Dr. Karim Kobeissi

Chapter 5: Demand Analysis

Demand - DefinitionAs in marketing, in economics demands are wants for specific

products backed by an ability to pay. In other words, demand

means the desire backed by a purchasing power. Hence want

alone is not enough. There must have necessary purchasing

power, i.e., .cash to purchase it. For example, everyone wants

to posses Ferrari car but only few have the ability to buy it.

So everybody cannot be said to have a demand for the car.

Thus the demand has two essentials (1) Willingness to

purchase and (2) Purchasing power.

Demand AnalysisDemand analysis means an attempt to determine the factors

affecting the demand of a product and to measure such factors and their influences. The demand analysis includes the study of (A) law of demand, (B) demand schedule, (C) demand function and (D) demand forecasting. Main objectives of demand analysis are:

1) To determine the factors affecting the demand2) To measure the elasticity of demand3) To forecast the demand 4) To manage the demand5) To allocate the recourses efficiently

A- Law of DemandThe law of demand which explains the directions of changes in

demand, shows the relation between price and quantity

demanded of a product in the market: ” A fall in price leads to

an increase in quantity demanded and vice versa”.

So the relationship described by the law of demand is an inverse

or negative relationship because the variables (price and

demand) move in opposite direction. It shows the cause and

effect relationship between price and quantity demand.

B- Demand Schedule Individual Demand Schedule Individual Demand Curve

Market Demand Schedule

Determinants of Demand Demand of a product may change. It may increase or

decrease due to changes in certain factors. These factors are called determinants of demand. These factors include:

1) Price of a product 2) Nature of a product 3) Income and wealth of consumer 4) Taste and preferences of consumer 5) Price of related products [substitutes (Pepsi & Coca - Cola)

and compliment (cars & wheels) products]6) Consumers’ expectations7) Advertisement etc...

C- Demand FunctionThere is a functional relationship between demand and its various

determinants. I.e., a change in any determinant will affect the

demand. When this relationship expressed mathematically, it is called

Demand Function. Demand function of a product can be written as

follows:

D = f (P, Y, T, Ps, E) Where,

D= Quantity demanded ; P= Price of the product

Y= Income of the consumer ; T= Taste and preference of the consumer

Ps = Price of substitute ; E= Consumer’s expectations

f = Function of (indicates how variables are related)

Extension and Contraction of DemandThe change in demand due to change in

price Only, where other factors remaining constant, is called extension and contraction of demand.

When the quantity demanded of a product rises due to a fall in price, it is called extension of demand. On the other hand, when the quantity demanded falls due to a rise in price, it is called contraction of demand.

On the demand curve, the area (a) to (c) is extension of demand and the area (a) to (b) is contraction of demand. As result of change in price of a product, the consumer moves along the same demand curve.

S h i ft i n D e m a n dWhen the demand changes due to changes

in other factors than the product’s price, it is called shift in demand. If the consumer buy more goods due to change in other factors, it is called increase in demand or upward shift. If the consumer buy fewer goods due to change in other factors, it is called downward shift or decrease in demand.

DD is the original demand curve. Demand curve shift upward due to change in other factors than the product’s price, where price remaining the same.

In the adjacent diagram, the demand curve (D1) shows an upward shift or increase in demand and the demand curve (D2) shows a downward shift or decrease in demand.

Elasticity of DemandAlthough the law of demand explains the directions of

changes in demand, it does not tell us the rate at which

demand changes to change in price. The concept of

elasticity of demand was introduced to show the rate at

which changes in demand take place.

Elasticity of demand can be defined as “the degree of

responsiveness in quantity demanded to a change in

price”. Thus it represents the rate of change in quantity

demanded due to a change in price.

Price Elasticity of DemandPrice Elasticity of demand measures the change in quantity demanded

to a change in price. It is the ratio of percentage change in quantity

demanded to a percentage change in price. This can be measured by

the following formula:

E.g., A 10% increase in quantity demanded in response to a 20% price decrease yields a price elasticity of 0.5 %

Price elasticity (E) = % change in quantity demanded

% change in price

(in %)

Types of Price Elasti city of DemandThere are five types of price elasticity

of demand (Degree of elasticity of demand).

1) Perfectly Elastic Demand (infinitely elastic)

When a small change in price leads to infinite change in quantity demanded (e.g., different prices for coca cola cans in two adjacent vending machines), it is called perfectly elastic demand. In this case the demand curve is a horizontal straight line as shown beside (Ep = ∞).

Types of Price Elasti city of Demand2) Perfectly Inelastic Demand

In this case, even a large change in price

fails to bring about a change in quantity

demanded. I.e. the change in price will

not affect the quantity demanded and

quantity remains the same whatever the

change in price (e.g., a change in the

insulin price).

Here, the demand curve will be a vertical

straight line as shown beside and Ep = 0.

Types of Price Elasti city of Demand3) Relatively Elastic Demand

Here a small change in price

leads to very big change in

quantity demanded (e.g.

furniture, cars). In this

case demand curve will be

fatter one and Ep >1.

Types of Price Elasti city of Demand4) Relatively Inelastic Demand

Here quantity demanded

changes less than

proportionate to changes in

price.

A large change in price leads to

small change in demand (e.g.

electricity; water). In this case

demand curve will be steeper

and Ep <1.

Types of Price Elasti city of Demand5) Unit Elasticity of Demand

Here the change in demand is exactly

equal to the change in price (while

there are no perfect examples of

unitary elastic demand in real life, a

close example is clothing). When both

are equal, Ep = 1, the elasticity is said

to be unitary.

The F ive Types of Pr ice E lasti c i ty of Demand

Importance of Elasticity of DemandThe concept of elasticity of demand is much of practical

importance:1. Production- Producers generally decide their production level on the

basis of demand for their product. Hence elasticity of demand helps to fix the level of output A producer can fix a higher price for the product which have inelastic demand and lower price for product which have elastic demand.

2. Price fixation- Each seller under monopoly and imperfect competition has to take into account the elasticity of demand while fixing their price. If the demand for the product is inelastic, he can fix a higher price.

3. Public finance- This assists the government in formulating tax policies. In order to impose tax on a product, the government should take into consideration its demand elasticity.

4. Nationalization- Elasticity of demand helps the government to decide about nationalization of industries.

Determinants of Elasticity of DemandElasticity of demand varies from product to product, time to time and

market to market. This is due to influence of various factors:

1. Nature of commodity- Demand for necessary products (salt, rice, etc,) are inelastic. Demand for comfort and luxury products (e.g., perfume) are elastic.

2. Availability/range of substitutes – A product against which lot of substitutes are available (e.g. Soft drink), the demand for that is elastic. But for the products which have no substitutes (e.g. surgical operation), their demand are inelastic.

3. Extent /variety of uses- a product having a variety of uses (e.g. steel, electricity) has a comparatively elastic demand.

4. Postponement/urgency of demand- if the consumption of a product can be post pond (e.g. An entertainment application), then it will have elastic demand. Urgent products (e.g., drugs) has inelastic demand.

5. Income level- income level also influences the elasticity. E.g. Rich man will not curtail the consumption quantity of fruit, milk etc, even if their price rises, but a poor man will not follow it.

6. Amount of money spend on the commodity- where an individual spends only a small portion of his income on the commodity, a price change doesn't significantly affect the demand for the commodity, and the demand is inelastic... (e.g., match box, salt Etc)

7. Durability of commodity- if the commodity is durable or repairable at a substantially less amount (e. g. cars), the demand for it is elastic.

Computing Price Elasticity

We use the Average Method of Computation Use

absolute values of (E):

– Take the quantity before and the quantity after the price

change and average them.

– Divide the change in quantity by the average quantity to

get the percentage change in quantity.

• If quantity went from 2 to 4, then the average is 3.

The change in quantity is 2, so the percentage

change is 2/3 or 0.667 = 66.7%

Computing Price Elasticity (con)• We do the same thing to get the percentage change in

price:

– Take the price before and the price after and average them.

– Divide the change in price by the average price to get the

percentage change in price.

• If price went from 45 to 40, then the average is 42.5.

The change is 5, so the percentage change is 5/42.5, or

0.118 = 11.8 %

Computi ng Price Elasti city (con)• The % change in quantity demanded is 66.7 and the % change in price is

11.8.

• We can now compute the price elasticity of demand:

I E I (note that we use absolute values of E) = 66.7% / 11.8% = 5.65 % > 1

The demand of the product (X) is Elastic.

A 1% change in price brings about a 5.65% change in quantity

demanded if we increase the price by 1 % then the quantity

demanded will decrease by 5.65% - On the contrary if we decrease

the price by 1% then the quantity demanded will increase by 5.65%.

Price elasticity (E) = % change in quantity demanded

% change in price

(in %)

D- Demand Forecasting Accurate demand forecasting is essential for a firm to enable

it to produce the required quantities at the right time and

to arrange well in advance for the various factors of

production. Forecasting helps the firm to assess the

probable demand for its products and plan its production

accordingly It is helpful in decision making and forward

planning.

N.B. Demand forecasting is also a vital tool for marketing

management (e.g., Back to School ads).

Methods of Demand Forecasting

Forecasting methods are classified into two groups:

Forecasting Methods

• Casual Models:

Causal Model

Year 2000 Demand

Price PopulationAdvertising

……

• Time Series Models:

Time Series Model

Year 2000 Demand

Demand1999 Demand1998

Demand1997……

-Forecasting based on causal relationships and time series models

Quantitative Forecasting

Quantitative Forecasting Methods - Causal Models

• Causal models establish a cause-and-effect relationship (s)

between one / many independent variable (X) and one dependent

variable (Y).

• Uses leading indicators (e.g., X = advertising budget; = product ‘s

price;…..) to predict the future (Y).

Quantitative Forecasting Methods - Causal Models

• Curve Fitting: Simple Linear Regression Method

– One Independent Variable (X) is used to predict one Dependent Variable

(Y): Y = a + b X

– Given n observations (Xi, Yi), we can fit a line to the overall pattern of

these data points.

– The Least Squares Method in statistics can give us the best a and b in the

sense of minimizing (Yi - a - bXi)2

– When two or more independent variables are used to predict the

dependent variable:

Y = b0 + b1X1 + b2X2 + … + bpXp

then we need to use Multiple Linear Regression Method to forecast (Y).

Quantitative Forecasting Methods - Causal Models

• A common tool of causal modeling is Linear RegressionFind a straight line that fits the data best.

y = Intercept + slope * x (= b0 + b1x)

Slope = b1 = change in y / change in xIntercept = b0 = Value of (Y) when (X) = 0.

0

2

4

6

8

10

12

10 11 12 13 14 15 16 17 18 19 20

Best line!

Intercept

Linear Regression Forecasting - Causal Model

XXX

YXXYb

2

• Identify dependent (y) and independent (x) variables

• Solve for the slope of the line

• Solve for the y intercept

• Develop your equation for the trend line

Y=a + bX

XbYa

22 XnX

YXnXYb

Linear Regression Forecasting - Causal Modeling Problem

A maker of golf shirts has been tracking the

relationship between demand and advertising. Use

linear regression to find out what demand (Y) might

be if the company invested 53,000 $ (X = 53000 $)

in advertising next year.

22 XnX

YXnXYb

Demand $ (Y)

Adv.$ (X)

XY X^2

Y^2

1 130 32 4160 1024

16,900

2 151 52 7852 2704

22,801

3 150 50 7500 2500

22,500

4 158 55 8690 3025

24964

5 153.85 53

Tot 589 189 28202

9253

87165

Avg

147.25 47.25

153.85531.1592.9Y

1.15X92.9bXaY

92.9a

47.251.15147.25XbYa

1.1547.2549253

147.2547.25428202b

2

XbYa

Y=a + bX

Linear Regression Forecasting in SPSS

Quantitative Forecasting Methods- Time Series Models

• Assumes information needed to generate a forecast is contained in a

time series of data.

• A time series is a series of observations over time of some quantity of

interest (a random variable). Thus, if Xi is the random variable of interest

at time i, and if observations are taken at times1 i 1, 2, . . . , t, then the

observed values {X1 = x1, X2 = x2, . . . , Xt = xt} are a time series.

• Assumes the future will follow same patterns as the past The

mathematical model can then be used to generate future forecasts.

The Evolution of the Monthly Demand of a Product Illustrates a Time Series

Quantitative Forecasting Methods - Time Series Models

Forecaster looks for data patterns as:

– Data = time series pattern + random fluctuations

• Typical Time Series Patterns : - (a) Stationary Pattern – the data is represented by a constant level superimposed with random fluctuations.

– (b) Trend Pattern – the data is represented by a linear trend

(increasing or decreasing) superimposed with random fluctuations.

– (c) Trend Plus Seasonality Pattern – the data is represented by a

linear trend + a seasonal component together superimposed with

random fluctuations.

• Random fluctuations cannot be predicted

Typical Time Series Patterns

(a) Stationary Pattern (b) Trend Pattern (c) Trend Plus Seasonality Pattern

Quantitative Methods – Forecasting Stationary Patterns

• Simple Mean Forecasting Method:

– The forecast is equal to the average of all available data

– Good for forecasting Level Patterns

• Simple Moving Average Forecasting Method :

– The forecast is equal to the average value over a specified

historical period (e.g.: the last four weeks).

– Each new forecast drops the oldest data point & adds a new

observation

– Good for forecasting Stationary Patterns

n/AF t1t

n/AF t1t

Quantitative Methods – Forecasting Stationary Patterns• Weighted Moving Average Forecasting Method :

• When emphasizing one period over others is desired (such as for recent years), the

Weighted Moving Average Forecasting Method can be used.

• All weights must add to 100% or 1.00

e.g. Ct .5, Ct-1 .3, Ct-2 .2 (weights add to 1.0)

• Allows emphasizing one period over others; above indicates more weight on recent

data (Ct=.5)

- Good for forecasting Stationary Patterns

Quantitative Methods – Forecasting Stationary Patterns

• Simple Exponential Smoothing Forecasting Method :

The Simple Exponential Smoothing is the most frequently used time series

method because of ease of use and minimal amount of data needed

• Need just three pieces of data to start:

– Last period’s forecast (Ft)

– Last periods actual value (At)

– Select value of smoothing coefficient, , between 0 and 1.0

• Higher values (e.g. .7 or .8) may place too much weight on last

period’s random variation.

- Good for forecasting Stationary Patterns

tt1t Fα1αAF

Forecasting Stationary Patterns - Problem

• Determine forecast for periods 7 & 8

• 2-period moving average

• 4-period moving average

• 2-period weighted moving average with

t-2 weighted 0.4 and t-1 weighted 0.6

• Simple Exponential smoothing with

alpha (α) = 0.2 and the period 6 forecast

being 375 F6 = 375.

Period Actual

1 300

2 315

3 290

4 345

5 320

6 360

7 375

8

Forecasting Stationary Patterns - Solution

Period Actual 2-Period 4-Period

2-Period Weighted

Moving Average

Simple Exponential Smoothing

1 300        

2 315        

3 290        

4 345        

5 320        

6 360        

7 375 340.0 328.8 344.0 372.0

8   367.5 350.0 369.0 372.6

tt1t Fα1αAF

Quantitative Methods – Forecasting Trend Patterns

• The Linear Regression Forecasting Method can be used

Quantitative Methods – Forecasting Trend Plus Seasonality Pattern• The General Procedure (Seven Steps Process):Step 1- Calculate the average demand per season Step 2- Calculate the overall average demand over all four quarters Step 3- Calculate the seasonal factor by dividing the average demand for

each quarter by this overall average demand

Step 4- Calculate the seasonally adjusted demand volume [show what the demand volumes would have been if the demands that occur because of the time of the year (e.g., Christmas shopping, back to-school shopping, etc.) had been spread evenly throughout the year instead] for each value in the time series by applying the following formula:

Quantitative Methods – Forecasting Trend Plus Seasonality Pattern

Step 5- Select any time series forecasting method.

Step 6- Apply this method to the seasonally adjusted time

series to obtain a forecast of the next seasonally adjusted

value (or values).

Step 7- Multiply this forecast by the corresponding seasonal

factor to obtain a forecast of the next actual value (without

seasonal adjustment).

Forecasting Trend Plus Seasonality Pattern - Problem

The COMPUTER CLUB WAREHOUSE (commonly referred to as CCW)

sells various computer products at bargain prices by taking

telephone orders directly from customers at its call center. The next

slide shows the average number of calls received per day in each of

the four quarters of the past three years. Note how the call volume

jumps up sharply in each Quarter 4 because of Christmas sales.

There also is a tendency for the call volume to be a little higher in

Quarter 3 than in Quarter 1 or 2 because of back-to-school sales.

Question: obtain a forecast of the next actual value (without

seasonal adjustment).

Forecasting Trend Plus Seasonality Pattern - Solution

Step 1- To quantify these seasonal effects, the second

column of Table 1 shows the average daily call

volume for each quarter over the past three years.

Step 2- Underneath this column, the overall average

over all four quarters is calculated to be 7,529.

Step 3- Dividing the average for each quarter by this

overall average gives the seasonal factor shown in

the third column.

The Average Number of Calls Received Per Day at the CCW Call Center in Each of the Four Quarters of the Past Three Years

Table 1: Calculation of the Seasonal Factors for the CCW Problem

Step 4- Calculating the seasonally adjusted demand volume for each value in the time series by applying the following formula:

The Average Number of Calls Received Per Day at the CCW Call Center in Each of the Four Quarters of the Past Three Years

Time Series Forecasting Methods

Look at the data (Scatter Plot)

Forecast using one or more techniques

Evaluate the technique and pick the best one.

Observations from the scatter Plot

Techniques to try Ways to evaluate

Data is reasonably stationary (no trend or seasonality)

Heuristics - Averaging methods Simple Mean Simple Moving Averages Simple Exponential Smoothing

MAD MAPE Standard Error BIAS

Data shows a consistent trend

Regression Linear Non-linear Regressions (not covered in this course)

MAD MAPE Standard Error BIAS R-Squared

Data shows both a trend and a seasonal pattern

Classical decomposition Find Seasonal Index Use regression analyses to find the trend component

MAD MAPE Standard Error BIAS R-Squared

Qualitative / Judgmental Forecasting Methods

Several qualitative / judgmental forecasting methods that solely use

expert judgment are available. These methods are especially

valuable when little or no historical data are available or when

major changes in the market place make these data unreliable for

forecasting purposes.

Qualitative / Judgmental Forecasting Methods

Type Characteristics Strengths WeaknessesExecutive opinion

A group of managers meet & come up with a forecast

Good for strategic or new-product forecasting

One person's opinion can dominate the forecast

Market research

Uses surveys & interviews to identify customer preferences

Good determinant of customer preferences

It can be difficult to develop a good questionnaire

Delphi method

Seeks to develop a consensus among a group of experts

Excellent for forecasting long-term product demand, technological changes, and

Time consuming to develop