amount. AFC will never fall below a minimum amount because in the short run, plant capacity is fixed and output cannot be enlarged to an unlimited extent.

5. Average variable cost: (AVC)

The average variable cost is variable cost per unit of output. AVC can be computed by dividing the TVC by total units of output. Thus AVC = TVC/Q. The AVC will come down in the beginning and then rise as more units of output are produced with a given plant. This is because as we add more units of variable factors in a fixed plant, the efficiency of the inputs first increases and then it decreases. The AVC curve is a U shaped cost curve. It has three phases.

a. Decreasing phase

In the first phase from A to B, AVC declines, As output expands, AVC declines because when we add more quantity of variable factors to a given quantity of fixed factors, output increases more efficiently and more than proportionately due to the operation of increasing returns.

b. Constant phase

In the II phase, i.e. at B, AVC reaches its minimum point. When the proportion of both fixed and variable factors are the most ideal, the output will be the optimum. Once the firm

Output O

Cos

t of p

lan

y

x

AVC

A C

B


operates at its normal full capacity, output reaches its zenith and as such AVC will become the minimum.

c. Increasing phase

In the III phase, from B to C, AVC rises when once the normal capacity is crossed, the AVC rises sharply. This is because additional units of variables factors will not result in more than proportionate output. Hence, greater output may be obtained but at much greater AVC. The old proverb “Too many cooks spoil the broth” aptly applies to this III stage. It is clear that as long as increasing returns operate, AVC falls and when diminishing returns set in, AVC tends to increase.

6. Average total cost (ATC) or Average cost (AC)

Ac refers to cost per unit of output. AC is also known as the unit cost since it is the cost per unit of output produced. AC is the sum of AFC and AVC. Average total cost or average cost is obtained by dividing the total cost by total output produced. AC = TC/Q Also AC is the sum of AFC and AVC. In the short run AC curve also tends to be U shaped. The combined influence of AFC and AVC curves will shape the nature of AC curve.

As we observe, average fixed cost begin to fall with an increase in output while average variable costs come down and rise. As long as the falling effect of AFC is much more than the rising effect of AVC, the AC tends to fall. At this stage, increasing returns and economies of scale operate and complete utilization of resources force the AC to fall. When the firm produces the optimum output, AC becomes minimum. This is called as least – cost output level. Again, at the point where the rise in AVC exactly counter balances the fall in AFC, the balancing effect causes AC to remain constant.

In the third stage when the rise in average variable cost is more than drop in AFC, then the AC shows a rise, When output is expanded beyond the optimum level of output,

Output O

Cos

t of p

lan

y

x

AC

A

B

C


diminishing returns set in and diseconomies of scale starts operating. At this stage, the indivisible factors are used in wrong proportions. Thus, AC starts rising in the third stage.

The short run AC curve is also called as “Plant curve”. It indicates the optimum utilization of a given plant or optimum plant capacity.

7. Marginal Cost (MC)

Marginal cost may be defined as the net addition to the total cost as one more unit of output is produced. In other words, it implies additional cost incurred to produce an additional unit.

For example, if it costs Rs. 100 to produce 50 units of a commodity and Rs. 105 to produce 51 units, then MC would be Rs. 5. It is obtained by calculating the change in total costs as a result of a change in the total output. Also MC is the rate at which total cost changes with output. Hence, MC = D TC / D TQ, where D TC stands for change in total cost and D TQ stands for change in total output. Also MCn = TCn –TC n1

It is necessary to note that MC is independent of TFC and it is directly related to TVC as we calculate the cost of producing only one unit. In the short run, the MC curve also tends to be U shaped.

The shape of the MC curve is determined by the laws of returns. If MC is falling, production will be under the conditions of increasing returns and if MC is rising, production will be subject of diminishing returns.

The table indicates the relationship between AC & MC

Output in Units TC in Rs. AC in Rs. Difference in Rs.

Output O

Cos

t of p

lan

y

x

MC

A

B

C


MC

1 150 150 -

2 190 95 40

3 220 73 30

4 236 59 16

5 270 54 34

6 324 54 54

7 415 59 91

8 580 72 165

Relation between AC and MC

From the diagram it is clear that:

1. Both MC and AC fall at a certain range of output and rise afterwards.

2. When AC falls, MC also falls but at certain range of output MC tends to rise even though AC continues to fall. However, MC would be less than AC. This is because MC is attributed to a single unit where as in case of AC, the decreasing AC is distributed over all the units of output produced.

Output O

Cos

t of p

lan

y

x

MC AC

AC = MC


3. So long as AC is falling, MC is less than AC. Hence, MC curve lies below AC curve. It indicates that fall in MC is more than the fall in AC. MC reaches its minimum point before AC reaches its minimum.

AC=MC

4. When AC is rising, after the point of intersection, MC will be greater than AC. This is because in case of MC, the increasing MC is attributed to a single unit, where as in case of AC, the increasing AC is distributed over all the output produced.

5. So long as the AC is rising, MC is greater and AC. Hence, AC curve lies to the left side of the MC curve. It indicates that rise in MC is more than the rise in AC.

6. MC curve cuts the AC curve at the minimum point of the AC curve. This is because, when MC decreases, it pulls AC down and when MC increases, it pushes AC up. When AC is at its minimum, it is neither being pulled down or being pushed up by the MC. Thus, When AC is minimum, MC = AC. The point of intersection indicates the least cost combination point or the optimum position of the firm. At output Q the firm is working at its “Optimum Capacity” with lowest AC. Beyond Q, there is scope for “Maximum Capacity” with rising cost.

Cost Output Relationship in the Long Run

Long run is defined as a period of time where adjustments to changed conditions are complete. It is actually a period during which the quantities of all factors, variable as well as fixed factors can be adjusted. Hence, there are no fixed costs in the long run. In the short run, a firm has to carry on its production within the existing plant capacity, but in the long run it is not tied up to a particular plant capacity. If demand for the product increases, it can expand output by enlarging its plant capacity. It can construct new buildings or hire them, install new machines, employ administrative and other permanent staff. It can make use of the existing as well as new staff in the most efficient way and there is lot of scope for making indivisible factors to become divisible factors.

On the other hand, if demand for the product declines, a firm can cut down its production permanently. The size of the plant can also be reduced and other expenditure can be minimized.


Hence, production cost comes down to a greater extent in the long run. As all costs are variable in the long run, the total of these costs is total cost of production.

Hence, the distinction between fixed and variables costs in the total cost of production will disappear in the long run. In the long run only the average total cost is important and considered in taking long term output decisions.

Long run average cost is the long run total cost divided by the level of output. In brief, it is the per unit cost of production of different levels of output by changing the size of the plant or scale of production.

The long run cost – output relationship is explained by drawing a long run cost curve through short – run curves as the long period is made up of many short – periods as the day is made up of 24 hours and a week is made out of 7 days. This curve explains how costs will change when the scale of production is varied.

Output O

Cos

t of p

lan

y

x

SAC

SAC

SAC

SAC SAC

SAC

SAC

SAC

SAC

Q


The long run cost curves are influenced by the laws of return to scale as against the short run cost curves which are subject to the working of law of variable proportions.

In the short run the firm is tied with a given plant and as such the scale of operation remains constant. There will be only one AC curve to represent one fixed scale of output in the short run. In the long run as it is possible to alter the scale of production, one can have as many AC curves as there are changes in the scale of operations.

In order to derive LAC curve, one has to draw a number of SAC curves, each curve representing a particular scale of output. The LAC curve will be tangential to the entire family of SAC cures. It means that it will touch each SAC curve at its minimum point.

Production cost difference in the short run and long run

In the diagram, the LAC curve is drawn on the basis of three possible plant sizes. Consequently, we have three different SAC curves – SAC1, SAC2 and SAC3. They represent three different scales of output. For output OM3 the AC will be L2M2 in the short run as well as the long run. When output is to be expanded to OM3, it can be obtained at a higher average cost of production. K3, M3 is the short run AC because, scale of production would remain constant in the short run. But the same output of OM3 can be produced at a lower AC of L3M3 in the long run since the scale of production can be modified according to the

Output O

Cos

t of p

lan

y

x

SACLAC

SAC


requirements. The distance between K3L3 represent difference between the cost of production in the short run and long run.

Similarly, when output is contracted to OM1 in the short run, K1M1 will become the short run AC and L1M1 will be the long run AC. Hence, K1L1 indicates the differences between short run and long run cost of production. If we join points L1, L2 and L3 we get LAC curve.

Important features of long run AC curves

1. Tangent curve

Different SAC curves represent different operational capacities of different plants in the short run. LAC curve is locus of all these points of tangency. The SAC curve can never cut a LAC curve though they are tangential to each other. This implies that for any given level of output, no SAC curve can ever be below the LAC curve. Hence, SAC cannot be lower than the LAC in the ling run. Thus, LAC curve is tangential to various SAC curves.

2. Envelope curve

It is known as Envelope curve because it envelopes a group of SAC curves appropriate to different levels of output.

3. Flatter U shaped or dish shaped curve.

The LAC curve is also U shaped or dish shaped cost curve. But It is less pronounced and much flatter in nature. LAC gradually falls and rises due to economies and diseconomies of scale.

4. Planning curve.

The LAC cure is described as the Planning Curve of the firm because it represents the least cost of producing each possible level of output. This helps in producing optimum level of output at the minimum LAC. This is possible when the entrepreneur is selecting the optimum scale plant.

Optimum scale plant is that size where the minimum point of SAC is tangent to the minimum point of LAC.

5. Minimum point of LAC curve should be always lower than the minimum point of SAC curve.

This is because LAC can never be higher than SAC or SAC can never be lower than LAC. The LAC curve will touch the optimum plant SAC curve at its minimum point.


A rational entrepreneur would select the optimum scale plant. Optimum scale plant is that size at which SAC is tangent to LAC, such that both the curves have the minimum point of tangency. In the diagram, OM2 is regarded as the optimum scale of output, as it has the least per unit cost. At OM2 output LAC = SAC.

LAC curve will be tangent to SAC curves lying to the left of the optimum scale or right side of the optimum scale. But at these points of tangency, neither LAC is minimum nor will SAC be minimum.SAC curves are either rising or falling indicating a higher cost

Managerial Use of LAC

The study of LAC is of greater importance in managerial decision making process.

1. It helps the management in the determination of the best size of the plant to be constructed or when a new one is introduced in getting the minimum cost output for a given plant. But it is interested in producing a given output at the minimum cost.

2. The LAC curve helps a firm to decide the size of the plant to be adopted for producing the given output. For outputs less than cost lowering combination at the optimum scale i.e., when the firm is working subject to increasing returns to scale, it is more economical to under use a slightly large plant operating at less than its minimum cost – output than to over use smaller unit.

Conversely, at output beyond the optimum level, that is when the firm experience decreasing return to scale, it is more economical to over use a slightly smaller plant than to under use a slightly larger one. Thus, it explains why it is more economical to over use a slightly small plant rather than to under use a large plant.

3. LAC is used to show how a firm determines the optimum size of the plant. An optimum size of plant is one that helps in best utilization of resources in the most economical manner.

Long Run Marginal cost


A long run marginal cost curve can be derived from the long run average cost curve. Just as the SMC is related to the SAC, similarly the LMC is related to the LAC and, therefore, we can derive the LMC directly from the LAC. In the diagram we have taken three plant sizes (for the sake of simplicity) and the corresponding three SAC and SMC curves.

The LAC curve is drawn by enveloping the family of SAC curves. The points of tangency between the SAC and the LAC curves indicate different outputs for different plant sizes.

If the firm wants to produce ON output in the long run, it will have to choose the plant size corresponding to SAC1. The LAC curve is tangent to SAC1 at point A. For ON output, the average cost is NA and the corresponding marginal cost is NB If LAC curve is tangent to SAC1 curve at point A, the corresponding LMC curve will have to be equal to SMC1 curve at point B. The LMC will pass through point B. In other words, where LAC is equal to SAC curve (for a given output) the LMC will have to be equal to a given SMC.

If output OQ is to be produced in the long run, it will be done at point c which is the point of tangency between SAC2 and the LAC. At point C, the short –run average cost (SAC2) and the short run marginal cost (SMC2) are equal and, therefore, the LAC for output OQ is QC and the corresponding LMC is also QC. The LMC curve will, therefore pass through point C.

Output O

Cos

t of p

lan

y

x

SACLAC

SAC

SAC


Finally, for output OR, at point D the LAC is tangent to SAC3. For OR output at point E LMC is passing through SMC3. By connecting points B ,C and E, we can draw the long run marginal cost curve.

Cost of Production: Formulas

TC = cost per unit × total production. or TC = TFC + TVC

TFC = TC TVC or AFC × Q

TVC = TC – TFC or AVC × Q or addition of MC

AFC = AC – AVC or TFC/Q

AVC = AC – AFC or TVC/Q

AC = AFC + AVC or TC/Q

MC = TCn TCn1 or D TC / D TQ.

Review questions

1. Define production.

2. What is production function?

3. Who are the agents of production?

4. Explain returns to scale.

5. Explain short-term and long-term production function.

6. What is economics of scale?

7. Describe internal and external economics.


8. Explain the benefits and importance of production optimization.

9. Explain the managerial uses of production function.

10. What is cost concept?

11. What are the different kinds of cost concept?

12. What are the determinants of cost?

13. Explain short run and long run cost curves.

14. Describe cost output decision.

15. How to estimate cost?

16. What is isoquants?

17. Explain the types of isoquants.

unit - 3 mg 2452

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