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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.