Unit 2

UNIT –2:
DEMAND AND SUPPLY ANALYSIS
• Contents (8 Hrs)
• 2.1 Theory of Demand. Types of Demand. Determinants of demand , Demand Function
,Demand Schedule , Demand curve.
• 2.2 Law of Demand, Exceptions to the law of Demand , Shifts in demand curve.
• 2.3 Elasticity of Demand and its measurement. Price Elasticity. Income Elasticity. Arc
Elasticity. Cross Elasticity and Advertising Elasticity.
• 2.4 Uses of Elasticity of Demand for managerial decision making.
• 2.5 Demand forecasting meaning, significance and methods.( numerical Exercises).
• 2.6 Supply Analysis; Law of Supply, Supply Elasticity; Analysis and its uses for managerial
decision making.
• 2.7 Price of a Product under demand and supply forces.
• 1.5 Utility Analysis. Cardinal Utility and Ordinal Utility.
7/7/2017Deepak Srivastava
1

2.1 THEORY OF DEMAND. TYPES OF DEMAND. DETERMINANTS OF
DEMAND , DEMAND FUNCTION ,DEMAND SCHEDULE , DEMAND
CURVE.
• Theory of Demand
• What is demand ?
• “Demand for anything means the quantity of that commodity, which is desired
to be bought, at a given price, per unit of time.”
• It is interpreted as your want backed up by your purchasing power.
2
Demand for a
commodity
implies:
Desire to acquire
it,
Willingness to pay
for it, and
Ability to pay for
it.

TYPES OF DEMAND.
Direct and derived demand
Recurring and replacement demand
Complementary and competing demand
Demand for capital goods and consumer goods
Demand for perishable goods and durable goods
Individual and market demand
3

DETERMINANTS OF DEMAND
• The demand for a commodity arises from the consumer’s
willingness and ability to purchase the commodity. The
demand theory says that the quantity demanded of a
commodity is a function of or depends on not only the price
of a commodity, but also on income of the person, price of
related goods – both substitutes and complements – tastes of
consumer, price expectation and all other factors. Demand
function is a comprehensive formulation which specifies the
factors that influence the demand for the product.
4

DETERMINANTS OF DEMAND
Dx = Demand for item x
Px = Price of item x
Py = Price of substitutes
Pz = Price of complements
B = Income of consumer
E = Price expectation of the user
A = Advertisement Expenditure
T = Taste or preference of user Notes
U = All other factors
5

THE DEMAND FUNCTION
Dx = f(Px, Py, Pz, B, A, E, T, U)
6

THE RELATIONSHIP…
7

DEMAND SCHEDULE AND DEMAND CURVE
• A demand curve considers only the price-demand relation,
other factors remaining the same. The inverse relationship
between the price and the quantity demanded for the
commodity per time period is the demand schedule for the
commodity and the plot of the data (with price on the
vertical axis and quantity on the horizontal axis) gives the
demand curve of the individual.
8

0
0.5
1
1.5
2
2.5
Demand
for X
PriceofX
Demand Curve
10

2.2 LAW OF DEMAND, EXCEPTIONS TO
THE LAW OF DEMAND , SHIFTS IN
DEMAND CURVE.
• Law of Demand
• The Law of demand explains the functional relationship between price
of a commodity and the quantity demanded of the commodity.
• It is observed that the price and the demand are inversely related
which means that the two move in the opposite direction.
• An increase in the price leads to a fall in quantity demanded and vice
versa.
• This relationship can be stated as “Other things being equal, the
demand for a commodity varies inversely as the price”.
11

2.2 LAW OF DEMAND, EXCEPTIONS TO THE LAW OF
DEMAND , SHIFTS IN DEMAND CURVE.
12
According to Law of Demand, there is an inverse relationship
between the price of a commodity and the quantity demanded
(other things remaining equal)

EXCEPTIONS TO THE LAW OF
DEMAND
•Conspicuous goods : These are certain goods which are purchases to project the status and prestige of the
consumer. For e.g. expensive cars, diamond jewellery, etc. such goods will be purchased more at a higher price and
less at a lower price.
Giffen goods : These are special category of inferior goods whose demand increases even if with a rise in price. For
eg. coarse grain, clothes, etc.
Share’s speculative market : It is found that people buy shares of those company whose price is rising on the
anticipation that the price will rise further. On the other hand, they buy less shares in case the prices are falling as
they expect a further fall in price of such shares. Here the law of demand fails to apply.
Bandwagon effect : Here the consumer demand of a commodity is affected by the taste and preference of the social
class to which he belongs to. If playing golf is fashionable among corporate executive, then as the price of golf
accessories rises, the business man may increase the demand for such goods to project his position in the society.
Veblen effect : Sometimes the consumer judge the quality of a product by its price. People may have the expression
that a higher price means better quality and lower price means poor quality. So the demand goes up with the rise in
price for eg. : Branded consumer goods.
13

MOVEMENTS AND SHIFTS IN
DEMAND CURVE
• If the quantity demanded of a commodity increases or decreases due
to a fall or rise in the price of a commodity alone, ceteris paribus. It
is called movement along the demand curve which occurs only due
to change in price of that commodity, ceteris paribus, Extension of
Demand or movement along the demand curve to the right. When
the quantity demanded rises due to fall in price of that commodity,
and other parameters remaining constant it is called extension of
demand which is shown in the following diagram.
14

DEMAND CURVE
• Contraction or Movement towards left of demand curve : When the quantity
demanded of a commodity falls due to rise in the price of that commodity it
is called contraction of demand and is shown in the following diagram.
15

THEREFORE…
• Both the situation of extension and contraction can be shown in a single
diagram as below:
16
Movement along Demand Curve

DEMAND CURVE
• Change in Demand or shift of demand or Increase
and Decrease in demand : When the quantity
demanded of a commodity rises or falls due to
change in factors like income of the consumer, price
of related goods, etc. and keeping the price of the
commodity to be constant, it is called shift in
Demand.
17

DEMAND CURVE
• Increase in Demand or Shift of Demand Curve towards the Right : When the quantity
demanded of a commodity rises due to change in factors like income of the
consumable etc. price of the commodity remaining unchanged it is called increase
in demand.
18
Shift of Demand Curve (Rightward)

DEMAND CURVE
• Decrease in Demand or shift of Demand Curve towards the left : When the demand
for a commodity falls due to other factors, the price remaining constant, it is
termed as decrease in demand or shift of demand curve towards the left.
19
Shift of Demand Curve (Leftward)

2.3 ELASTICITY OF DEMAND
• 2.3 Elasticity of Demand and its measurement.
• Price Elasticity.
• Income Elasticity.
• Arc Elasticity.
• Cross Elasticity and
• Advertising Elasticity.
20

ELASTICITY OF DEMAND
•Introduction Elasticity is the measure of responsiveness.
It is the ratio of the percent change in one variable to the percent
change in another variable.
The key thing to understand is that we use elasticity when we want
to see how one thing changes when we change something else.
How does demand for a good change when we change its price?
How does the demand for a good change when the price of a
substitute good changes?
21

CONCEPT OF ELASTICITY
•The law of demand tells us that
consumers will respond to a price decline
by buying more of a product. It does not,
however, tell us anything about the degree
of responsiveness of consumers to a price
change. The contribution of the concept of
elasticity lies in the fact that it not only
tells us that consumer's demand responds
to price changes but also the degree of
responsiveness of consumers to a price
change. The figure shows two demand
curves. Let Da be the demand for cheese in
Switzerland and Db be the demand for
cheese in England.
22

CLASSIFICATION OF DEMAND CURVES
ACCORDING TO THEIR ELASTICITIES
•Depending on how the total revenue changes, when
price changes we can classify all demand curves in
the following five categories:
1. Perfectly inelastic demand curve
2. Inelastic demand curve
3. Unitary elastic demand curve
4. Elastic demand curve
5. Perfectly elastic demand curve 7/7/2017Deepak Srivastava
23

Perfectly Inelastic Demand : These are certain goods like salt, match box
etc. whose demand neither increase nor decrease with a change in price.
A perfectly inelastic demand curve is a vertical straight line parallel to Y –axis which shows
that whatever may be the change in price the demand will remain constant at OQ.
24

Perfectly Elastic Demand : That is [ed = ∞]. When the quantity demanded of a commodity changes
infinitely due to a slight or no decrease in price, such goods are said to have perfectly elastic demand.
A perfectly Elastic Demand Curve is a straight line parallel to X –axis.
25

Relatively Inelastic Demand (ed < 1)
In this type of goods and services the proportionate change in quantity demand is less than the change in
price. These are mostly essential goods of daily use like rice, wheat etc.
In the diagram change in quantity QQ1 is less than proportionate to the change in price
PP1.
26

Relatively Elastic Demand : In such type of goods the percentage change in quantity demanded of
a commodity is more than proportionate to the percentage change in price, eg. luxury car.
In the diagram we see that change in quantity demanded QQ1 is more than proportionate
to the change in price PP1.
27

Unit Elastic Demand (ed = 1)
Here the rate of change in demand is exactly equal to the rate of change in price. Therefore the products
or service with unit elasticity are neither elastic nor inelastic.
A Unit elastic Demand curve is a rectangular - hyperbola as shown above
28

NUMERICAL MEASUREMENT OF ELASTICITY
• What does it mean when we say that the elasticity of demand is 0.5? 0.4?
2.3? To answer this question we have to examine the following definition
for elasticity coefficient, Ed.
29

COMPUTATION OF ELASTICITY
COEFFICIENTS
31

ARC PRICE ELASTICITY OF
DEMAND
• The question is, how is it that we
get different demand responses for
the same range of price change?
The answer is that our initial
quantity demanded and price have
been different.
• When we calculate for price fall,
they are 2000 for initial quantity
demanded and 4 for initial price.
• When we calculate it for price rise
they are 3250 for initial quantity
demanded and 3 for initial price.
33

APPLICATIONS OF ELASTICITY
• The concept of elasticity has a wide range of
applications in economics. In particular, an
understanding of elasticity is fundamental in
understanding the response of supply and demand
in a market.
• Some common applications of elasticity include:
34

APPLICATIONS OF ELASTICITY
• Effect of changing price on firm's revenues: If the
demand for the product is price inelastic, the firm
would not want to lower its price since that would
reduce its total revenue, increase its total costs and
this will give it lower profits.
35

• Analysis of incidence of the tax burden and other government
policies: In economics, tax incidence is the analysis of the effect of a
particular tax on the distribution of economic welfare. Tax incidence
is said to "fall" upon the group that, at the end of the day, bears the
burden of the tax. The key concept is that the tax incidence or tax
burden does not depend on where the revenue is collected, but on
the price elasticity of demand (and price elasticity of supply). For
example, a tax on orange farmers might actually be paid by owners
of agricultural land or consumers of oranges.
36

• Effect of international trade and terms of trade
effects: Marshall-Lerner Condition gives a technical
reason why a reduction in value of a nation's
currency need not immediately improve its balance
of payments. The condition states that, for a
currency devaluation to have a positive impact on
trade balance, the sum of price elasticity of exports
and imports (in absolute value) must be greater
than 1.
37

• Analysis of consumption and saving behavior: the
way consumers respond to the change in prices or
other determinants of demand, determines their
consumption pattern and savings pattern. For
example, a consumer purchases 2 bottles of cold
drinks instead to 4, when price rose from 10 to 15.
Other things remaining constant, he is saving more
money than before.
38

• If the elasticity of the firm's sales with reference to
advertisement expenditure is positive and higher
than for its expenditure on product quality and
customer service, then the firms would find it more
beneficial to concentrate its sales efforts on
advertising rather than on product quality and
customer service.
39

2.5 DEMAND FORECASTING
MEANING, SIGNIFICANCE AND
METHODS.
• Estimating and Forecasting Demand
• To count is a modern practice, the ancient method was to
guess; and when numbers are guessed, they are always
magnified.
• SAMUEL JOHNSON
• If today were half as good as tomorrow is supposed to be,
it would probably be twice as good as yesterday was.
• NORMAN AUGUSTINE, AUGUSTINE’S LAWS
40

FORECAST: MEANING AND
SIGNIFICANCE
• In previous chapters, we used demand equations, but
we did not explain where they came from. Here, we
discuss various techniques for collecting data and using
it to estimate and forecast demand.
• Data-Driven Business
• What do they say?
• What do they do?
• What have they done?
• Computers are very good at uncovering patterns
from huge amounts of data, while humans are
good at explaining and exploiting those patterns.
41

FORECAST…
• A forecast is a statement about the future value of a variable such as
demand. That is, forecasts are predictions about the future. The better
those predictions, the more informed decisions can be.
• Some forecasts are long range, covering several years or more. Long-range
forecasts are especially important for decisions that will have long-term
consequences for an organization or for a town, city, country, state, or
nation.
• One example is deciding on the right capacity for a planned power plant that
will operate for the next 20 years.
• Other forecasts are used to determine if there is a profit potential for a new
service or a new product: Will there be sufficient demand to make the
innovation worthwhile?
• Many forecasts are short term, covering a day or week. They are especially
helpful in planning and scheduling day-to-day operations.
42

FORECAST…
• Forecast A statement about the future value of a variable of interest.
• Forecasts are a basic input in the decision processes of operations
management because they provide information on future demand. The
importance of forecasting to operations management cannot be overstated.
• Two aspects of forecasts are important.
• One is the expected level of demand; the other is the degree of accuracy
that can be assigned to a forecast (i.e., the potential size of forecast error).
The expected level of demand can be a function of some structural
variation, such as a trend or seasonal variation. Forecast accuracy is a
function of the ability of forecasters to correctly model demand, random
variation, and sometimes unforeseen events.
43

FORECAST…
• Forecasts affect decisions and activities throughout an organization, in accounting, finance,
human resources, marketing, and management information systems (MIS), as well as in
operations and other parts of an organization. Here are some examples of uses of forecasts
in business organizations:
• Accounting. New product/process cost estimates, profit projections, cash management.
• Finance. Equipment/equipment replacement needs, timing and amount of
funding/borrowing needs.
• Human resources. Hiring activities, including recruitment, interviewing, and training; layoff
planning, including outplacement counseling.
• Marketing. Pricing and promotion, e-business strategies, global competition strategies.
• MIS. New/revised information systems, Internet services.
• Operations. Schedules, capacity planning, work assignments and workloads, inventory
planning, make-or-buy decisions, outsourcing, project management.
• Product/service design. Revision of current features, design of new products or services.
44

FORECASTING
DEMAND
The Walt Disney World
forecasting department has 20
employees who formulate
forecasts on volume and
revenue for the theme parks,
water parks, resort hotels, as
well as merchandise, food, and
beverage revenue by location.
45

ELEMENTS OF A GOOD FORECAST
•Timely Accurate Reliable
Meaningf
ul units
In writing
Simple to
understan
d and use
Cost-
effective
46

NEED AND SIGNIFICANCE
•Effective Planning
Reduction of Uncertainty
Resource Allocation
Competitive Strategy
Managerial Control

STEPS IN THE FORECASTING
PROCESS
• There are six basic steps in the forecasting process:
1. Determine the purpose of the forecast. How will it be used and when will it be
needed? This step will provide an indication of the level of detail required in the
forecast, the amount of resources (personnel, computer time, dollars) that can be
justified, and the level of accuracy necessary.
2. Establish a time horizon. The forecast must indicate a time interval, keeping in
mind that accuracy decreases as the time horizon increases.
3. Obtain, clean, and analyze appropriate data. Obtaining the data can involve
significant effort. Once obtained, the data may need to be “cleaned” to get rid of
outliers and obviously incorrect data before analysis.
4. Select a forecasting technique.
5. Make the forecast.
6. Monitor the forecast. A forecast has to be monitored to determine whether it is
performing in a satisfactory manner. If it is not, reexamine the method,
assumptions, validity of data, and so on; modify as needed; and prepare a revised
forecast.
48

METHODS OF FORECASTING
•There are two general approaches to forecasting: qualitative and
quantitative.
Qualitative methods consist mainly of subjective inputs, which
often defy precise numerical description.
Quantitative methods involve either the projection of historical
data or the development of associative models that attempt to
utilize causal (explanatory) variables to make a forecast.
49

TECHNIQUES OF DEMAND
FORECASTING
Demand
Forecasting
Survey Methods
Consumer Survey:
Direct Interview
Complete
Enumeration
Sample Survey
End- Use Method
Opinion Poll
Methods
Expert Opinion
Sample Survey
Delphi Method
Market Studies &
Experiments
Market Test
Laboratory Test
Statistical Methods
Trend Projection
Graphical Method
Trend Fitting Or
LSM
Box- Jenkins
Method
Barometric
Methods
Lead – Leg
Indicators
Diffusion Indices
Econometric
Method
Regression
Methods
Simple: Bivariate
Multivariate
Simultaneous
Equations
50

QUALITATIVE- QUANTITATIVE
• Qualitative techniques permit inclusion of soft information (e.g.,
human factors, personal opinions, hunches) in the forecasting process.
Those factors are often omitted or downplayed when quantitative
techniques are used because they are difficult or impossible to quantify.
• Quantitative techniques consist mainly of analyzing objective, or
hard, data. They usually avoid personal biases that sometimes contaminate
qualitative methods. In practice, either approach or a combination of both
approaches might be used to develop a forecast.
51

QUALITATIVE TECHNIQUES
(SURVEY METHODS)
•Used to make short-run forecast of demand
• This method includes
• Survey of potential consumers
• Opinion poll of experts

CONSUMER SURVEY METHOD-
DIRECT INTERVIEWS
• Consumers can be interviewed by any of the
following methods depending on the purpose time
and cost of survey
(a) Complete enumeration
(b) Sample survey
(c) End-use method

(A) COMPLETE ENUMERATION
• Almost all potential users of the product are contacted and asked
about their future plan of purchasing the product in question.
• The quantities indicated by the consumers are added together to
obtain the probable demand for the product
• This method has certain limitations ,it can be use successfully only in
case of those products whose consumers are concentrated in a
certain region of locality
Dp = q1 + q2 + q3 + …. qn = 𝑖=1
𝑛
𝑞𝑖
Dp= Total probable demand
q1, q2, q3 denote demand by individual 1, 2, 3, etc.

(A) COMPLETE ENUMERATION
• In case of widely dispersed market this method may not be
physically possible or prove very costly in terms of both
money and time
• Consumers themselves may not know their actual demand
in future hence may be unable or unwilling to answer the
query
• Even if they answer their answers to hypothetical questions
may be hypothetical not real

(B) SAMPLE SURVEY METHOD
•This method is used when population of the target market is very large.
Only a sample of potential consumers or users is selected for interview.
Consumers to be surveyed are selected from the relevant market through a sampling method.
Method of survey may be direct interview of mailed questionnaire.
Less costly and less time consuming.
Can be used to verify demand forecasted by using quantitative methods.
Should be used to supplement the quantitative methods.

(B) SAMPLE SURVEY METHOD
Dp =
𝐻𝑟
𝐻𝑠
∗ (𝐻 ∗ 𝐴𝑑)
• Where Dp = probable demand forecast;
• Hr = No. of household reporting demand for the
product;
• Hs = No. of household survey or sampled house
holds;
• Ad = Average expected consumption by the
reporting households

(C) THE END-USE METHOD
• First Stage- Identify all possible users of
the product, manager need to have
knowledge of the product and its uses.
• Second Stage- Technical norms of
consumption.
• Third Stage- Desired or targeted level
of output.
• Fourth Stage -Aggregate demand.
•Forecasting
demand for
inputs by
consuming
industries
and various
other sectors.

OPINION POLL METHODS-EXPERT
OPINION METHOD
• Experts-Possess knowledge of market (sales representatives,
sales executives, professional marketing experts, consultants.
• Sales representatives can assess the demand for the target
product in the areas region or cities they represent.
• Being in close touch with the consumers or users of goods are
supposed to know the future purchase plan of their customers.
• They are in position to provide at least an approximate estimate
of likely demand for their firm’s product in their region or area.
• The estimates thus obtained from different regions are added
up to get overall probable demand for the product.

EXPERT OPINION METHOD-
LIMITATIONS
• Reliable only an extent depending on the skills and
expertise of sales representatives
• Some times inadequate information available to sales
representatives

DELPHI-METHOD
OLAF HELMER
• Refers to a group decision-making technique of forecasting demand. In this
method, questions are individually asked from a group of experts to obtain
their opinions on demand for products in future. These questions are
repeatedly asked until a consensus is obtained.
• In addition, in this method, each expert is provided information regarding
the estimates made by other experts in the group, so that he/she can revise
his/her estimates with respect to others’ estimates. In this way, the
forecasts are cross checked among experts to reach more accurate decision
making.
• Every expert is allowed to react or provide suggestions on others’ estimates.
However, the names of experts are kept anonymous while exchanging
estimates among experts to facilitate fair judgment and reduce halo effect.
• The main advantage of this method is that it is time and cost effective as a
number of experts are approached in a short time without spending on
other resources. However, this method may lead to subjective decision
making.

MARKET EXPERIMENT METHOD
•Involves collecting necessary information regarding the current and future demand for a
product. This method carries out the studies and experiments on consumer behavior under
actual market conditions. In this method, some areas of markets are selected with similar
features, such as population, income levels, cultural background, and tastes of consumers.
The market experiments are carried out with the help of changing prices and expenditure, so
that the resultant changes in the demand are recorded. These results help in forecasting
future demand.

LIMITATIONS
•Refers to an expensive method; therefore, it may not be
affordable by small-scale organizations
Affects the results of experiments due to various social-
economic conditions, such as strikes, political instability,
natural calamities

QUANTITATIVE TECHNIQUES-
STATISTICAL METHODS
• Statistical methods are complex set of methods of demand forecasting. These
methods are used to forecast demand in the long term. In this method, demand is
forecasted on the basis of historical data and cross-sectional data.
• Historical data refers to the past data obtained from various sources, such as
previous years’ balance sheets and market survey reports. On the other hand,
cross-sectional data is collected by conducting interviews with individuals and
performing market surveys. Unlike survey methods, statistical methods are cost
effective and reliable as the element of subjectivity is minimum in these methods.
• Statistical methods are considered to be superior owing to the following reasons:
• The element of subjectivity is minimum.
• Method of estimation is scientific as it is based on the theoretical relationship
between the dependent and independent variable.
• Estimates are relatively more reliable.

DIFFERENT STATISTICAL
METHODS
•Trend Projection
Method
Barometric Method
Econometric
Methods

TREND PROJECTION METHOD
• Classical method of demand forecasting.
• Study of movement of variables through timeline.
• Require a long and reliable time series data.
• This method is used under the assumption that factors responsible for the
past trends in the variables to be projected will continue to play their part in
future in same manner and extent.
• In projecting demand for a product trend method is applied to time series
data on sales.
• Firms may obtain time series data on sales from their own sales department
and books of account.
• New firms can obtain necessary data from the older firms belonging to
same industry.

TREND PROJECTION METHOD
Trend Projection
Method
Graphical Method
Fitting Trend
Equation or Least
Square Methods
Linear Trends
Exponential
Trends
Box- Jenkins
Methods
Autoregressive
Model
Moving Average
Model
Autoregressive-
Moving Average
Model
68

GRAPHICAL METHOD
• Helps in forecasting the future sales of an organization with the help of a
graph. The sales data is plotted on a graph and a line is drawn on plotted
points.
• Method is very
simple and least
expensive.
• Projections made
through this method
are not very reliable.
• Trend line involves
personal bias of
analyst.

FITTING TREND EQUATION OR
LEAST SQUARE METHOD
• There can be two methods of fitting a line:
Y= a + bX…..(i)
In case it is a linear function having a positive relationship between the
hypothesized variables (X and Y)
• An elementary method or rudimentary method
• Free hand drawing a line through the center of the scatter points plotted by the
given set of data and then extrapolating the values of constant ‘a’ and ‘b’.
• This is a crude method with a considerable level of subjectivity inherent, therefore
lesser reliable.
• The regression Analysis
• The mathematical and formal method derivation and estimation of a linear function.
• Can be applied to estimate both the bivariate and multivariate functions.
• We shall be limiting our discussion to bivariate linear functions.
70

REGRESSION ANALYSIS: ESTIMATING
THE ERROR TERM
FIG. 5.2, PG. NO. 89, D.N. DWIVEDI
71

REGRESSION
ANALYSIS:
ESTIMATING THE
ERROR TERM
The concept of error term (e) can be
explained with the help of the fig. 5.2
which reproduces the scatter diagram
of fig. 5.1.
Implies that NM – PM= -PN or
et = Yt – (a + bX)
72
et= Yt - Yc
e1996= Y1996 -
Yc

THE ORDINARY LEAST SQUARE
(OLS) METHOD
∑Y = Na + b∑X …(5.15)
∑XY = a∑X + b∑X2 …(5.16)
• These equations are normal equations which can be solved for determining the
values of constants a and b. By solving these equations, we get
a =
(∑ 𝑋2
) ∑ 𝑌 −(∑ 𝑋)(∑ 𝑋𝑌)
N∑ 𝑋2
− ∑ 𝑋 2
b =
N∑ 𝑋𝑌 −(∑ 𝑋)(∑ 𝑌)
N∑ 𝑋2
− ∑ 𝑋 2
• Once the numerical values of a and b are determined, by substituting the values of
a and b in the basic equation of the line i.e. Y = a + bX, we get the regression
equation.
73

TABLE 5.2 REGRESSION OF SALES
ON ADVERTISEMENT
EXPENDITURE
74
Year
Advertisement
Expenditure (X)
Sales (Y) X2
XY
1995 5 45 25 225
1996 8 50 64 400
1997 10 55 100 550
1998 12 58 144 696
1999 10 58 100 580
2000 15 72 225 1080
2001 18 70 324 1260
2002 20 85 400 1700
2003 21 78 441 1638
2004 25 85 625 2125
N= 10 ∑X = 144 ∑XY = 656 ∑X
2
= 2448 ∑XY= 10254

ON SUBSTITUTING…
a =
( 𝑋 2
) 𝑌 −( 𝑋 )( 𝑋 𝑌 )
N 𝑋 2
− 𝑋 2
a =
(2 4 4 8 ) 656 −(144)(10254)
10(2448) − 144 2 =34.54
b =
N)( 𝑋 𝑌 −( 𝑋 )( 𝑌 )
N 𝑋 2
− 𝑋 2
b =
10)(10254 −(144)(656)
10(2448) − 144 2 = 2.15
Thus,
Y = 34.54 + 2.15X ……… (regression equation)
Sales2005= 34.54 +2.15 (30) = 99000 (approx.)
75

METHODS WITH THE HELP OF
EXAMPLES
• Box-Jenkins method-only explanation

BAROMETRIC METHOD
• Follows the methods used in weather forecasting
• Many economist use economic indicator as a barometer to forecast trend in
business activities
• Method was developed and used in 1920 by the Harvard economic service.

BAROMETRIC METHOD
• It may be noted at the outset that the barometric technique was developed
to forecast the general trend in overall economic activities
• This method can nevertheless to be used to forecast demand prospects for
a product not the actual quantity expected to be demanded

BAROMETRIC METHOD
• For example the allotment of land by DDA to the group housing societies
indicates higher demand for building material-cement , steel , bricks
• The basic approach of barometric technique is to construct an index of
relevant economic indicators and to forecast future trends on the basis of
movement in index of economic indicators

BAROMETRIC METHOD
• The indicators used in method are classified as
(a). Leading indicators
(b).Coincidental Indicators
(c). Lagging indicators
• A time series of various indicators is prepared
to read the future economic trend

BAROMETRIC METHOD
• Leading- Net business investments, New orders for durable goods, indexes
of prices of materials
• Coincidental –unemployment rate, GNP,
• Lagging- outstanding loans, lending rate for short term loans

ECONOMETRIC METHODS
• Combine statistical tools with economic theories to estimate economic
variables and to forecast intended economic variables.
• Widely used to forecast demand for a product, for group of products, for a
economy as whole.
• Single-equation regression serve the purpose of demand forecasting in the
case of most of the commodities.
• Demand for salt and sugar-population.
• Demand for vegetables.

SIMPLE OR BIVARIATE
REGRESSION
• A single independent variable is used to estimate value of dependent
variable
• Similar to trend fitting
• In trend fitting the independent variable is time where as in regression
equation the independent variable is the single most important determinant
of demand

• Simple or Bivariate Regression-Numerical Example
• Multi-variate Regression-Equation with numerical example

Unit 2

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Unit 2