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week_5_elasticity_bus180.pptx
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Elasticity: A Measure
of Responsiveness
1. The Price Elasticity of Demand
1. Arc (or Midpoint or Interval) and Point price
elasticity
2. Elasticity and Total Revenue relationships
3. Why some products are inelastic and others
are elastic
2. Income Elasticities
3. Cross Elasticities of Demand
4. Combined Effects of Elasticities
Price Elasticity of Demand
1.The price elasticity of
demand measures the
responsiveness of
consumers to price
changes.
Price Elasticity of Demand
2. Price elasticity is
calculated by dividing the
percentage change in
quantity demanded by
the percentage change in
price.
Price Elasticity of Demand
3. Values greater than one indicate
elastic demand; consumers change
quantities demanded more than
proportionately when prices change.
Values less than one indicate inelastic
demand; consumers change quantities
demanded less than proportionately
when prices change.
Price Elasticity of Demand
4. Elasticity will be greater when
there are many substitute
products, when the good is
important to the consumer’s
budget, and when the time
period considered is long.
Price Elasticity of Demand
5. Price elasticity ranges from
perfectly inelastic to unit elasticity
to perfectly elastic. Along a linear
demand curve, elasticity is greater
than one above the midpoint of the
demand curve and less than one
below the midpoint.
Elasticity: A Measure
of Responsiveness
1.Elasticity information tells firms whether price
changes will increase or decrease total revenue;
2.If demand is elastic, price increases reduce the
firm’s total revenue.
3.If demand is inelastic, price increases increase
the firm’s total revenue.
4.The price elasticity of supply is calculated
similarly; supply is expected to be more elastic
as the time period being considered increases.
The Price Elasticity of Demand
Computing Percentage Changes and Elasticities
1. The price elasticity of demand is a measure of
the responsiveness of the quantity demanded
to changes in the price; equal to the absolute
value of the percentage change in quantity
demanded divided by the percentage change in
price.
2. Formula: Ed = |(% change in quantity
demanded)/ (% change in price)|
The Price Elasticity of Demand
Computing Percentage Changes and Elasticities
1. Remember that the percent changed can be
computed in two ways.
1. The simplest approach to compute a percentage
change is to use the initial value of the variable in the
denominator.
2. The midpoint or arc method is more precise. Here we
compute the percentage change by dividing the
change in the variable by the average value of the
variable, or the midpoint between the old value and
the new one.
Computing Percentage Changes and Elasticities
• 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
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.
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
Price Elasticity
(both point price and arc elasticity)
• If ED = -1, unit elastic
• If ED > -1, inelastic, example: – 0.43
• If ED < -1, elastic, example: -4.0
Straight line
demand curve
example
price
elastic region
unit elastic
inelastic region
quantity
Price Elasticity and the Demand Curve
(Note:Elasticity is not the same as slope.)
1.
2.
3.
4.
5.
If price elasticity of demand is greater than 1,
demand is elastic.
If price elasticity of demand is less than 1,
demand is inelastic.
If price elasticity of demand is equal to 1,
demand is unit elastic.
If price elasticity of demand is zero, it is
perfectly inelastic. The quantity demanded
does not change no matter what happens to
the price, so the demand curve is vertical.
If price elasticity of demand is infinite, it is
perfectly elastic. The quantity demanded falls
to zero at any price above the vertical
intercept, so the demand curve is horizontal.
FIGURE 3.4 Perfectly Elastic and
Inelastic Demand Curves
Elasticity and the Availability of
Substitutes
1. The price elasticity of demand for a particular product
depends on the availability of substitutes.
2. The demand for a product will be relatively elastic if:
1. There are good substitutes for the product.
2. Consumers have time to respond to the price change:
3. It takes time to find alternatives;
4. thus, demand will be more elastic the greater the time
period considered.
Other Determinants of the Price
Elasticity of Demand
1. If the product represents a large fraction of the
consumer’s budget, the demand will be elastic.
2. If a good is unimportant to the budget,
demand is relatively inelastic.
3. For large budget-share items, consumers are
more responsive because the amount spent on
the good is high relative to consumer income.
4. If a good is a luxury good, it tends to have an
elastic demand.
Price Elasticity and Total Revenue
Total Revenue is the money a firm generates from
selling its product = Price per unit x Quantity
sold.
1. Elastic Versus Inelastic Demand
❖ When a firm increases its price, there are two
effects:
❖ A gain from the increased price on each product or
service sold, and
❖ a reduction in the quantity sold.
❖ Which effect is larger?
Price Elasticity and Total Revenue
2. If demand is elastic, there is a negative
relationship between price and total revenue.
Consumers will purchase many fewer units, and
the price increases will not compensate for lost
revenues from the reduction in units. Thus,
total revenue will fall because the percentage
change in quantity is greater than the
percentage change in price.
Price Elasticity and Total Revenue
3. If demand is inelastic, there is a positive
relationship between price and total revenue.
Consumers will purchase a few units less, but
the price rise will more than compensate for
lost revenues from the reduction in units. Thus,
total revenue will rise because the percentage
change in quantity is less than the percentage
change in price.
Price Elasticity and Total Revenue
4. If demand is unit elastic, consumers will
purchase fewer units, and the price rise will
exactly compensate for lost revenues from the
reduction in units. Thus, total revenue will
remain constant, because the percentage
change in quantity is equal to the percentage
change in price.
Price Elasticity and Total Revenue
5. For a price reduction,
total revenue rises when
demand is elastic and
falls when demand is
inelastic.
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?
( Figure 3.5)
Another Way to
Remember
•
•
•
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
Elastic
Unit Elastic
A
Inelastic
B
Q
TR
Q
FIGURE 3.5 Price Elasticity over
Demand Function
FIGURE 3.5 Price Elasticity over
Demand Function
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 )
• For a perfectly elastic demand, ED = infinity. Hence, MR = P.
• If ED = -2, then MR = .5•P, or is half of the
price.
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
Other Elasticities of Demand
1. An effective way to understand the other
elasticities concepts is to first review the
concepts of inferior and normal goods as
well as substitutes and complements.
Other Elasticities of Demand
2. Income elasticity of demand: A measure of
the responsiveness of the quantity demanded
to changes in consumer income.
1. Equal to the (% change in quantity demanded)/
(% change in income).
2. Goods with positive income elasticities are
called normal; as income rises, consumers will
purchase more of these goods.
3. Goods with negative income elasticity are called
inferior; as income rises, consumers will
purchase less of such goods.
Other Elasticities of Demand
3. Cross-price elasticity of demand: A measure of
the responsiveness of the quantity demanded to
changes in the price of a related good.
1. Equal to the (% change in quantity of X demanded)/
(% change in price of Y).
2. Goods with positive cross-price elasticities are
called substitutes; as the price of good Y rises,
consumers will purchase more of good X.
3. Goods with negative cross-price elasticities are
called complements; as the price of good Y rises,
consumers will purchase less of good X.
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%
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 Ford Focus
2. Expenditures on 2005 Ford Focus with 150,000 miles
Which of the above is likely to have a positive income elasticity?
Which of the above might have a negative income elasticity?
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.
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%.
Cross Price Elasticities
Ecross = %QA / %PB = (QA/PB)(PB /QA)
• Substitutes have positive cross price elasticities:
Coffee and Tea
• Complements have negative cross price
elasticities: Bagels and Cream Cheese
Blockbuster
• When the cross price elasticity is zero or insignificant,
the products are not related
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)
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?
Example: Combined Effects of Elasticities
A:Total revenue will rise slightly (about + .5%), as the
price rises 3% and the quantity of snow- blowers sold
falls 2.5%.
The Price Elasticity of Supply
1. The price elasticity of supply measures the
responsiveness of quantity supplied to changes in price.
1.
2.
Equal to the (% change in quantity supplied)/ (% change in
price).
Numerical example :When the price of milk increases from
$1/gallon to $1.20/gallon, the quantity supplied increases
from 100 million gallons to 102 million gallons (using the
initial-value method).
1.
2.
3.
The percentage change in price is the absolute change ($0.20)
divided by the initial quantity ($1.00), or 20%.
In panel (A), the percentage change in quantity is the absolute
change (2 million) divided by the initial quantity (100 million), 2%,
resulting in an elasticity of 2/20 = 0.10 (inelastic).
In panel (B), the percentage change in quantity is 50 million divided
by 100 million, 50%, resulting in an elasticity of 50/20 = 2.5 (elastic).
What Determines the Price Elasticity
of Supply
1. Price elasticity is related to the slope of the supply
curve.
2. Factors affecting the slope of the supply curve affect
the elasticity.
1. If marginal cost increases rapidly with total output (ex.,
crude oil prices increase with gasoline production), the
supply curve is relatively steep and supply is relatively
inelastic.
2. If marginal cost increases slowly with total output (ex.,
the price of wood isn't affected much by increase in pencil
production), the supply curve is relatively flat and supply is
relatively elastic.
The Role of Time: Short-Run Versus
Long-Run Supply Elasticity
1. Short-run supply is less elastic than long-run
supply because in the short run production
facilities and the number of firms are fixed.
2. In the long run, a price change will alter the
number of firms and the quantity will change
more.
Extreme Cases: Perfectly Inelastic
Supply and Perfectly Elastic Supply
1. If supply is vertical, it is perfectly
inelastic, or has an elasticity of zero.
The quantity supplied does not
change no matter what happens to
the price.
2. If supply is horizontal, it is perfectly
elastic, or has an elasticity of
infinity. The quantity supplied falls
to zero at any price above the
vertical intercept.
Using Elasticities to Predict Changes
in Equilibrium Price
1.
The Price Effects of a Change in Demand (See Figure 4.5)
1.
2.
3.
a. Percentage change in equilibrium price = (Percentage
change in demand) / (Es + Ed)
The Price Effects of a Change in Supply
1.
4.
5.
The Price-Change Formula: A formula that shows the
percentage change in equilibrium price resulting from a
change in demand or supply, given values for the price
elasticity of supply (Es) and the price elasticity of demand
(Ed). In terms of demand – the formula is as follows:
In terms of supply the formula is as follows:
a. Percentage change in equilibrium price = 2 (Percentage
change in supply) / (Es + Ed)
...
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