UNIT-III

Demand Forecasting

A demand forecast is the prediction of what will happen to your company's existing product sales. It

would be best to determine the demand forecast using a multi-functional approach. The inputs from sales

and marketing, finance, and production should be considered. The final demand forecast is the consensus

of all participating managers. You may also want to put up a Sales and Operations Planning group

composed of representatives from the different departments that will be tasked to prepare the demand

forecast.

Determination of the demand forecasts is done through the following steps:

•  Determine the use of the forecast

•  Select the items to be forecast

•  Determine the time horizon of the forecast

•  Select the forecasting model(s)

•  Gather the data

•  Make the forecast

•  Validate and implement results

The time horizon of the forecast is classified as follows:

Description Forecast Horizon

Short-range Medium-range Long-range

Duration Usually less than 3

months, maximum of 1

year

3 months to 3 years More than 3 years

Applicability Job scheduling, worker

assignments

Sales and production

planning, budgeting

New product development,

facilities planning

How is demand forecast determined?

There are two approaches to determine demand forecast – (1) the qualitative approach, (2) the

quantitative approach. The comparison of these two approaches is shown below:

Description Qualitative Approach Quantitative Approach

Applicability Used when situation is vague & little

data exist (e.g., new products and

technologies)

Used when situation is stable & historical

data exist

(e.g. existing products, current technology)

Considerations Involves intuition and experience Involves mathematical techniques

Techniques Jury of executive opinion

Sales force composite

Delphi method

Consumer market survey

Time series models

Causal models

 

Qualitative Forecasting Methods

Your company may wish to try any of the qualitative forecasting methods below if you do not have

historical data on your products' sales.

Qualitative Method Description

Jury of executive opinion The opinions of a small group of high-level managers are pooled and

together they estimate demand. The group uses their managerial

experience, and in some cases, combines the results of statistical models.

Sales force composite Each salesperson (for example for a territorial coverage) is asked to project

their sales. Since the salesperson is the one closest to the marketplace, he

has the capacity to know what the customer wants. These projections are

then combined at the municipal, provincial and regional levels.

Delphi method A panel of experts is identified where an expert could be a decision maker,

an ordinary employee, or an industry expert. Each of them will be asked

individually for their estimate of the demand. An iterative process is

conducted until the experts have reached a consensus.

Consumer market survey The customers are asked about their purchasing plans and their projected

buying behavior. A large number of respondents is needed here to be able

to generalize certain results.

Quantitative Forecasting Methods

There are two forecasting models here – (1) the time series model and (2) the causal model. A time series

is a s et of evenly spaced numerical data and is o btained by observing responses at regular time periods.

In the time series model , the forecast is based only on past values and assumes that factors that influence

the past, the present and the future sales of your products will continue.

On the other hand, t he causal model uses a mathematical technique known as the regression analysis that

relates a dependent variable (for example, demand) to an independent variable (for example, price,

advertisement, etc.) in the form of a linear equation. The time series forecasting methods are described

below:

Time Series

Forecasting Method

Description

Naïve Approach Assumes that demand in the next period is the same as demand in most recent

period; demand pattern may not always be that stable

For example:

If July sales were 50, then Augusts sales will also be 50

 

Time Series

Description

Forecasting Method

Moving Averages

(MA)

MA is a series of arithmetic means and is used if little or no trend is present in the

data; provides an overall impression of data over time

A simple moving average uses average demand for a fixed sequence of periods and

is good for stable demand with no pronounced behavioral patterns.

Equation:

F 4 = [D 1 + D2 + D3] / 4

F – forecast, D – Demand, No. – Period

(see illustrative example – simple moving average)

A weighted moving average adjusts the moving average method to reflect

fluctuations more closely by assigning weights to the most recent data, meaning,

that the older data is usually less important. The weights are based on intuition and

lie between 0 and 1 for a total of 1.0

Equation:

WMA 4 = (W) (D3) + (W) (D2) + (W) (D1)

WMA – Weighted moving average, W – Weight, D – Demand, No. – Period

(see illustrative example – weighted moving average)

Exponential

Smoothing

The exponential smoothing is an averaging method that reacts more strongly to

recent changes in demand by assigning a smoothing constant to the most recent

data more strongly; useful if recent changes in data are the results of actual change

(e.g., seasonal pattern) instead of just random fluctuations

F t + 1 = a D t + (1 - a ) F t

Where

F t + 1 = the forecast for the next period

D t = actual demand in the present period

F t = the previously determined forecast for the present period

•  = a weighting factor referred to as the smoothing constant

(see illustrative example – exponential smoothing)

Time Series

Decomposition

The time series decomposition adjusts the seasonality by multiplying the normal

forecast by a seasonal factor

(see illustrative example – time series decomposition)

 

Production Function:

 

A given output can be produced with many different combinations of factors of production (land, labor,

capita! and organization) or inputs. The output, thus, is a function of inputs. The functional relationship

that exists between physical inputs and physical output of a firm is called production function.

 

Formula:  

In abstract term, it is written in the form of formula:

 

Q = f (x1, x2, ......., xn)

 

Q is the maximum quantity of output and x1, x2, xn are quantities of various inputs. The functional

relationship between inputs and output is governed by the laws of returns.

 

The laws of returns are categorized into two types.

 

(i) The law of variable proportion seeking to analyze production in the short period.

 

(ii) The law of returns to scale seeking to analyze production in the long period.

 

Law of Variable Proportions/Law of Non Proportional Returns/Law of Diminishing Returns:

(Short Run Analysis of Production): 

There were three laws of returns mentioned in the history of economic thought up till Alfred Marshall's

time. These laws were the laws of increasing returns, diminishing returns and constant returns. Dr.

Marshall was of the view that the law of diminishing returns applies to agriculture and the law of

increasing returns to industry. Much time was wasted in discussion of this issue. However, it was later on

recognized that there are not three laws of production. It is only one law of production which has three

phases, increasing, diminishing and negative production. This general law of production was named as

the Law of Variable Proportions or the Law of Non-Proportional Returns.

 

The Law of Variable Proportions which is the new name of the famous law of Diminishing Returns has

been defined by Stigler in the following words:

 

"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 produce will decrease i.e., the marginal product will

diminish".

 According to Samuelson:"An increase in some inputs relative to other fixed inputs will in a given

state of technology cause output to increase, but after a point, the extra output resulting from the

same addition of extra inputs will become less".

  

Assumptions:

 The law of variable proportions also called the law of diminishing returns holds good under the following

assumptions:

                  

(i) Short run. The law assumes short run situation. The time is too short for a firm to change the quantity

of fixed factors. All the, resources apart from this one variable, are held unchanged in quantity and

quality.

 

(ii) Constant technology. The law assumes that the technique of production remains unchanged during

production.

 

(iii) Homogeneous factors. Each factor unit in assumed to he identical in amount and quality.

 

Explanation and Example:

 The law of variable proportions is, now explained with the help of table and graph.

Fixed Inputs

(Land Capital)

Variable

Resource (labor)

Total Produce

(TP Quintals)

Marginal        Product                (MP

Quintals)

Average Product

(AP Quintals)

30

30

1

2

10

25

10 

15

Increasing marginal

return

10

12.5

 

30

30

30

30

30

3

4

5

6

7

37

47

55

60

63

12

10

8

5

3

Diminishing

marginal returns

12.3

11.8

11.0

10.0

9.0

 

30

30

8

9

63

62

0

-1

Negative marginal

returns

7.9

6.8

 

In the table above, it is assumed that a farmer has only 30 acres of land for cultivation. The investment on

it in the form of tubewells, machinery etc., (capital) is also fixed. Thus land and capital with the farmer is

fixed and labor is the variable resource.

 

As the farmer increases units of labor from one to two to the amount of other fixed resources (land and

capital), the marginal as well as average product increases. The total product also increase at an

increasing rate from 10 to 25 quintals. It is the stage of increasing returns.

 

The stage of increasing returns with the employment of more labor does not last long. It is shown in the

table that with the employment of 3rd labor at the farm, the marginal product and the average product

(AP) both fall but marginal product (MP) falls more speedily than the average product AP). The fall in

MP and AP continues as more men are put on the farm.

 

The decrease, however, remains positive up to the 7th labor employed. On the employment of 7th worker,

the total production remains constant at 63 quintals. The marginal product is zero. if more men are

employed the marginal product becomes negative. It is the stage of negative returns. We here find the

behavior of marginal product (MP). it shows three stages. In the first stage, it increases, in the 2nd it

continues to fall and in the 3rd stage it becomes negative.                  

  

Three Stages of the Law:

 There are three phases or stages of production, as determined by the law of variable proportions:

 (i) Increasing returns.

 (ii) Diminishing returns.

 (iii) Negative returns.

 Diagram/Graph:

 These stages can be explained with the help of graph below:

 

 

(i) Stage of Increasing Returns. The first stage of the law of variable proportions is generally called the

stage of increasing returns. In this stage as a variable resource (labor) is added to fixed inputs of other

resources, the total product increases up to a point at an increasing rate as is shown in figure 11.1.

 

The total product from the origin to the point K on the slope of the total product curve increases at an

increasing rate. From point K onward, during the stage II, the total product no doubt goes on rising but its

slope is declining. This means that from point K onward, the total product increases at a diminishing rate.

In the first stage, marginal product curve of a variable factor rises in a part and then falls. The average

product curve rises throughout .and remains below the MP curve. 

                        

Causes of Initial Increasing Returns:

 The phase of increasing returns starts when the quantity of a fixed factor is abundant relative to the

quantity of the variable factor. As more and more units of the variable factor are added to the constant

quantity of the fixed factor, it is more intensively and effectively used. This causes the production to

increase at a rapid rate. Another reason of increasing returns is that the fixed factor initially taken is

indivisible. As more units of the variable factor are employed to work on it, output increases greatly due

to fuller and effective utilization of the variable factor.

 

(ii) Stage of Diminishing Returns. This is the most important stage in the production function. In stage

2, the total production continues to increase at a diminishing rate until it reaches its maximum point (H)

where the 2nd stage ends. In this stage both the

marginal product (MP) and average product of the variable factor are diminishing but are positive.  

Causes of Diminishing Returns:

 The 2nd phase of the law occurs when the fixed factor becomes inadequate relative to the quantity of the

variable factor. As more and more units of a variable factor are employed, the marginal and average

product decline. Another reason of diminishing returns in the production function is that the fixed

indivisible factor is being worked too hard. It is being used in non-optima! proportion with the variable

factor, Mrs. J. Robinson still goes deeper and says that the diminishing returns occur because the factors

of production are imperfect substitutes of one another.

 

(iii) Stage of Negative Returns. In the 3rd stage, the total production declines. The TP, curve slopes

downward (From point H onward). The MP curve falls to zero at point L2 and then is negative. It goes

below the X axis with the increase in the use of variable factor (labor).

 

Causes of Negative Returns:

 The 3rd phases of the law starts when the number of a variable, factor becomes, too excessive relative, to

the fixed factors, A producer cannot operate in this stage because total production declines with the

employment of additional labor.

 

A rational producer will always seek to produce in stage 2 where MP and AP of the variable factor are

diminishing. At which particular point, the producer will decide to produce depends upon the price of the

factor he has to pay. The producer will employ the variable factor (say labor) up to the point where the

marginal product of the labor equals the given wage rate in the labor market.

 

Importance:

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

 (i) It is helpful in understanding clearly the process of production. It explains the input output relations.

We can find out by-how much the total product will increase as a result of an increase in the inputs.

 (ii) The law tells us that the tendency of diminishing returns is found in all sectors of the economy which

may be agriculture or industry.

 (iii) The law tells us that any increase in the units of variable factor will lead to increase in the total

product at a diminishing rate. The elasticity of the substitution of the variable factor for the fixed factor is

not infinite.

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

standard of living of mankind. The fact, however, is that we can suspend the operation of diminishing

returns by continually improving the technique of production through the progress in science and

technology. 

Law of Diminishing Returns/Law of Increasing Cost:

 

The law of diminishing returns (also called the Law of Increasing Costs) is an important law of micro

economics. The law of diminishing returns states that:

 

"If an increasing amounts of a variable factor are applied to a fixed quantity of other factors per

unit of time, the increments in total output will first increase but beyond some point, it begins to

decline".

 

Richard A. Bilas describes the law of diminishing returns in the following words:

 

"If the input of one resource to other resources are held constant, total product (output) will

increase but beyond some point, the resulting output increases will become smaller and smaller".

 

The law of diminishing return can be studied from two points of view, (i) as it applies to agriculture and

(ii) as it applies in the field of industry.

                  

(1) Operation of Law of Diminishing Returns in Agriculture: 

        

Traditional Point of View. The classical economists were of the opinion that the taw of diminishing

returns applies only to agriculture and to some extractive industries, such as mining, fisheries urban land,

etc. The law was first stated by a Scottish farmer as such. It is the practical experience of every farmer

that if he wishes to raise a large quantity of food or other raw material requirements of the world from a

particular piece of land, he cannot do so. He knows it fully that the producing capacity of the soil is

limited and is subject to exhaustation.

 

As he applies more and more units of labor to a given piece of land, the total produce no doubt increases

but it increases at a diminishing rate.

 

For example, if the number of labor is doubled, the total yield of his land will not be double. It will be less

than double. If it becomes possible to increase the. yield in the very same ratio in which the units of labor

are increased,  then the raw material requirements of the whole world can be met by intensive cultivation

in a single flower-pot. As this is not possible, so a rational farmer increases the application of the units of

labor on a piece of land up to a point which is most profitable to him. This is in brief, is the law of

diminishing returns. Marshall has stated this law as such:

 

"As Increase in capital and labor applied to the cultivation of land causes in general a less than

proportionate increase in the amount of the produce raised, unless it happens to coincide with the

improvement in the act of agriculture".

 Explanation and Example:

 This law can be made more clear if we explain it with the help, of a schedule and a curve.

 

Fixed Input Inputs of Variable

Resources

Total Produce TP

(in tons)

Marginal product MP  

(in tons)

12 Acres

12 Acres

12 Acers

12 Acres

12 Acers

12 Acres

1 Labor

2 Labor

3 Labor

4 Labor

5 Labor

6 Labor

50

120

180

200

200

195

50

70

60

20

0

-5

 

In the schedule given above, a firm first cultivates 12 acres of land (Fixed input) by applying one unit of

labor and produces 50 tons of wheat.. When it applies 2 units of labor, the total produce increases to 120

tons of wheat, here, the total output increased to more than double by doubling the units of labor. It is

because the piece of land is under-cultivated. Had he applied two units of labor in the very beginning, the

marginal return would have diminished by the application of second unit of labor.

 

In our schedules the rate of return is at its maximum when two units of labor are applied. When a third

unit of labor is employed, the marginal return comes down to 60 tons of wheat With the application of 4 th

unit. the marginal return goes down to 20 tons of wheat and when 5 th unit is applied it makes no addition

to the total output. The sixth unit decreased it. This tendency of marginal returns to diminish as successive

units of a variable resource (labor) are added to a fixed resource (land), is called the law of diminishing

returns. The above schedule can be represented graphically as follows:

 

Diagram/Graph:

 

 

In Fig. (11.2) along OX are measured doses of labor applied to a piece of land and along OY, the

marginal return. In the beginning the land was not adequately cultivated, so the additional product of the

second unit increased more than of first. When 2 units of labor were applied, the total yield was the

highest and so was the marginal return. When the number of workers is increased from 2 to 3 and more.

the MP begins to decrease. As fifth unit of labor was applied, the marginal return fell down to zero and

then it decreased to 5 tons.

 

Assumptions: 

The table and the diagram is based on the following assumptions:

 (i) The time is too short for a firm to change the quantity of fixed factors.

 (ii) It is assumed that labor is the only variable factor. As output increases, there occurs no change in the

factor prices.

 (iii) All the units of the variable factor are equally efficient. 

(iv) There are no changes in the techniques of production.

 

(2) Operation of the Law in the Field of Industry:

 

The modern economists are of the opinion that the law of diminishing returns is not exclusively confined

to agricultural sector, but it has a much wider application. They are of the view that whenever the supply

of any essential factor of production cannot be increased or substituted proportionately with the other

sectors, the return per unit of variable factor begins to decline. The law of diminishing returns is

therefore, also called the Law of Variable Proportions.

 

In agriculture, the law of diminishing returns sets in at an early stage because one very important factor,

i.e., land is a constant factor there and it cannot be increased in right proportion with other variable

factors, i.e., labor and capital. In industries, the various factors of production can be co-operated, up to a

certain point. So the additional return per unit of labor and capital applied goes on increasing till there

takes place a dearth of necessary agents of production. From this, we conclude that the law of diminishing

return arises from disproportionate or defective combination of the various agents of production. Or we

can any that when increasing amounts of a variable factor are applied to fixed quantities of other factors,

the output per unit of the variable factor eventually decreases.

 

Mrs. John Robinson goes deeper into the causes of diminishing returns and says that:

 

"If all factors of production become perfect substitute for one another, then the law of diminishing returns

will not operate at any stage".

 

For instance, if sugarcane runs short of demand and some other raw material takes its place as its perfect

substitute, then the elasticity of substitution between sugarcane and the other raw material will be infinite.

The price of sugarcane will not rise and so the law of diminishing returns will not operate.

 

The law of diminishing returns, therefore, in due to Imperfect substitutability of factors of production.

                          

The law of diminishing returns is also called as the Law of Increasing Cost. This is because of the fact

that as one applies successive units of a variable factor to fixed factor, the marginal returns begin to

diminish. With the cost of each variable factor remaining unchanged by assumptions and the marginal

returns registering .decline, the cost per unit in general goes on increasing. This tendency of the cost per

unit to rise as successive units of a variable factor are added to a given quantity of a fixed factor is called

the law of Increasing Cost.

       

Importance:

 The law of diminishing returns occupies an important place in economic theory. The British classical

economists particularly Malthus, and Ricardo propounded various economic theories, on its basis.

Malthus, the pessimist economist, has based his famous theory of Population on this law.

 The Ricardian theory of rent is also based on the law of diminishing return. The classical economists

considered the law as the inexorable law of nature.

Law of Increasing Returns/Law of Diminishing Cost:

The law of increasing returns is also called the law of diminishing costs. The law of increasing return

states that:

 "When more and more units of a variable factor is employed, while other factor remain fixed, there is an

increase of production at a higher rate. The tendency of the marginal return to rise per unit of variable

factors employed in fixed amounts of other factors by a firm is called the law of increasing return".

 An increase of variable factor, holding constant the quantity of other factors, leads generally to improved

organization. The output increases at a rate higher than the rate of increase in the employment of variable

factor.

 The increase in output faster than inputs continues so long as there is not deficiency of an essential factor

in the process of production. As soon as there occurs shortage or a wrong or defective combination in

productive process, the marginal product begins to decline. The law of diminishing return begins to

operate. We can, therefore, say that there are no separate laws applicable to agriculture and to industries.

It is only the law of variable proportions which applies to a!! the different industries. However, the

duration of stages in each productive undertaking will vary. They will depend upon the availability of

resources, their combination in right proportions, etc., etc.

 

Application of the Law of Increasing Returns in Industries:

 

There are certain manufacturing industries where the factors of production can be combined and

substituted up to a certain limit, it is the law of increasing returns which operates. In the words of Prof.

Chapman:

 

"The expansion of an industry in which there is no dearth of necessary agents of production tends to be

accompanied, other things being equal, by increasing returns".

 

The increasing returns mainly arises from the fact that large scale production is able to secure certain

economies of production, both internal and external. When an industry is expanded, it reaps advantages of

division of labor, specialized machinery, commercial advantages, buying and selling wholesale,

economies in overhead expenses, utilization of by products, use of extensive publicity and advertisement,

availability of cheap credit, etc.. etc.

 

The law of increasing returns also operates so long as a factor consists of large indivisible units and the

plant is producing below its capacity. In that case, every additional investment will result in the increase

of marginal productivity and so in lowering the cost of production of the commodity produced. The

increase in the marginal productivity continues till the plant begins to produce to its full capacity.

  

Assumptions:

 The law rests upon the following assumptions:

 (i) There is a scope in the improvement of technique of production.

 (ii) At least one factor of production is assumed to be indivisible.

 (iii) Some factors are supposed to be divisible. 

 Example:

 

The law of increasing returns can also be explained with the help of a schedule and a curve.

 

Inputs Total Returns (meters of cloth) Marginal Returns

(meters of cloth)

1 100 100

2 250 150

3 450 200  

4 750   300

5 1200 450

6 1850 650

7 2455 605

8 3045 600

 

In the above table it is dear that as the manufacturer goes on expanding his business by investing

successive units of inputs, the marginal return goes on increasing up to the 6th unit and then it beings to

decline steadily, Here, a question ca be asked as to why the law of diminishing returns has operated in an

industry?

 

The answer is very simple. The marginal returns has diminished after the sixth unit because of the non-

availability of a factor or factors of production or. the size of the business has become so large that it has

become unwieldy to manage it, or the plant is producing to its full capacity and it is not possible further to

reap the economies of large scale production, etc., etc.

 

Diagram/Graph:

 

 

In figure 11.3, along OX axis are measured the units of inputs applied and along OY axis the marginal

return is represented. PF is the curve representing the law of increasing returns.

 

Compatibility of Diminishing and Increasing Returns:

It is often pointed out by the classical economists that the law of diminishing returns is exclusively

confined to agriculture and other extractive industries, such as mining fisheries, etc. while manufacturing

industries obey the law of increasing returns. In the words of Marshall:

 

"While the part which Nature plays in production shows a tendency to diminishing returns and the part

which man plays shows a tendency to increasing returns".

 

The modern economists differ with this view and are of the opinion that the law of diminishing returns

applies both to agriculture and the industry. The only difference is that in agriculture the law of

diminishing returns begins to operate at an early stage and in an industry somewhere at a later stage.

 

The law of increasing returns is also named as the Law of Diminishing Cost. When the addition to output

becomes larger, as the firm adds successive units of a variable input to some fixed inputs, the per unit cost

begins to decline. The tendency of the cost per unit to decline with increased application of a variable

factor to fixed factors is called the Law of Diminishing Cost.

Law of Constant Returns/Law of Constant Cost:

 The law of constant returns also called law of constant cost. It is said to operate when with the addition

of successive units of one factor to fixed amount of other factors, there arises a proportionate increase in

total output. The yield of equal return on the successive doses of inputs may occur for a very short period

in the process of production. The law of constant return may prevail in those industries which represent a

combination of manufacturing as well as extractive industries.

 

On the side of manufacturing industries, every increased investment of labor and capital may result in a

more than proportionate increase in the total output. While on the other extractive side, an increase in

investment may cause, in general, a less than proportionate increase in the amount of produce raised. If

the tendency of the marginal return to increase is just balanced by the tendency of the marginal return to

diminish yielding an equal return, we have the operation of the law of constant returns. In the words of

Marshall:

 

"If the actions of the law of increasing and diminishing returns are balanced, we have the law of constant

return".

 

In actual life, the law of constant returns can operate only if the following conditions are fulfilled:

 

(i) There should not be any increase in the prices of raw materials in the industry. This can only be

possible if commodities are available in large supply.

 

(ii) The prices of various factors of production should remain the same. The .supply of various factors of

production needed for a particular industry should be perfectly elastic.   

 

(iii) The productive services should not be fixed and indivisible.

 

If we study the above mentioned conditions carefully, we will easily conclude that in the actual world, it

is not possible to find an industry which obeys the law of constant returns. The law of constant returns

can operate for a very short period when the marginal return moves towards the optimum point and

begins to decline. If the marginal return, at the optimum level remains the same with the increased

application of inputs for a short while, then we have the operation of law of constant returns. The law is

represented now in the form of a table and a curve.

 

Productive doses           Total Return         

(meters of cloth)

          Marginal Return         

(meters of cloth)

1 60 60

2 120 60

3 180 60 

4 240 60

5 300 60

 

In the table given above, the marginal return remains the same, i.e. 60 meters of cloth with the increased

investment of inputs.

 

Diagram/Graph:

 

 

In figure (11.4) along OX are measured the productive resources and along OY is represented the

marginal return. CR is the fine representing the law of constant returns. It is parallel to the base axis.

Law of Returns to Scale:

 

The law of returns are often confused with the law of returns to scale. The law of returns operates in the

short period. It explains the production behavior of the firm with one factor variable while other factors

are kept constant. Whereas the law of returns to scale operates in the long period. It explains the

production behavior of the firm with all variable factors.

 

There is no fixed factor of production in the long run. The law of returns to scale describes the

relationship between variable inputs and output when all the inputs, or factors are increased in the same

proportion. The law of returns to scale analysis the effects of scale on the level of output. Here we find

out in what proportions the output changes when there is proportionate change in the quantities of all

inputs. The answer to this question helps a firm to determine its scale or size in the long run.

 

It has been observed that when there is a proportionate change in the amounts of inputs, the behavior of

output varies. The output may increase by a great proportion, by in the same proportion or in a smaller

proportion to its inputs. This behavior of output with the increase in scale of operation is termed as

increasing returns to scale, constant returns to scale and diminishing returns to scale. These three laws of

returns to scale are now explained, in brief, under separate heads.

 

(1) Increasing Returns to Scale:

 If the output of a firm increases more than in proportion to an equal percentage increase in all inputs, the

production is said to exhibit increasing returns to scale.

 

For example, if the amount of inputs are doubled and the output increases by more than double, it is said

to be an increasing returns returns to scale. When there is an increase in the scale of production, it leads to

lower average cost per unit produced as the firm enjoys economies of scale.

 

(2) Constant Returns to Scale:

 When all inputs are increased by a certain percentage, the output increases by the same percentage, the

production function is said to exhibit constant returns to scale.

 

For example, if a firm doubles inputs, it doubles output. In case, it triples output. The constant scale of

production has no effect on average cost per unit produced.

 

(3) Diminishing Returns to Scale:

 The term 'diminishing' returns to scale refers to scale where output increases in a smaller proportion than

the increase in all inputs.

 

For example, if a firm increases inputs by 100% but the output decreases by less than 100%, the firm is

said to exhibit decreasing returns to scale. In case of decreasing returns to scale, the firm faces

diseconomies of scale. The firm's scale of production leads to higher average cost per unit produced.

 

Graph/Diagram:

 

The three laws of returns to scale are now explained with the help of a graph below:

 

 

The figure 11.6 shows that when a firm uses one unit of labor and one unit of capital, point a, it produces

1 unit of quantity as is shown on the q = 1 isoquant. When the firm doubles its outputs by using 2 units of

labor and 2 units of capital, it produces more than double from      q = 1 to q = 3.

 

So the production function has increasing returns to scale in this range. Another output from quantity 3 to

quantity 6. At the last doubling point c to point d, the production function has decreasing returns to scale.

The doubling of output from 4 units of input, causes output to increase from 6 to 8 units increases of two

units only. 

Concept of Cost of Production:

 Definition and Meaning:

 

By "Cost of Production" is meant the total sum of money required for the production of a specific

quantity of output. In the word of Gulhrie and Wallace:

 

"In Economics, cost of production has a special meaning. It is all of the payments or expenditures

necessary to obtain the factors of production of land, labor, capital and management required to produce a

commodity. It represents money costs which we want to incur in order to acquire the factors of

production".

 

In the words of Campbell:

 "Production costs are those which must be received by resource owners in order to assume that

they will continue to supply them in a particular time of production".

 

Elements of Cost of Production:

 

The following elements are included in the cost of production:

 

(a) Purchase of raw machinery, (b) Installation of plant and machinery, (c) Wages of labor, (d) Rent of

Building, (e) Interest on capital, (f) Wear and tear of the machinery and building, (g) Advertisement

expenses, (h) Insurance charges, (i) Payment of taxes, (j) In the cost of production, the imputed value of

the factor of production owned by the firm itself is also added, (k) The normal profit of the entrepreneur

is also included In the cost of production.

 

Types/Classifications of Cost of Production:

  

Prof, Mead in his book, "Economic Analysis and Policy" has classified these costs into three main

sections:

 

(1) Production Costs:

 It includes material costs, rent cost, wage cost, interest cost and normal profit of the entrepreneur.

 

(2) Selling Costs:

 It includes transportation, marketing and selling costs.

 

(3) Sundry Costs: 

It includes other costs such as insurance charges, payment of taxes and rate, etc., etc.

 

Concept of Economic Costs:

 We have discussed the important types of cost which a firm has to face. The cost of production from the

point of view of an individual firm is split up into the following parts. 

                  

(1) Explicit Cost:

 Explicit cost is also called money cost or accounting cost. Explicit cost represents all such expenditure

which are incurred by an entrepreneur to pay for the hired services of factors of production and in buying

goods and services directly. In other words, we can say that they are the expenses which the business

manager must take into account of because they must actually be paid by the firm.

 Example: The explicit cost includes wages and salary payments, expenses on the purchase of raw

material, light, fuel, advertisements, transportation, taxes and depreciation charges.

                       

(2) Implicit Cost:

 The implicit costs are the imputed value of the entrepreneur's own resources and services. Implicit costs

can be defined as:"Expenses that an entrepreneur does not have to pay out of his own pocket but are costs

to the firm because they represent an opportunity cost".

Example: For instance, if a person is working as a manager in his own firm or has invested his own

capital or has built the factory at his own land, the reward of all these factors of production at least equal

to their transfer prices is, included in the expenses of a business.

 

Implicit costs, thus, are the alternative costs of the self-owned and self-employed resources of a firm. The

total costs of a business enterprise is the sum total of explicit and implicit costs. If the implicit costs are

not included in the firm's total cost, the cost of the firm will be understated and it will result in serious

error.

                                   

(3) Real Cost:

 Real costs are the pains and inconveniences experienced by labor to produce a commodity. These costs

are not taken in the costing of a commodity by the firm. Real cost has been defined differently by

different economists.

 Classical economists understood by real costs the pains and sacrifices of labor. Alfred Marshall calls real

cost as social cost and describes it:

 "Real costs of efforts of various qualities and real costs of waiting".

 The Austrian School of Economists have criticized the meaning given to real cost by the classical

economists and new classical economists. They say that to give a subjective value to cost is a hopeless

task as when real cost is expressed in terms of sacrifices or pains, it is not amenable to precise

measurement and thus it fails to explain the phenomenon of prices.

 

(4) Opportunity Cost:

 The concept of opportunity cost has a very important place in economic analysis. It is defined as:  "The

value of a resource in its next best use. It is the amount of income or yield that could have been earned by

investing in the next best alternative".

 Example: The opportunity cost of a good can be given a money value. For instance, a labor is working in

a factory and is getting $2000 P.M. The entrepreneur is paying him this amount because he can earn this

amount in the next best alternative employment. If he pays less than this amount, he will move to next

best alternative occupation, where he can get $2000 P.M.

So in order to obtain a productive service say labor in the present occupation, the cost should be equal to

the amount which he can get in some alternative occupation. Similarly, a piece of land or capital must be

paid as much as they could earn in their next best alternative use. The total alternative earnings of the

various factors employed in the production of a good constitute the opportunity cost of a good. In a

money economy, opportunity or transfer cost is defined as the amount of money which a firm must make

to resource suppliers m order to attract these resources away from alternative lines of production. In the

words of Lipsay:

 

"The opportunity cost of using any factor is what is currently foregone by using it".

 The idea of opportunity cost has an important bearing on the decisions involving scarcity of resources,

their alternative uses and the choice.

Analysis of Short Run Cost of Production:

 Short run is a period of time over which at least one factor must remain fixed. For most of the firms, the

fixed resource or factors which cannot be increased to meet the rising demand of the good is capital i.e.,

plant and machinery.

 

Short run, then, is a period of time over which output can be changed by adjusting the quantities of

resources such as labor, raw material, fuel but the size or scale of the firm remains fixed.

In the long run there is no fixed resource. All the factors of production are variable. The length of the

long run differs from industry to industry depending upon the nature of production.

 

For example, a balloon making firm can change the size of firm more quickly than a car manufacturing

firm.

 

Categories/Types of Costs in the Short Run:

 The total cost of a firm in the short run is divided into two categories (1) Fixed cost and (2) Variable cost.

The two types of economic costs are now discussed in brief.

     

(1) Total Fixed Cost (TFC): 

Total fixed cost occur only in the short run. Total Fixed cost as the name implies is the cost of the firm's

fixed resources, Fixed cost remains the same in the short run regardless of how many units of output are

produced. We can say that fixed cost of a firm is that part of total cost which does not vary with changes

in output per period of time. Fixed cost is to be incurred even if the output of the firm is zero.

 For example, the firm's resources which remain fixed in the short run are building, machinery and even

staff employed on contract for work over a particular period.

 

(2) Total Variable Cost (TVC):   

Total variable cost as the name signifies is the cost of variable resources of a firm that are used along

with the firm's existing fixed resources. Total variable cost is linked with the level of output. When output

is zero, variable cost is zero. When output increases, variable cost also increases and it decreases with the

decrease in output. So any resource which can be varied to increase or decrease with the rate of output is

variable cost of the firm.

 

For example, wages paid to the labor engaged in production, prices of raw material which a firm. incurs

on the production of output are variable costs. A firm can reduce its variable cost by lowering output but

it cannot decrease its fixed cost. These expenses remain fixed in the short run. In the long run there are no

fixed resources. All resources are variable. Therefore, a firm has no fixed cost in the long run. All long

run costs are variable costs.

 

(3) Total Cost (TC):           

Total cost is the sum of fixed cost and variable cost incurred at each level of output. Total cost of

production of a firm equals its fixed cost plus its:

 Formula:

TC = TFC + TVC

 Where:

 TC = Total cost.,TFC = Total fixed cost., TVC = Total variable cost.

 Explanation:Short run costs of a firm is now explained with the help of a schedule and diagrams. 

(in Dollars)

Units of Output (in Hundred)Total Fixed

CostTotal Variable Cost Total Cost

0 1000 0 1000

1 1000 60 1060

2 1000 100 1100

3 1000 150 1150

4 1000 200 1200

5 1000 400 1400

6 1000 700 1700

7 1000 1100 2100

 

The short run cost data of the firm shows that total fixed cost TFC (column 2) remains constant at $1000/-

regardless of the level of output.

 

The column 3 indicates variable cost which is associated with the level of output. Total variable cost is

zero when production is zero. Total variable cost increases with the increase in output. The variable does

not increase by the same amount for each increase in output. Initially the variable cost increases by a

smaller amount up to 3rd unit of output and after which it increases by larger amounts.

 

Column (4) indicates total cost which is the sum of TFC + TVC. The total cost increases for each level of

output. The rise in total cost is more sharp after the 4th level of output. The concepts of costs, i.e., (1) total

fixed cost (2) total variable cost and (3) total cost can be illustrated graphically.

 

(i) Total Fixed Cost Curve/Diagram:

 

 

In this diagram (13.1) the total fixed cost of a firm is assumed to be $1000 at various levels of output. It

remains the same even if the firm's output is zero.

 

(ii) Total Variable Cost Curve/Diagram:

 

 

In the figure (13.2), the total variable cost curve (TVC) increases with the higher level of output. It starts

from the origin. Then increases at a diminishing rate up to the 4th units of output. It then begins to rise at

an increasing rate.

 

Total Cost Curve Curve/Diagram:

 

 

In the figure (13.3), total cost curve which is the sum of the total fixed cost and variable cost at various

levels of output has nearly the same shape. The difference between the two is by only a fixed amount of

$1,000. The total variable cost curve and the total cost curve begin to rise more rapidly as production is

increased. The reason for this is that after a certain

output, the business has passed its most efficient use of its fixed costs machinery, building etc., and its

diminishing return begins to set in.

 

Analytical Importance of Fixed and Variable Costs:

In the time of distinction between fixed cost and variable cost is a matter of degree, it all depends upon

the contracts of a firm and .the period of time under consideration.

 

For example, if a firm makes contract with the labor for a certain period, then the firm has to bear the cost

of the labor irrespective of the total produce. Under such conditions, the wages paid to the labor will be

classified as fixed cost and not variable cost, as discussed under the heading of variable cost. Secondly,

when the period of time is short, the distinction between fixed cost and variable cost can be made rigid

but not in a longer period of time all fixed costs change into variable cost in the long run.

Average Cost:

The entrepreneurs are no doubt interested in the total costs but they are equally concerned in knowing the

cost per unit of the product. The unit cost figures can be derived from the total fixed cost, total variable

cost and total cost by dividing each of them with corresponding output.

 

Types/Classifications:

 (1) Average Fixed Cost (AFC): Average fixed cost refers to fixed cost per unit of output. Average fixed

Cost is found out by dividing the total fixed cost by the corresponding output.

AFC = TFC

output (Q)

 

For instance, if the total fixed cost of a shoes factory is $5,000 and it produces 500 pairs of shoes, then the

average fixed cost is equal to $10 per unit. If it produces 1,000 pairs of shoes, the average fixed cost is $5

and if the total output is 5,000 pairs of shoes, then the average fixed cost is $1 pair of shoe. From the

above example, it is clear, that the fixed cost, i.e., $5,000 remains the same whether the output is 1,000 or

5,000 units.

 

The average fixed cost begins to fall with the increase in the number of units produced, In our example

stated above, average fixed cost in the beginning was $10. As the output of the firm increased, it

gradually came down to $1. The AFC diminishes with every increase in the quantity of output produced

but it never becomes zero.

 

Diagram/Curve:

 

 

The concept of average fixed cost can be explained with the help of the curve, in the diagram (13.4) the

average fixed cost curve gradually falls from left to right showing the level of output. The larger the level

of output, the lower is the average fixed cost and smaller the level of output, the greater is the average

fixed cost. The AFC never becomes zero.

 

(2) Average Variable Cost (AVC): Average variable cost refers to the variable expenses per unit of

output Average variable cost is obtained by dividing the total variable cost by the total output.  

For instance, the total variable cost for producing 100 meters of cloth is $800, the average variable cost

will be $8 per meter.

 

Formula:

AVC = TVC

                                                                        (Q)

 

When a firm increases its output, the average variable cost decreases in the beginning, reaches a

minimum and then increases. Here, a question can be asked as to why AVC decreases in the beginning

reaches a minimum and then increases. The answer to this question is very simple.

 

When in the beginning, a firm is not producing to its full capacity, then the various factors of production

employed for the manufacture of a particular commodity remain partially absorbed. As the output of the

firm is increased, they are used to its fullest extent. So the AVC begins to decrease. When the plant works

to its full capacity, the AVC is at its minimum. If the production is pushed further from the plant capacity,

then less efficient machinery and less, efficient labour may have to be employed. This results in the rise

of AVC. It is in this way we say that as the output of a firm increases, the AVC decreases in the

beginning, reaches a minimum and then increases. The AVC can also be represented in the form of a

curve.

 

Diagram/Curve:

 

 

The shape of the average variable cost curve (Fig. 13.5) is like a flat U-shaped curve. It shows that when

the output is increased, there is a steady fall in the average variable cost due to increasing returns to

variable factor. It is minimum when 500 meters of doth are produced. When production is increased to

600 meters, of cloth or more, the average variable cost begins to increase due to diminishing returns to the

variable factor.

 

(3) Average Total Cost (ATC):  Average total cost refers to cost (both fixed and variable) per unit of

output. Average total cost is obtained by dividing the total cost by the total number of commodities

produced by the firm or when the total sum of average variable cost and average fixed cost is added

together, it becomes equal to average total cost.

 Formula:

   

ATC =   Total Cost (TC)

                                                                  Output (Q)

 

As the output of a firm increases, average total cost like the average variable cost decreases in the

beginning reaches a minimum and then it increases. The reasons for decline of ATC in the beginning are

that it is the sum of AFC and AVC.

 

Average fixed cost and average variable costs have both the tendency to fall as output is increased.

Average total cost will continue falling so long average variable cost does not rise. Even if average

variable cost continues rising, it is not necessary that the average total cost will rise. It can be due to the

fact that the increase in average variable cost is less than the fall in average fixed cost. The increase in

average variable cost is counterbalanced by a rapid fall of average fixed cost. If the rise in the average

variable cost is greater than the fall in average fixed cost, then the average total cost will rise.The

tendency to rise on the part of average total cost-in the beginning is slow, after a certain point it begins to

increase rapidly.

 Diagram/Curve: 

 

The average total cost is represented here by a shaped curve in Fig. (13.6). The average total cost curve is

also like a U-shaped curve. It shows that as production increases from 100 meters to 200 meters of cloth,

the cost falls rapidly, reaches a minimum but then with higher level of output, the average fixed cost

begins to increase.

 

Short Run and Long Run Average Cost Curves: Relationship and Difference:

Short Run Average Cost Curve:

 In the short run, the shape of the average total cost curve (ATC) is U-shaped. The, short run average cost

curve falls in the beginning, reaches a minimum and then begins to rise. The reasons for the average cost

to fall in the beginning of production are that the fixed factors of a firm remain the same. The change only

takes place in the variable factors such as raw material, labor, etc.

 As the fixed cost gets distributed over the output as production is expanded, the average cost, therefore,

begins to fall. When a firm fully utilizes its scale of operation (plant size), the average cost is then at its

minimum. The firm is then operating to its optimum capacity. If a firm in the short-run increases its level

of output with the same fixed plant; the economies of that scale of production change into diseconomies

and the average cost then begins to rise sharply.

Long Run Average Cost Curve:

In the long run, all costs of a firm are variable. The factors of production can be used in varying

proportions to deal with an increased output. The firm having time-period long enough can build larger

scale or type of plant to produce the anticipated output. The shape of the long run average cost curve is

also U-shaped but is flatter that the short run curve as is illustrated in the following diagram:

 

Diagram/Figure:

 

In the diagram 13.7 given above, there are five alternative scales of plant SAC 1 SAC2, SAC3, SAC4 and,

SAC5. In the long run, the firm will operate the scale of plant which is most profitable to it.

 

For example, if the anticipated rate of output is 200 units per unit of time, the firm will choose the

smallest plant It will build the scale of plant given by SAC1 and operate it at point A. This is because of

the fact that at the output of 200 units, the cost per unit is lowest with the plant size 1 which is the

smallest of all the four plants. In case, the volume of sales expands to 400, units, the size of the plant will

be increased and the desired output will be attained by the scale of plant represented by SAC2 at point B,

If the anticipated output rate is 600 units, the firm will build the size of plant given by SAC3 and operate it

at point C where the average cost is $26 and also the lowest The optimum output of the firm is obtained at

point C on the medium size plant SAC3.

 

If the anticipated output rate is 1000 per unit of time the firm would build the scale of plant given by

SAC5 and operate it at point E. If we draw a tangent to each of the short run cost curves, we get the long

average cost (LAC) curve. The LAC is U-shaped but is flatter than tile short run cost curves.

Mathematically expressed, the long-run average cost curve is the envelope of the SAC curves.

 

In this figure 13.7, the long-run average cost curve of the firm is lowest at point C. CM is the minimum

cost at which optimum output OM can be, obtained.

Marginal Cost (MC):  Marginal Cost is an increase in total cost that results from a one unit increase in

output. It is defined as:"The cost that results from a one unit change in the production rate".

 

For example, the total cost of producing one pen is $5 and the total cost of producing two pens is $9, then

the marginal cost of expanding output by one unit is $4 only (9 - 5 = 4).

 

The marginal cost of the second unit is the difference between the total cost of the second unit and total

cost of the first unit. The marginal cost of the 5th unit is $5. It is the difference between the total cost of

the 6th unit and the total cost of the, 5th unit and so forth.

 

Marginal Cost is governed only by variable cost which changes with changes in output. Marginal cost

which is really an incremental cost can be expressed in symbols.

 

Formula:

Marginal Cost = Change in Total Cost = ΔTC

                                                              Change in Output        Δq

 

The readers can easily understand from the table given below as to how the marginal cost is computed:

  

Units of Output Total Cost (Dollars) Marginal Cost (Dollars)

1 5 5

2 9 4

3 12 3

4 16 4

5 21 5

6 29 8

 

Graph/Diagram:

 

 

MC curve, can also be plotted graphically. The marginal cost curve in fig. (13.8) decreases sharply with

smaller Q output and reaches a minimum. As production is expanded to a higher level, it begins to rise at

a rapid rate. 

 

Long Run Marginal Cost Curve:

 

The long run marginal cost curve like the long run average cost curve is U-shaped. As production

expands, the marginal cost falls sharply in the beginning, reaches a minimum and then rises sharply.

 

Relationship Between Log Run Average Cost and Marginal Cost:

 

The relationship between the long run average total cost and log run marginal cost can be understood

better with the help of following diagram:

 

 

It is clear from the diagram (13.9), that the long run marginal cost curve and the long run average total

cost curve show the same behavior as the short run marginal cost curve express with the short run average

total cost curve. So long as the average cost curve is falling with the increase in output, the marginal cost

curve lies below the average cost curve.

 

When average total cost curve begins to rise, marginal cost curve also rises, passes through the minimum

point of the average cost and then rises. The only difference between the short run and long run marginal

cost and average cost is that in the short run, the fall and rise of curves LRMC is sharp. Whereas In the

long run, the cost curves falls and rises steadily.

Relation of Average Variable Cost and Average Total Cost to Marginal Cost:

 

Before we explain, the relation of average variable cost (AVC) and average total cost (ATC) to marginal

cost (MC), it seems necessary that the various types of costs and their relationship should be shown in the

form of a table. This is illustrated in the table below:

 

Units of

Output

Total Fixed

Cost

(TFC)    

Total Variable

Cost (TVC)

Average Total

Cost (ATC)

Average

Fixed Cost

(AFC)

Average

Variable Cost

(AVC)  

Marginal Cost

(MC)         

($) ($) ($) ($) ($) ($)

1 30 15 45 30 15 15

2 30 16.9 23.4 15 8.4 1.9

3 30 18.4 16.1 10.1 6.1 1.5

4 30 19.4 12.3 7.5 4.8 1

5 30 20 10 6 4.0 0.6

6 30 22 8.7 5 3.7 2

7 30 25 7.8 4.3 3.6 3

8 30 30 7.5 3.7 3.7 5

9 30 36 7.3 3.3 4 6

10 30 43 7.3 3 4.3 7

11 30 60 8.2 2.7 5.5 17

12 30 90 10 2.5 7.5 30

13 30 125 11.9 2.3 9.6 35

14 30 165 13.9 2.1 11.8 40

15 30 210 16 2 14.8 45

16 30 270 18.7 1.9 16.7 60

 

From the table, the reader can understand the relation of various types of costs to each other. We take,

first of all, the relation of average total cost to marginal cost. As production increases, the average total

cost and the marginal cost both begin to decrease.

 

The average total cost goes on decreasing up to the 9th unit and then after 10, it begins to rise. The

marginal cost goes on falling up to 5th unit and then it begins to increase. So long as the average total cost

does not rise, the marginal cost remains below it. When average total cost begins to increase, toe marginal

cost rises more than the average total cost.

 

Summing Up:

When average cost is falling, the marginal cost is always lower than the

average cost.                       

When average cost is rising, marginal cost lies above AC and rises faster

than AC.

The marginal cost curve must cut the average cost curve at the minimum

point of AC.

 

Average Variable Cost and Marginal Cost:

 The relation of average variable cost and marginal cost is also very clear from the diagram given below.

The AVC goes on falling up to the 7th unit, and then it steadily moves upwards. On the other hand the

marginal cost falls up to the 5th unit and then rises more rapidly than average variable cost.

 Diagram/Figure:

 

In the diagram (13.10) AFC, AVC, ATC and MC curves are shown. Here, units of production are

measured along OX and cost along OY. ATC and AVC both fall in the beginning, reach a minimum point

and then begin to rise. So is the case with the marginal cost

curve. It first falls and then after rising, sharply crosses through the lowest point of average variable cost

and average total cost and rises.