Download Calculating the Price Elasticity of Demand

price elasticity of demand
Wk 8
• Responsiveness of changes in quantity
demanded to a change in price of the product.
• It is measured by the formula: percentage
change in quantity demanded/percentage
change in price.
• For example, if the price of butter is reduced
by 10% and the demand increases by 20%, the
price elasticity of demand is 2.
• Goods with a price elasticity of less than 1 are said to
be inelastic.
• Goods with a price elasticity greater than 1 are said to
be elastic.
• A firm wishing to increase revenue (price x quantity)
should increase the price of its products if demand is
inelastic.
• This is because the percentage fall in quantity
demanded will be less than the percentage increase in
price.
• Conversely, a firm with an elastic demand for its
products should reduce price to increase revenue.
• The Price Elasticity of Demand (commonly
known as just price elasticity) measures the
rate of response of quantity demanded due to
a price change.
• The formula for the Price Elasticity of Demand
(PEoD) is: PEoD = (% Change in Quantity
Demanded)/(% Change in Price)
Calculating the Price Elasticity of
Demand
• You may be asked the question "Given the
following data, calculate the price elasticity of
demand when the price changes from $9.00 to
$10.00”.
• First we'll need to find the data we need.
• We know that the original price is $9 and the new
price is $10, so we have Price(OLD)=$9 and
Price(NEW)=$10.
• From the chart we see that the quantity
demanded when the price is $9 is 150 and when
the price is $10 is 110.
• Since we're going from $9 to $10, we have
QDemand(OLD)=150 and
QDemand(NEW)=110, where "QDemand" is
short for "Quantity Demanded". So we have:
• Price(OLD)=9
Price(NEW)=10
QDemand(OLD)=150
QDemand(NEW)=110
• To calculate the price elasticity, we need to know
what the percentage change in quantity demand
is and what the percentage change in price is.
• It's best to calculate these one at a time.
• Calculating the Percentage Change in Quantity
Demanded
• The formula used to calculate the percentage
change in quantity demanded is:
[QDemand(NEW) - QDemand(OLD)] /
QDemand(OLD)
• By filling in the values we wrote down, we get:
• [110 - 150] / 150 = (-40/150) = -0.2667
• We note that % Change in Quantity
Demanded = -0.2667 (We leave this in
decimal terms.
• In percentage terms this would be -26.67%).
• Now we need to calculate the percentage
change in price.
Calculating the Percentage Change in
Price
• Similar to before, the formula used to
calculate the percentage change in price is:
[Price(NEW) - Price(OLD)] / Price(OLD)
• By filling in the values we wrote down, we get:
• [10 - 9] / 9 = (1/9) = 0.1111
• We have both the percentage change in
quantity demand and the percentage change
in price, so we can calculate the price
elasticity of demand.
Final Step of Calculating the Price
Elasticity of Demand
• We go back to our formula of: PEoD = (%
Change in Quantity Demanded)/(% Change in
Price)
• We can now fill in the two percentages in this
equation using the figures we calculated
earlier.
• PEoD = (-0.2667)/(0.1111) = -2.4005
• When we analyze price elasticities we're
concerned with their absolute value, so we
ignore the negative value.
• We conclude that the price elasticity of
demand when the price increases from $9 to
$10 is 2.4005.
How Do We Interpret the Price Elasticity of
Demand?
• A good economist is not just interested in
calculating numbers.
• The number is a means to an end; in the case
of price elasticity of demand it is used to see
how sensitive the demand for a good is to a
price change.
• The higher the price elasticity, the more
sensitive consumers are to price changes.
• A very high price elasticity suggests that when
the price of a good goes up, consumers will
buy a great deal less of it and when the price
of that good goes down, consumers will buy a
great deal more.
• A very low price elasticity implies just the
opposite, that changes in price have little
influence on demand.
• Often an assignment or a test will ask you a
follow up question such as "Is the good price
elastic or inelastic between $9 and $10".
• To answer that question, you use the following
rule of thumb:
• If PEoD > 1 then Demand is Price Elastic (Demand
is sensitive to price changes)
• If PEoD = 1 then Demand is Unit Elastic
• If PEoD < 1 then Demand is Price Inelastic
(Demand is not sensitive to price changes)
• Recall that we always ignore the negative sign
when analyzing price elasticity, so PEoD is
always positive.
• In the case of our good, we calculated the
price elasticity of demand to be 2.4005, so our
good is price elastic and thus demand is very
sensitive to price changes.
Price elasticity of supply:
Data
• Price
$7
$8
$9
$10
$11
Quantity Demanded
200
180
150
110
60
Quantity Supplied
50
90
150
210
250
PEoS = (% Change in Quantity Supplied)/(%
Change in Price
The Price Elasticity of Supply measures the rate
of response of quantity demand due to a price
change.
If you've already read The Price Elasticity of
Demand and understand it, you may want to
just skim this section, as the calculations are
similar.
• PEoS = (% Change in Quantity Supplied)/(%
Change in Price.
• Calculating the Price Elasticity of Supply
• You may be asked "Given the following data,
calculate the price elasticity of supply when
the price changes from $9.00 to $10.00" Using
the chart on the bottom of the page, I'll walk
you through answering this question.
• First we need to find the data we need. We know that
the original price is $9 and the new price is $10, so we
have Price(OLD)=$9 and Price(NEW)=$10.
• From the chart we see that the quantity supplied
(make sure to look at the supply data, not the demand
data) when the price is $9 is 150 and when the price is
$10 is 110.
• Since we're going from $9 to $10, we have
QSupply(OLD)=150 and QSupply(NEW)=210, where
"QSupply" is short for "Quantity Supplied".
• Price(OLD)=9
Price(NEW)=10
QSupply(OLD)=150
QSupply(NEW)=210
• To calculate the price elasticity, we need to
know what the percentage change in quantity
supply is and what the percentage change in
price is.
• It's best to calculate these one at a time.
Calculating the Percentage Change in Quantity
Supply
• The formula used to calculate the percentage
change in quantity supplied is: [QSupply(NEW) QSupply(OLD)] / QSupply(OLD)
• By filling in the values we wrote down, we get:
• [210 - 150] / 150 = (60/150) = 0.4
• So we note that % Change in Quantity Supplied =
0.4 (This is in decimal terms.
• In percentage terms it would be 40%).
• Now we need to calculate the percentage change
in price.
Calculating the Percentage Change in
Price
• Similar to before, the formula used to calculate
the percentage change in price is: [Price(NEW) Price(OLD)] / Price(OLD)
• By filling in the values we wrote down, we get:
• [10 - 9] / 9 = (1/9) = 0.1111
• We have both the percentage change in quantity
supplied and the percentage change in price, so
we can calculate the price elasticity of supply.
• Final Step of Calculating the Price Elasticity of
Supply
• We go back to our formula of: PEoS = (% Change
in Quantity Supplied)/(% Change in Price)
• We now fill in the two percentages in this
equation using the figures we calculated.
• PEoD = (0.4)/(0.1111) = 3.6
• When we analyze price elasticities we're
concerned with the absolute value, but here that
is not an issue since we have a positive value. We
conclude that the price elasticity of supply when
the price increases from $9 to $10 is 3.6.
How Do We Interpret the Price Elasticity of Supply?
• The price elasticity of supply is used to see how
sensitive the supply of a good is to a price change.
• The higher the price elasticity, the more sensitive
producers and sellers are to price changes.
• A very high price elasticity suggests that when the
price of a good goes up, sellers will supply a great deal
less of the good and when the price of that good goes
down, sellers will supply a great deal more.
• A very low price elasticity implies just the opposite,
that changes in price have little influence on supply.
• Often you'll have the follow up question "Is
the good price elastic or inelastic between $9
and $10". To answer that, use the following
rule of thumb:
• If PEoS > 1 then Supply is Price Elastic (Supply
is sensitive to price changes)
• If PEoS = 1 then Supply is Unit Elastic
• If PEoS < 1 then Supply is Price Inelastic
(Supply is not sensitive to price changes)
• Recall that we always ignore the negative sign
when analyzing price elasticity, so PEoS is
always positive.
• In our case, we calculated the price elasticity
of supply to be 3.6, so our good is price elastic
and thus supply is very sensitive to price
changes.
Income Elasticity of Demand
• The Income Elasticity of Demand measures
the rate of response of quantity demand due
to a raise (or lowering) in a consumers
income. The formula for the Income Elasticity
of Demand (IEoD) is given by: IEoD = (%
Change in Quantity Demanded)/(% Change in
Income)
• Calculating the Income Elasticity of Demand
•
•
•
•
•
•
•
Data
Income
$20,000
$30,000
$40,000
$50,000
$60,000
Quantity Demanded
60
110
150
180
200
• On an assignment or a test, you might be asked
"Given the following data, calculate the income
elasticity of demand when a consumer's income
changes from $40,000 to $50,000".
• The first thing we'll do is find the data we need.
We know that the original income is $40,000 and
the new price is $50,000 so we have
Income(OLD)=$40,000
and
Income(NEW)=$50,000.
• From the chart we see that the quantity demanded
when income is $40,000 is 150 and when the price is
$50,000 is 180.
• Since we're going from $40,000 to $50,000 we have
QDemand(OLD)=150 and QDemand(NEW)=180, where
"QDemand" is short for "Quantity Demanded".
• So you should have these four figures written down:
• Income(OLD)=40,000
Income(NEW)=50,000
QDemand(OLD)=150
QDemand(NEW)=180
• To calculate the price elasticity, we need to know what
the percentage change in quantity demand is and what
the percentage change in price is. It's best to calculate
these one at a time.
• Calculating the Percentage Change in Quantity
Demanded
• The formula used to calculate the percentage change in
quantity
demanded
is:
[QDemand(NEW)
QDemand(OLD)] / QDemand(OLD)
• By filling in the values we wrote down, we get:
• [180 - 150] / 150 = (30/150) = 0.2
• So we note that % Change in Quantity Demanded
= 0.2 (We leave this in decimal terms. In percentage
terms this would be 20%) and we save this figure
for later. Now we need to calculate the percentage
change in price.
• Calculating the Percentage Change in Income
• Similar to before, the formula used to calculate the
percentage change in income is: [Income(NEW) Income(OLD)] / Income(OLD)
• By filling in the values we wrote down, we get:
• [50,000 - 40,000] / 40,000 = (10,000/40,000) =
0.25
• We have both the percentage change in quantity
demand and the percentage change in income, so
we can calculate the income elasticity of demand.
• Final Step of Calculating the Income Elasticity of
Demand
• We go back to our formula of: IEoD = (% Change
in Quantity Demanded)/(% Change in Income)
• We can now fill in the two percentages in this
equation using the figures we calculated earlier.
• IEoD = (0.20)/(0.25) = 0.8
• Unlike price elasticities, we do care about
negative values, so do not drop the negative
sign if you get one. Here we have a positive
price elasticity, and we conclude that the
income elasticity of demand when income
increases from $40,000 to $50,000 is 0.8.
How Do We Interpret the Income Elasticity of
Demand?
• Income elasticity of demand is used to see how sensitive
the demand for a good is to an income change.
• The higher the income elasticity, the more sensitive
demand for a good is to income changes.
• A very high income elasticity suggests that when a
consumer's income goes up, consumers will buy a great
deal more of that good.
• A very low price elasticity implies just the opposite, that
changes in a consumer's income has little influence on
demand.
• Often an assignment or a test will ask you the follow up
question "Is the good a luxury good, a normal good, or an
inferior good between the income range of $40,000 and
$50,000?" To answer that use the following rule of thumb:
• If IEoD > 1 then the good is a Luxury Good and
Income Elastic
• If IEoD < 1 and IEOD > 0 then the good is a
Normal Good and Income Inelastic
• If IEoD < 0 then the good is an Inferior Good and
Negative Income Inelastic
• In our case, we calculated the income elasticity of
demand to be 0.8 so our good is income inelastic
and a normal good and thus demand is not very
sensitive to income changes.
Cross-Price Elasticity of Demand
• The Cross-Price Elasticity of Demand measures
the rate of response of quantity demanded of
one good, due to a price change of another
good.
• If two goods are substitutes, we should expect
to see consumers purchase more of one good
when the price of its substitute increases.
• Similarly if the two goods are complements,
we should see a price rise in one good cause
the demand for both goods to fall.
OR
• The cross elasticity of demand and cross price
elasticity of demand measures the responsiveness of
the demand of a good to a change in the price of
another good.
• It is measured as the percentage change in demand for
the first good that occurs in response to a percentage
change in price of the second good. For example, if, in
response to a 10% increase in the price of fuel, the
demand of new cars that are fuel inefficient decreased
by 20%, the cross elasticity of demand would be
−20%/10% = −2.
The formula used to calculate the coefficient cross elasticity of demand is
• CPEoD = (% Change in Quantity Demand for
Good X)/(% Change in Price for Good Y)
• Calculating the Cross-Price Elasticity of Demand
• You're given the question: "With the following
data, calculate the cross-price elasticity of
demand for good X when the price of good Y
changes from $9.00 to $10.00." Using the chart
on the bottom of the page, we'll answer this
question.
• We know that the original price of Y is $9 and the
new price of Y is $10, so we have Price(OLD)=$9
and Price(NEW)=$10.
• From the chart we see that the quantity
demanded of X when the price of Y is $9 is 150
and when the price is $10 is 190.
• Since we're going from $9 to $10, we have
QDemand(OLD)=150 and QDemand(NEW)=190.
You should have these four figures written down:
• Price(OLD)=9
Price(NEW)=10
QDemand(OLD)=150
QDemand(NEW)=190
• To calculate the cross-price elasticity, we need to calculate
the percentage change in quantity demanded and the
percentage change in price. We'll calculate these one at a
time.
• Calculating the Percentage Change in Quantity Demanded
of Good X
• The formula used to calculate the percentage change in
quantity demanded is: [QDemand(NEW) - QDemand(OLD)]
/ QDemand(OLD)
• [190 - 150] / 150 = (40/150) = 0.2667
• So we note that % Change in Quantity Demanded =
0.2667 (This in decimal terms. In percentage terms this
would be 26.67%).
• Calculating the Percentage Change in Price of Good Y
• The formula used to calculate the percentage change in
price is: [Price(NEW) - Price(OLD)] / Price(OLD)
• We fill in the values and get:
• [10 - 9] / 9 = (1/9) = 0.1111
• We have our percentage changes, so we can complete the
final step of calculating the cross-price elasticity of demand.
• Final Step of Calculating the Cross-Price Elasticity of
Demand
• We go back to our formula of: CPEoD = (% Change in
Quantity Demanded of Good X)/(% Change in Price of
Good Y)
• We can now get this value by using the figures we
calculated earlier.
• CPEoD = (0.2667)/(0.1111) = 2.4005
• We conclude that the cross-price elasticity of demand for X
when the price of Y increases from $9 to $10 is 2.4005.
How Do We Interpret the Cross-Price Elasticity of Demand?
• The cross-price elasticity of demand is used to see how
sensitive the demand for a good is to a price change of
another good.
• A high positive cross-price elasticity tells us that if the
price of one good goes up, the demand for the other
good goes up as well.
• A negative tells us just the opposite, that an increase
in the price of one good causes a drop in the demand
for the other good.
• A small value (either negative or positive) tells us that
there is little relation between the two goods.
• Often an assignment or a test will ask you a follow up
question such as "Are the two goods complements or
substitutes?".
• To answer that question, you use the following rule of
thumb:
• If CPEoD > 0 then the two goods are substitutes
• If CPEoD =0 then the two goods are independent
(no relationship between the two goods
• If CPEoD < 0 then the two goods are
complements
• In the case of our good, we calculated the crossprice elasticity of demand to be 2.4005, so our
two goods are substitutes when the price of good
Y is between $9 and $10.