Transcript No Slide Title

Demand Analysis
• Demand Relationships
• The Price Elasticity of Demand
» Arc and point price elasticity
» Elasticity and revenue relationships
» Why some products are inelastic and others
are elastic
• Income Elasticities
• Cross Elasticities of Demand
• Combined Effects of Elasticities
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.
Slide 1
Health Care & Cigarettes
• Raising cigarette taxes reduces smoking
» In Canada, over $4 for a pack of cigarettes
reduced smoking 38% in a decade
• But cigarette taxes also helps fund health
care initiatives
» The issue then, should we find a tax rate
that maximizes tax revenues?
» Or a tax rate that reduces smoking?
Slide 2
Demand Analysis
• An important contributor to firm risk arises
from sudden shifts in demand for the
product or service.
• Demand analysis serves two managerial
objectives:
(1) it provides the insights necessary for
effective management of demand, and
(2) it aids in forecasting sales and revenues.
Slide 3
Slide 4
FIGURE 3.1 Demand for SUV (Ford
Explorer) as Gasoline Price Doubled
Slide 5
Downward Slope to the Demand Curve
• Economists presume consumers are maximizing their utility
• This is used to derive a demand curve from utility maximization
» income effect -- as the price of a good declines, the
consumer can purchase more of all goods since his or her
real income increased. So as the price falls, we typically
buy more.
Slide 6
Downward Slope to the Demand Curve
» substitution effect -- as the price declines, the good
becomes relatively cheaper. A rational consumer
maximizes satisfaction by reorganizing consumption
until the marginal utility in each good per dollar is equal.
We buy more.
Slide 7
FIGURE 3.2 Consumption Choice on a
Business Trip
Slide 8
Downward Slope to the Demand Curve
» targeting, switching, and positioning – marketing
efforts such as loyalty programs affect demand.
Slide 9
The Price Elasticity of Demand
• Elasticity is measure of responsiveness or
sensitivity
• Beware of using slopes
price
per
bu.
price
per
bu.
bushels
Slopes
change
with a
change in
units of
measure
hundred tons
Slide 10
Price Elasticity
• ED = % change in Q / % change in P
• Shortcut notation: ED = %Q / %P = Q / P ∙ Base P / Base
Q.
• A percentage change from 100 to 150 is 50%
• A percentage change from 150 to 100 is -33%
• For arc price elasticities, we use the average as the base, as in
100 to 150 is +50/125 = 40%, and 150 to 100 is -40%
• Arc Price Elasticity -- averages over the two points
Average quantity
ED = Q/ [(Q1 + Q2)/2]
P/ [(P1 + P2)/2]
arc price
elasticity
D
Average price
Slide 11
Arc Price Elasticity Example
•
•
•
•
Q = 1000 when the price is $10
Q= 1200 when the price is reduced to $6
Find the arc price elasticity
Solution: ED = %Q/ %P = +200/1100
-4/8
or -.3636.
The answer is a number.
A 1% increase in price reduces quantity by
.36 percent.
Slide 12
Point Price Elasticity Example
•
Need a demand curve or demand function to
find the price elasticity at a point.
ED = %Q/ %P =(Q/P)(P/Q)
If Q = 500 - 5•P, find the point price
elasticity at P = 30; P = 50; and P = 80
1. ED = (Q/P)(P/Q) = - 5(30/350) = - .43
2. ED = (Q/P)(P/Q) = - 5(50/250) = - 1.0
3. ED = (Q/P)(P/Q) = - 5(80/100) = - 4.0
Slide 13
Price Elasticity
(both point price and arc elasticity)
• If ED = -1, unit elastic
• If ED > -1, inelastic, e.g., - 0.43
• If ED < -1, elastic, e.g., -4.0
price
elastic region
unit elastic
Straight line
demand curve
example
inelastic region
quantity
Slide 14
FIGURE 3.4 Perfectly Elastic and
Inelastic Demand Curves
Slide 15
TR and Price Elasticities
• If you raise price, does TR rise?
• Suppose demand is elastic, and raise price.
TR = P•Q, so, %TR = %P+ %Q
• If elastic, P , but Q a lot
• Hence TR FALLS !!!
• Suppose demand is inelastic, and we decide
to raise price. What happens to TR and TC
and profit?
Slide 16
( Figure 3.5)
Another Way to
Remember
Elastic
Unit Elastic
A
•
•
•
Linear demand curve
TR on other curve
Look at arrows to see
movement in TR
A. Increasing price in the
inelastic region raises
revenue
B. Increasing price in the
elastic region lowers
revenue
Inelastic
B
Q
TR
Q
Slide 17
FIGURE 3.5 Price Elasticity over
Demand Function
Slide 18
FIGURE 3.5 Price Elasticity over
Demand Function
Slide 19
MR and Elasticity
• Marginal revenue is TR /Q
• To sell more, often price must decline, so
MR is often less than the price.
 MR = P ( 1 + 1/ED )
equation 3.7
• For a perfectly elastic demand, ED = -B.
Hence, MR = P.
• If ED = -2, then MR = .5•P, or is half of the
price.
Slide 20
Slide 21
Empirical Price Elasticities
Selections from Table 3.4
•
•
•
•
•
•
•
•
Apparel (whole market) -1.1
Apparel (one firm) -4.1
Beer -.84
Wine -.55
Liquor -.50
Regular coffee -.16
Instant coffee -.36
Adult visits to dentist
» Men -.65
» Women -.78
» Children -1.4
•
•
•
•
•
•
•
•
•
•
•
Furniture -3.04
Glassware & China -1.2
Household appliances -.64
Flights to Europe -1.25
Shoes -.73
Soybean meal -1.65
Telephones -.10
Tires -.60
Tobacco products -.46
Tomatoes -2.22
Wool -1.32
Slide 22
Factors Affecting the Elasticity of Demand
• The availability and the closeness of substitutes
» more substitutes, more elastic
• The percentage of the consumer's budget
» larger proportion of the budget, more elastic
• Positioning as income superior
» Products that are viewed as superior goods with large income
elasticities, tend to be more elastic. (Clash for Clunkers lowered prices and
helped sales of larger cars more than tiny ones)
• The longer the time period of adjustment
» more time, generally, more elastic
» Predictable end-of-season discounts more elastic than
unexpected “midnight madness” sales.
Slide 23
Income Elasticity
EY = %Q/ %Y = (Q/Y)( Y/Q)
point income
EY = Q/ [(Q1 + Q2)/2] arc income
Y/ [(Y1 + Y2)/2] elasticity
• arc income elasticity:
» suppose dollar quantity of food expenditures of families
of $20,000 is $5,200; and food expenditures rises to
$6,760 for families earning $30,000.
» Find the income elasticity of food
» %Q/ %Y = (1560/5980)•(10,000/25,000) = .652
» With a 1% increase in income, food purchases rise
.652%
Slide 24
Income Elasticity Definitions
•
If EY >0, then it is a normal or income superior good
»
»
•
•
some goods are luxuries: EY > 1 with a high income elasticity
some goods are necessities: EY < 1 with a low income elasticity
If EY is negative, then it’s an inferior good
Consider these examples:
1. Expenditures on new automobiles
2. Expenditures on new Ford Focus
3. Expenditures on 2005 Ford Focus with 150,000 miles
Which of the above is likely to have the largest income elasticity?
Which of the above might have a negative income elasticity?
Slide 25
Point Income Elasticity Problem
• Suppose the demand function is:
Q = 10 - 2•P + 3•Y
• find the income and price elasticities at a price
of P = 2, and income Y = 10
• So: Q = 10 -2(2) + 3(10) = 36
• EY = (Q/Y)( Y/Q) = 3( 10/ 36) = .833
• ED = (Q/P)(P/Q) = -2(2/ 36) = -.111
• Characterize this demand curve, which
means describe them using elasticity terms.
Slide 26
Slide 27
Advertising Elasticity
EA = %Q/ %ADV = (Q/ADV)( ADV/Q)
• If the Advertising elasticity is .60, then a 1%
increase in Advertising Expenditures increases
the quantity of goods sold by .60%.
Slide 28
Cross Price Elasticities
Ecross = %QA / %PB = (QA/PB)(PB /QA)
• Substitutes have positive cross price
elasticities: Butter & Margarine
• Complements have negative cross price
elasticities: DVD machines and the rental
price of DVDs at Blockbuster
• When the cross price elasticity is zero or
insignificant, the products are not related
Slide 29
Antitrust & Cross Price Elasticities
• Whether a product is a monopoly or in a
larger industry is dependent on the
closeness of the substitutes
• DuPont’s cellophane was at first viewed as
a monopoly. Economists showed that the
cross price elasticity with other products
such as aluminum foil, waxed paper, and
other flexible wrapping paper was Positive,
the large, DuPont showed its cellophane
was not a monopoly in this larger market.
Slide 30
Slide 31
Combined Effect of
Demand Elasticities
• Most managers find that prices and income change every year. The
combined effect of several changes are additive.
%Q = ED(% P) + EY(% Y) + Ecross(% PR)
» where P is price, Y is income, and PR is the price of a related
good.
• If you knew the price, income, and cross price elasticities, then you
can forecast the percentage changes in quantity. The forecast for
period 2 is:
Q2 = Q1[ 1 + ED(% P) + EY(% Y) + Ecross(% PR)
Slide 32
Example: Combined Effects of Elasticities
• Toro has a price elasticity of -2 for snow blowers
• Toro snow blowers have an income elasticity of 1.5
• The cross price elasticity with professional snow removal
for residential properties is +.50
• What will happen to the quantity sold if you raise price 3%,
income rises 2%, and professional snow removal companies
raises its price 1%?
» %Q = EP • %P +EY • %Y + Ecross • %PR = -2 • 3% + 1.5 • 2%
+.50 • 1% = -6% + 3% + .5%
» %Q = -2.5%. We expect sales to decline 2.5%.
Q:
Will Total Revenue for your product rise or fall?
Slide 33
Example: Combined Effects of Elasticities
A:
Total revenue will rise slightly (about + .5%),
as the price rises 3% and the quantity of snowblowers sold falls 2.5%.
Slide 34
Estimating Demand
• A chief uncertainty for managers is the future. Managers
fear what will happen to their product.
» Managers use forecasting, prediction & estimation to
reduce their uncertainty.
» The methods that they use vary from consumer surveys
or experiments at test stores to statistical procedures on
past data such as regression analysis.
• Objective: Learn how to interpret the results of regression
analysis based on demand data.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.
Slide 35
Demand Estimation
Using Marketing Research Techniques
• Consumer Surveys
» ask a sample of consumers their attitudes
• Consumer Focus Groups
» experimental groups try to emulate a market (but
beware of the Hawthorne effect = people often behave
differently in when being observed)
• Market Experiments in Test Stores
» get demand information by trying different prices
• Historical Data - what happened in the past is guide
to the future using statistics is an alternative
Slide 36
Statistical Estimation of Demand Functions:
Plot Historical Data
Price
• Look at the relationship
of price and quantity
over time
• Plot it
» Is it a demand curve or
a supply curve?
» The problem is this does
not hold other things
equal or constant.
Is this curve demand
or supply?
2004
2007
2010
2009
2008 2006
2005
quantity
Slide 37
Statistical Estimation of Demand Functions
• Steps to take:
» Specification of the model -- formulate the
demand model, select a Functional Form
• linear
Q = a + b•P + c•Y
• double log
log Q = a + b•log P + c•log Y
• quadratic
Q = a + b•P + c•Y+ d•P2
» Estimate the parameters -• determine which are statistically significant
• try other variables & other functional forms
» Develop forecasts from the model
Slide 38
Specifying the Variables
• Dependent Variable -- quantity in units,
quantity in dollar value (as in sales
revenues)
• Independent Variables -- variables thought
to influence the quantity demanded
» Instrumental Variables -- proxy variables for
the item wanted which tends to have a
relatively high correlation with the desired
variable: e.g., Tastes
Time Trend
Slide 39
Functional Forms: Linear
• Linear Model Q = a + b•P + c•Y
» The effect of each variable is constant, as in
Q/P = b and Q/Y = c, where P is price and Y is
income.
» The effect of each variable is independent of
other variables
» Price elasticity is: ED = (Q/P)(P/Q) = b•P/Q
» Income elasticity is: EY = (Q/Y)(Y/Q)= c•Y/Q
» The linear form is often a good approximation of
the relationship in empirical work.
Slide 40
Functional Forms: Multiplicative or
Double Log
• Multiplicative Exponential Model Q = A • Pb • Yc
» The effect of each variable depends on all the other
variables and is not constant, as in Q/P = bAPb-1Yc and
Q/Y = cAPbYc-1
» It is double log (log is the natural log, also written as ln)
Log Q = a + b•Log P + c•Log Y
» the price elasticity, ED = b
» the income elasticity, EY = c
» This property of constant elasticity makes this approach
easy to use and popular among economists.
Slide 41
A Simple Linear Regression Model
• Yt = a + b Xt + t
Y
• time subscripts & error term
• Find “best fitting” line
t = Yt - a - b Xt
t2 = [Yt - a - b Xt] 2 .
a
_
Y
• mint 2= [Yt - a - b Xt] 2 .
Solution:
slope b = Cov(Y,X)/Var(X) and
intercept a = mean(Y) - b•mean(X)
Y
X
_
X
Slide 42
Simple Linear Regression:
Assumptions & Solution Methods
• Spreadsheets - such as
1. The dependent
» Excel, Lotus 1-2-3, Quatro
variable is random.
Pro, or Joe Spreadsheet
2. A straight line
• Statistical calculators
relationship exists.
3. The error term has a • Statistical programs such as
mean of zero and a
» Minitab
finite variance: the
» SAS
independent
» SPSS
variables are indeed
» For-Profit
independent.
» Mystat
Slide 43
Assumption 2: Theoretical
Straight-Line Relationship
Slide 44
Assumption 3: Error Term Has A
Mean Of Zero And A Finite Variance
Slide 45
Assumption 3: Error Term Has A
Mean Of Zero And A Finite Variance
Slide 46
FIGURE 4.4 Deviation of the Observations
about the Sample Regression Line
Slide 47
Sherwin-Williams Case
• Ten regions with data on promotional expenditures (X) and
sales (Y), selling price (P), and disposable income (M)
• If look only at Y and X: Result: Y = 120.755 + .434 X
One use of a regression is to make predictions.
• If a region had promotional expenditures of 185, the
prediction is Y = 201.045, by substituting 185 for X
• The regression output will tell us also the standard error
of the estimate, se . In this case, se = 22.799
• Approximately 95% prediction interval is Y ± 2 se.
• Hence, the predicted range is anywhere from 155.447 to
246.643.
Slide 48
Sherwin-Williams Case
Slide 49
Figure 4.5 Estimated Regression Line
Sherwin-Williams Case
Slide 50
T-tests
• Different
samples would
yield different
coefficients
• Test the
hypothesis that
coefficient
equals zero
» Ho: b = 0
» Ha: b 0
RULE: If absolute value of the
estimated t > Critical-t, then
REJECT Ho.
» We say that it’s significant!
• The estimated t = (b - 0) / b
• The critical t is:
» Large Samples, critical t2
• N > 30
» Small Samples, critical t is on Student’s t
Distribution, page B-2 at end of book, usually
column 0.05, & degrees of freedom.
• D.F. = # observations, minus number of
independent variables, minus one.
• N < 30
Slide 51
Sherwin-Williams Case
• In the simple linear
•
regression:
Y = 120.755 + .434 X
•
• The standard error of the
slope coefficient is
.14763. (This is usually
available from any
regression program used.)
• Test the hypothesis that •
the slope is zero, b=0.
The estimated t is:
t = (.434 – 0 )/.14763 = 2.939
The critical t for a sample of 10, has
only 8 degrees of freedom
» D.F. = 10 – 1 independent variable – 1 for
the constant.
» Table B2 shows this to be 2.306 at the .05
significance level
Therefore, |2.939| > 2.306, so we reject
the null hypothesis.
• We informally say, that promotional
expenses (X) is “significant.”
Slide 52
USING THE REGRESSION EQUATION
TO MAKE PREDICTIONS
• A regression equation can be used to make
predictions concerning the value of Y, given
any particular value of X.
• A measure of the accuracy of estimation with
the regression equation can be obtained by
calculating the standard deviation of the
errors of prediction (also known as the
standard error of the estimate).
Slide 53
Correlation Coefficient
• We would expect more promotional expenditures to be
associated with more sales at Sherwin-Williams.
• A measure of that association is the correlation coefficient, r.
• If r = 0, there is no correlation. If r = 1, the correlation is
perfect and positive. The other extreme is r = -1, which is
negative.
Slide 54
Analysis of Variance
• R-squared is the percentage of the
Y
variation in dependent variable
that is explained
•
• As more variables are included,
R-squared rises
• Adjusted R-squared, however,
can decline
» Adj R2 = 1 – (1-R2)[(N-1)/(N-K)]
» As K rises, Adj R2 may decline.
^
Yt
^
Yt predicted
_
Y
_
X
X
Slide 55
FIGURE 4.7 Partitioning the Total
Deviation
Slide 56
Slide 57
Association and Causation
• Regressions indicate association, but beware of jumping to the
conclusion of causation
• Suppose you collect data on the number of swimmers at a local beach
and the temperature and find:
• Temperature = 61 + .04 Swimmers, and R2 = .88.
» Surely the temperature and the number of swimmers is positively
related, but we do not believe that more swimmers CAUSED the
temperature to rise.
» Furthermore, there may be other factors that determine the
relationship, for example the presence of rain or whether or not it
is a weekend or weekday.
• Education may lead to more income, and also more income may lead
to more education. The direction of causation is often unclear. But the
association is very strong.
Slide 58
Multiple Linear Regression
• Most economic relationships involve several
variables. We can include more independent
variables into the regression.
• To do this, we must have more observations (N) than
the number of independent variables, and no exact
linear relationships among the independent variables.
• At Sherwin-Williams, besides promotional expenses
(PromExp), different regions charge different selling
prices (SellPrice) and have different levels of
disposable income (DispInc)
• The next slide gives the output of a multiple linear
regression, multiple, because there are three
independent variables
Slide 59
Figure 4.8 Computer Output:
Sherwin-Williams Company
Dep var: Sales (Y)
N=10
R-squared = .790
Adjusted R2 = .684 Standard Error of Estimate = 17.417
Variable
Constant
PromExp
SellPrice
DispInc
Coefficient Std error
310.245
95.075
.008
0.204
-12.202
4.582
2.677
3.160
Analysis of Variance
Source
Sum of Squares DF
Regression
6829.8 3
Residual
1820.1 6
T
P(2 tail)
3.263
0.038
-2.663
0.847
Mean Squares
2276.6
303.4
.017
.971
.037
.429
F
p
7.5 .019
Slide 60
Interpreting Multiple Regression Output
• Write the result as an equation:
Sales = 310.245 + .008 ProExp -12.202 SellPrice
+ 2.677 DispInc
• Does the result make economic sense?
» As promotion expense rises, so does sales. That makes sense.
» As the selling price rises, so does sales. Yes, that’s reasonable.
» As disposable income rises in a region, so does sales. Yup. That’s reasonable.
• Is the coefficient on the selling price statistically significant?
» The estimated t value is given in Figure 4.8 to be -2.663 on SellPrice.
» The critical t value, with 6 ( which is 10 – 3 – 1) degrees of freedom in table
B2 is 2.447
» Therefore |-2.663| > 2.447, so reject the null hypothesis, and assert that the
selling price is significant!
Slide 61
Soft Drink Demand Estimation
A Cross Section Of 48 States
Linear estimation yields:
Intercept
Price
Income
Temperature
Coefficients Standard Error
159.17
94.16
-102.56
33.25
1.00
1.77
3.94
0.82
t Stat
1.69
-3.08
0.57
4.83
Regression Statistics
Multiple R
0.736
R Square
0.541
Adjusted R Square
0.510
Standard Error
47.312
Observations
48
Slide 62
Find The Linear Elasticities
Linear Specification write as an equation:
Cans = 159.17 -102.56 Price +1.00 Income + 3.94 Temp
The price elasticity in Alabama is = (Q/P)(P/Q) = -102.56(2.19/200)= -1.123
The price elasticity in Nevada is = (Q/P)(P/Q) = -102.56(2.19/166) = -1.353
The price elasticity in Wisconsin is = (Q/P)(P/Q) = -102.56(2.38/97)= -2.516
The estimated elasticities are elastic for individual states.
We can estimate the elasticity from the whole samples as:
(Q/P)  (Mean P/Mean Q) = 102.56 x ($2.22/160) = -1.423,
which is also elastic.
Slide 63