Quantitative Demand Analysis

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Quantitative Demand Analysis
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Outline of the lecture

• I. The Elasticity Concept
• Own Price Elasticity
• Elasticity and Total Revenue
• Cross-Price Elasticity
• Income Elasticity
• II. Direct vs. Indirect Methods of Demand
  Estimation
• III. Economic Forecasting

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The Economic Concept of Elasticity

• Elasticity The sensitivity of one variable to
  another or, more precisely, the percentage change
  in one variable relative to a percentage change
  in another.

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The Price Elasticity of Demand

• The percentage change in quantity demanded
  caused by a 1 percent change in price.

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• Point elasticity Elasticity measured at a given
  point of a demand (or a supply) curve.

Arc elasticity Elasticity which is measured
over a discrete interval of a demand curve.
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• Interpretation of values
• Because of the negative relationship between P
  and Q, EP is negative.
• If EP gt 1, demand is price elastic
• If EP lt 1, demand is price inelastic
• The most important determinant of price
  elasticity of demand is the availability of
  substitutes.

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• Elasticity differs along a linear demand curve.
  

Price
4
Ep -1
2
Q 8 - 2P
Ep 0
Quantity
4
8
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• Limiting cases
• Perfect elasticity

Price
P
D
Quantity
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• Limiting cases
• 2. Perfect inelasticity

Price
D
Quantity
Q
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Determinants of Elasticity

• Ease of substitution
• Proportion of total expenditures
• Durability of product
• Possibility of postponing purchase
• Possibility of repair
• Second hand market
• Length of time period

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• A long-run demand curve will be more elastic
  than a short-run curve.
• As the time period lengthens consumers find way
  to adjust to the price change

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The Price Elasticity of Demand and Revenue

• As price decreases
• revenue rises when demand is elastic
• falls when it is inelastic
• reaches it peak when elasticity of demand equals
  1.

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The Cross-Price Elasticity of Demand

• The percentage change in quantity consumed of
  one product as a result of a 1 percent change in
  the price of a related product.

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• The sign of cross-elasticity for substitutes is
  positive.
• The sign of cross-elasticity for complements is
  negative.

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Income Elasticity

• The percentage change in quantity demanded
  caused by a 1 percent change in income.

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• Categories of income elasticity
• Superior goods
• EM gt 1
• Normal goods
• 0 gt EM gt 1
• Inferior goods
• EM lt 1

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Other Elasticity Measures

• Elasticity is encountered every time a change in
  some variable affects quantities.
• Advertising expenditure
• Interest rates
• Population size

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Uses of Elasticities

• Pricing
• Managing cash flows
• Impact of changes in competitors prices
• Impact of economic booms and recessions
• Impact of advertising campaigns
• And lots more!

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Example 1 Pricing and Cash Flows

• ATTs own price elasticity of demand for long
  distance services is -8.64.
• ATT needs to boost revenues in order to meet
  its marketing goals.
• To accomplish this goal, should ATT raise or
  lower its price?

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Answer Lower price!
Since demand is elastic, a reduction in price
will increase quantity demanded by a greater
percentage than the price decline, resulting in
more revenues for ATT.
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Example 2 Quantifying the Change
If ATT lowered price by 3 percent, what would
happen to the volume of long distance telephone
calls routed through ATT?
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Answer
Calls would increase by 25.92 percent!
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Example 3 Impact of a change in a competitors
price

• According to an FTC Report by Michael Ward,
  ATTs cross price elasticity of demand for long
  distance services is 9.06.
• If competitors reduced their prices by 4 percent,
  what would happen to the demand for ATT services?

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Answer
ATTs demand would fall by 36.24 percent!
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Example 4 Advertising and the demand for
pharmaceuticals

• Three important parties sales representatives,
  physicians patients
• 30 of total revenue is spent on advertising
• What is the effect of this advertising on the
  demand for drugs?

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Answer

• Advertising elasticity ranged between 0.26 and
  0.27
• But advertising caused the demand to become less
  price elastic. (-2 before advertising and -1.5
  after it)

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Demand Estimation

• WHY???
• to determine the relationship between price and
  quantity of a given good or service
• Obviously, the more closely the firm can estimate
  demand conditions for its product, the more
  likely it is to determine its profit maximizing
  rate of output and price, or wether to produce at
  all.

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Which factors determine the demand?

• 1. Controllable factors (price, advertising,
  distribution channels, etc)
• 2. Non-controllable factors (consumers income,
  consumers preferences, prices of substitutes and
  complements, expectations, etc)

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Estimation Techniques

• Direct approach
• Obtaining direct data about consumer behaviour
• Indirect approach
• Using primary and secondary (existing) data

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Direct Approach

• Direct communication with consumers or
  observation of their behaviour.
• Techniques
• Survey (interviews)
• Focus group
• Market experiments, etc.

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• CASE small firm that would like to become the
  general representative for selling rollerblades
• POTENTIAL MARKET Younger consumers-aprox.
  100.000 people
• ??? What is the effect of price on potential
  selling quantity?

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Possible pricing policies
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Indirect Approach

• Uses secondary data and statistical procedures
• Data
• Time series
• Cross-sectional data

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Regression Analysis

• A statistical technique for finding the best
  relationship between a dependent variable and
  selected independent variables.
• Simple regression one independent variable
• Multiple regression several independent
  variables

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• Dependent variable
• depends on the value of other variables
• is of primary interest to researchers
• Independent variables
• used to explain the variation in the dependent
  variable

Linear regression model Qx?BxPxBsPsBcPc
BmPm Bx, Bs, Bc, Bm regression
coefficients ? -intercept
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How to proceed?

• Specification of relevant demand factors
• Specification of measurement scales
• Data
• Selection of model
• Coefficient estimation
• Statistical evaluation
• Identifying the demand function
• Practical use of estimated demand function

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Example Estimating Demand for Beer

• STEP 1 identifying relevant factors of short run
  demand for beer
• Intensivity of advertising (controllable)
• Weather (non-controllable)
• STEP 2 specification of measurement scales
• Quantity of beer consumed (N)
• Intensity of advertising (advertising outlays)
• Weather (average
  monthly temperature)

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• STEP 3 Data

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• STEP 4 selection of an appropriate
  regression model
• STEP 5 estimation of regression
  coefficients

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• STEP 6 statistical evaluation
• Good fit
• Coefficients statistically significant
• STEP 7

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• STEP 8 practical use
• Calculation of demand elasticity with respect to
  advertising
• December, 2nd year A5.000, T3
• July, 1st year A2.000, T31

EA(5.000,3) 0,381
EA(2.000,31) 0,098
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Estimating Linear Regression Equation
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The estimation of the regression equation
involves a search for the best linear
relationship between the dependent and the
independent variable.
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Simple Regression Y a bX u Y
dependent variable X independent variable a
intercept b slope u random factor
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• ORDINARY LEAST SQUARES (OLS)
• A statistical method designed to fit a line
  through a scatter of points is such a way that
  the sum of the squared deviations of the points
  from the line is minimized.
• OLS is blue.
• Many software packages perform OLS estimation.

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• ORDINARY LEAST SQUARES (OLS)
• Let be
• where a are parameters of linear function
• Then, the necessary condition for minimum of F(a)
  is

iN number of observations
jK number of parameters
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• How good is the regression model?
• A) Are all independent variables relevant?
• B) Is the model statistically significant?
• C) How well does regression line fit the data?

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• How confident can a researcher be about the
  extent to which the regression equation for the
  sample truly represent the unknown regression
  equation for population???

Each random sample from the population generates
its own intercept and slope coefficients.
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Evaluation the Quality of Regression Model

• To answer questions AB we use hypothesis testing
  (test of statistical significance)
• Hypothesis testing is a procedure based on sample
  evidence and probabilistic theory that help us to
  determine whether
• the hypothesis is the reasonable statement and
  should not be rejected
• the hypothesis is unreasonable statement and
  should be rejected

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Testing Procedure

• 5-Step testing procedure
• 1) State a null and alternative hypothesis
• 2) Select a level of significance
• 3) Identify the test statistics
• 4) Formulate a decision rule
• 5)Take a sample ? decision

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1) State a null and alternative
hypothesis Ho b 0 Ho b ?
0 or H1 b ? 0 H1 b ?? 0 In Ho we
put the statement we would like to reject.
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2) Select a level of significance Level of
significance probability of rejecting the null
hypothesis when it is actually true Type 1
error rejecting null hypothesis when it is
actually true (?) Type 2 error accepting null
hypothesis when it is actually false (?)
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3) Identify the test statistics A) testing for
statistical significance of the estimated
regression coefficients It can be demonstrated
mathematically that the standard deviation of
each samples estimate from the actual population
value has a t-distribution. Estimated
coefficients t-distribution with (n-k-1) degrees
of freedom N-number of observations K-number of
independent variables
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B) testing for statistical significance of the
entire regression model H0(?1, ?2, ...,
?N0) F test OR
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• 4) Formulate a decision rule
• Decision rule states condition of rejection or
  non-rejection
• Critical value dividing point between the region
  where the null hypothesis is rejected and the
  region where the null hypothesis is not rjected
• Significance level

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5) Take a sample ? decision Compare the
value of resulting statistics with critical value
and make the decision
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• Explanatory power of estimated regression
  equation

• Coefficient of determination (R2)
• A measure indicating the percentage of the
  variation in the dependent variable accounted for
  by variations in the independent variables.
• R2 is a measure of the goodness of fit of the
  regression model.

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If R2 1 the total deviation in Y from its mean
is explained by the equation.
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• If R2 0 the regression equation does not
  account for any of the variation of Y from its
  mean.

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• The closer R2 is to unity, the greater the
  explanatory power of the regression equation.
• An R2 close to 0 indicates a regression equation
  will have very little explanatory power.
• As additional independent variables are added,
  the regression equation will explain more of the
  variation in the dependent variable. This leads
  to higher R2 measures.

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• Adjusted coefficient of determination
• k number of independent variables
• n sample size

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Estimating Demand for Beer

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Additional Topics
Proxy variable an alternative variable used in
a regression when direct information in not
available Dummy variable a binary variable
created to represent a non-quantitative factor.
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The relationship between the dependent and
independent variables may be nonlinear.
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We could specify the regression model as
quadratic regression model. Y a b1x b2x2
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We could also specify the regression model as
power function. Y axb or log Qd log a
b(logX)
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Estimation of Non-Linear Regression Models

• Polynomial model
• Y a bX cX2 dX3
• We introduce new variables
• XX, X X2 in X X3
• Non-linear linear model
• Y a bX cX dX

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• Multiplicative model
• Y aXbWcZd
• We take logarithms
• log(Y) log(a) b?log(X) c?log(W) d?log(Z)
• Introduce new variables
• Ylog(Y), Xlog(X), Wlog(W) in Zlog(Z)
• Non-linear linear model
• Y log(a) bX cW dZ

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Problems with Linear Regression
1. Model Selection Solution test more models
and pick up the best one 2. Omission of the
relevant variable(s) Solution test the model
augmented with additional variables 3. Quality of
measurement 4. Multicolinearity Solution drop
variable(s) that cause multicolinearity
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5. Identification problem
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The Final Step
Check the residuals White Noise? No. Check the
model and procedures again.
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Forecasting Demand

• WHY?
• to quess the future demand art science at
  the same time
• to set objectives and create plans
• forecasted demand is a foundation for
  operational, tactical and strategic decisions

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Subjects of Forecasts

• Macro forecasts
• Gross domestic product
• Consumption expenditure
• Producer durable equipment expenditure
• Residential construction
• Industry forecasts
• Sales of an industry as a whole
• Sales of a particular product within an industry

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• Firm-level forecasts
• Sales
• Costs and expenses
• Employment requirements
• Square feet of facilities utilized

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Prerequisities of Good Forecast

• must be consistent with other parts of business
• should be based on adequate knowledge
• should take into consideration the economic and
  political environment

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Forecast Techniques

• QUALITATIVE (not just an emergency exit)
• Expert opinion (e.g. Delphi)
• Opinion polls and marketing research
• Economic indicators
• QUANTITATIVE
• Projections
• Econometric models

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Naive methods project past data without
explaining future trends. Causal (or
explanatory) forecasting attempts to explain the
functional relationships between the dependent
variable and the independent variables.
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Choosing the right technique depends on various
factors.

• the item to be forecast
• the relation between value and cost
• the quantity of historical data available
• the time allowed to prepare the forecast

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Time Series Analysis
Assumption behaviour in the future will be
similar to behavior in the past (BUT consider
environmental, political changes, govenmental
measures, etc) Forecasting of stock values is a
modern version of transforming lead into gold
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Time Series Components

• We can think of time series as consisting of
  several components besides the basic level B
• Trend T (long-term moving of the average)
• Cyclical component C (regular pattern of sequence
  of points above and belove the trend line) . Ex
  cyclical movements in the economy
• Seasonal component S (regular pattern of
  variability in a shorter period of time)
• Irregular component R (caused by unanticipated
  and nonrecurring factors - unpredictable)

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Forecasting methods

• LAST VALUE
• Forecast
• Can be a good estimate.
• LINEAR TREND
• Forecast

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Linear Trend
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?7,75
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Moving Average Method
NOTE the larger I, the slower response
to changes, but more stable predictions.
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Other Forecasting Methods

• Weighted moving average
• Exponential smoothing
• Decomposition (trend, seasonal effects, cyclical
  effects)
• ARIMA
• etc.

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Econometric Models

• Regression analysis ? estimation of
  coefficients
• ASSUMPTION the relationship between variables
  doesnt change from past into future
• ? on the basis of independent variables the
  dependent variable is predicted

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Forecasting Demand for Beer

• We have already estimated monthly demand function
  for beer
• Q 10.088,13 1.79 ? A 716,67 ? T
• For the month after we estimated
• average temperature T4
• advertising outlays A7.000
• therefore
• Q 10.088,13 1,79 ? 7.000 716,67 ? 4
  25.478

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