Transcript No Slide Title

DEMAND ANALYSIS
Overview of Chapter 3
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Demand Relationships
Demand Elasticities
Income Elasticities
Cross Elasticities of Demand
Combined Effects of Elasticities
2005 South-Western Publishing
Slide 1
Health Care & Cigarettes
• Raising cigarette taxes reduces smoking
» In Canada, $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
Demand Curves
• Individual
Demand Curve
$/Q
$5
20 Q /time unit
the greatest quantity
of a good demanded
at each price the
consumers are
willing to buy,
holding other
influences constant
Slide 4
Sam
+
Diane
=
Market
• The Market
Demand Curve is
the horizontal sum of
the individual
demand curves.
4
• The Demand
Function includes
all variables that
influence the
quantity demanded
3
7
Q = f( P, Ps, Pc, Y, N W, PE)
-
+
-
?
+
?
+
P is price of the good
PS is the price of substitute goods
PC is the price of complementary goods
Y is income, N is population, W is wealth, and
PE is the expected future price
Slide 5
Downward Slope to the Demand Curve
• Reasons that price and quantity are negatively related
include:
» income effect -- as the price of a good declines, the
consumer can purchase more of all goods since his or her
real income increased.
» 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:
Slide 6
Elasticity as Sensitivity
• 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 7
Price Elasticity
• ED = % change in Q / % change in P
• Shortcut notation: ED = %Q / %P
• A percentage change from 100 to 150 is 50%
• A percentage change from 150 to 100 is -33%
• For arc 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 8
Arc Price Elasticity Example
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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 9
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 10
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 11
Two Extreme Examples
( Figure 3.3)
D
D
D’
D’
Perfectly Elastic | ED| = B and Perfectly Inelastic |ED | = 0
Slide 12
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 13
( Figure 3.4 )
Another Way to
Remember
• Linear demand
curve
• TR on other curve
• Look at arrows to
see movement in
TR
Elastic
Unit Elastic
Inelastic
Q
TR
Q
Slide 14
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 on page 90
• For a perfectly elastic demand, ED = -B.
Hence, MR = P.
• If ED = -2, then MR = .5•P, or is half of the
price.
Slide 15
1979 Deregulation of Airfares
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Prices declined after deregulation
And passengers increased
Also total revenue increased
What does this imply about the price
elasticity of air travel?
» It must be that air travel was elastic, as a
price decrease after deregulation led to
greater total revenue for the airlines.
Slide 16
Determinants of the Price Elasticity
• The availability and the closeness of substitutes
» more substitutes, more elastic
• The more durable is the product
» Durable goods are more elastic than non-durables
• The percentage of the budget
» larger proportion of the budget, more elastic
• The longer the time period permitted
» more time, generally, more elastic
» consider examples of business travel versus vacation travel
for all three above.
Slide 17
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 18
Income Elasticity Definitions
•
If EY >0, then it is a normal or income superior good
»
»
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•
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 Chevrolets
3. Expenditures on 1996 Chevy Cavaliers 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 19
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 20
Cross Price Elasticities
EX = %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 21
PROBLEM:
Find the point price elasticity, the point
income elasticity, and the point cross-price
elasticity at P=10, Y=20, and Ps=9, if the
demand function were estimated to be:
QD = 90 - 8·P + 2·Y + 2·Ps
Is the demand for this product elastic or
inelastic? Is it a luxury or a necessity?
Does this product have a close substitute or
complement? Find the point elasticities of
demand.
Slide 22
Answer
• First find the quantity at these prices and
income: QD = 90 - 8·P + 2·Y + 2·Ps = 90 -8·10 +
2·20 + 2·9 =90 -80 +40 +18 = 68
• ED = (Q/P)(P/Q) = (-8)(10/68)= -1.17 which
is elastic
• EY = (Q/Y)(Y/Q) = (2)(20/68) = +.59 which
is a normal good, but a necessity
• EX = (QA/PB)(PB /QA) = (2)(9/68) = +.26
which is a mild substitute
Slide 23
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) + EX(% 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.
Slide 24
Example: Combined Effects of Elasticities
• Toro has a price elasticity of -2 for snow-throwers
• Toro snow throwers 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 + EX • %Px = -2 • 3% + 1.5 • 2%
+.50 • 1% = -6% + 3% + .5%
» %Q = -2.5%. We expect sales to decline.
Q:
A:
Will Total Revenue for your product rise or fall?
Total revenue will rise slightly (about + .5%), as the price went up 3%
and the quantity of snow-throwers sold will fall 2.5%.
Slide 25