Download Handout5 Elasticities

Elasticity of Demand
Economics 100: 12
Handout 5 Elasticities
Notes for Tuesday October 26 Lecture
Dr. J.A.-Tuffour
(DATE FOR QUIZ 2: THURSDAY NOVEMBER 4)
1. Own-price Elasticity: Ed
A. Elasticity is a measure of responsiveness. The most commonly used elasticity concept is price elasticity
of demand.
1. The price elasticity of demand is the percentage change in quantity demanded divided by the
percentage change in price. Put another way:
Numerical calculation:
Ed = Percentage change in quantity demanded
Percentage change in own - price
Ed = %ΔQd
%ΔP
2. Price elasticity of demand is treated as if it were positive. Price and quantity demanded are inversely
related — when prices rises, quantity demanded falls, and vice versa. Thus, by the Law of Demand,
price elasticity of demand is always negative. So economists have developed a convention and take
the absolute value, and talk about elasticity of demand as a positive number.
3. Demand can be classified as elastic or inelastic with respect to price.
a. Formally, demand is elastic if the percentage change in quantity is greater than the percentage
change in price or D>1. Common sense tells us that an elastic demand means that quantity
changes by a greater percentage than the percentage change in price. The same holds true for
supply.
b. Alternatively, demand is inelastic if the percentage change in quantity is less than the percentage
change in price or D <1. Common sense tells us that an inelastic demand means that quantity
doesn’t change much with a change in price. The same holds true for supply.
4. As elasticity increases, responsiveness of quantity to price also increases.
5. Elasticity is independent of units. Percentages, and not absolute numbers, allow us to have a measure
of responsiveness that is independent of units. Having a measure of responsiveness that is
independent of units makes comparisons of responsiveness of different goods easier.
II. Calculating Elasticities
A. To determine elasticity we need to divide the percentage change in quantity by the percentage change in
price.
Example 1: Suppose a 1% rise in the price of lean ground beef causes Mr.Ofram to decrease the demand for
lean ground beef by 2.5%. Find Mr. Ofram's price elasticity of demand for lean ground beef
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Elasticity of Demand
Ed = %ΔQd
%ΔP
=
__
=
?
Meaning that
A 1% rise in price
=> a
? (increase/decrease?- select one) in quantity demanded
A 1% fall in price
=> a
? (increase/decrease ?) in quantity demanded
A 10% rise in price
=> a
? (increase/decrease ?) in quantity demanded.
Example 2: In this example, you are given the actual prices and the corresponding quantities
demanded. You need to do a bit more work than you did in Example 1.
Price
P1 =5
B
P0 = 4
A
D0
20
40
Quantity demanded per week
a) Calculate the own-price elasticity of demand when the price rises from $4 to $5.
Information:
P0 =4, P1 = 5
P1- Po = ΔP =
Pave = (P1+ Po) /2
Qo = 40, Q1 = 20
Q1-Qo = ΔQ =
Qave = (Q1 + Qo )/2
Ed 
0
Q
0 P
0
d
0
Q

P
Qave
Pave
This means that
A 1% fall in price
=> a
? (increase/decrease ?) in quantity demanded
A 10% fall in price
=> a
? (increase/decrease ?) in quantity demanded
A 100% rise in price => a
? (increase/decrease ?) in quantity demanded.
b) Calculate the own-price elasticity of demand when the price falls from $5 to $4.
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Elasticity of Demand
Price
P0 = 5
A
P1 = 4
B
D0
20
Information:
PO =5, P1 = 4
Qo = 20, Q1 = 40
40
Quantity demanded per week
P1- Po = ΔP =
Q1-Qo = ΔQ =
Pave =
Qave =
Q
d
Qave

Q
Ed  0

0 P
P
0
Pave
0
This means that
A 1% fall in price
=> a
? (increase/decrease ?) in quantity demanded
A 10% fall in price
=> a
? (increase/decrease ?) in quantity demanded
A 100% rise in price =:> a
? (increase/decrease ?) in quantity demanded.
c) Calculate the own-price elasticity of demand when the price rises from $1 to $2. The objective here is
to determine whether the own –price elasticity of demand varies along the demand curve. Does demand
become more or less elastic at lower prices?
Information
Po= 1, P1=2
Qo= 16, Q1= 11
P1- Po = ΔP =
Q1,-Qo = ΔQ =
Pave
Qave
Q
Qave
Q d
Ed 

0 P
P
0
Pave
0
0
This means that
A 1% fall in price
=> a
? (increase/decrease ?) in quantity demanded
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Elasticity of Demand
A 10% fall in price
=> a
? (increase/decrease ?) in quantity demanded
A 1% rise in price
=> a
? (increase/decrease ?) in quantity demanded.
Elasticity and Demand Curves
Two important points to consider is (a) elasticity is related (but is not the same as) slope, and (b) elasticity
changes along straight-line demand curves.
A. Elasticity is not the same as slope. The relationship between elasticity and slope means that the steeper
the curve begins at a given point, the less elastic is supply or demand. But there are limiting examples of
this.
1. When the curves are flat, we call the curves perfectly elastic. Perfectly elastic curves are flat curves
in which quantity changes enormously in response to a proportional change in price (D = ∞).
2. When the curves are vertical, we call the curves perfectly inelastic. Perfectly inelastic curves are
vertical curves in which quantity does not change at all in response to an enormous proportional
change in price (D = 0).
B. Elasticity changes along straight-line curves. On straight-line demand curves, slope does not change;
elasticity does. Figure 6-3 summarizes these relationships.
C. To sum up, the five price elasticity of demand terms are: elastic (D >1); inelastic (D <1); unit elastic (D
= 1); perfectly elastic (D = ∞); and perfectly inelastic (D = 0)
Substitution and Price Elasticity of Demand
As a general rule, the more substitutes a good has, the more elastic is its supply and demand. Factors that
affect a good’s substitutability of demand differ from factors that affect a good’s substitutability of supply
A. Factors affecting substitution and demand.
1. The larger the time interval considered, or the longer the run, the more elastic is the good’s demand
curve.
a. There are more substitutes in the long run than in the short run.
b. The long run provides more options for change.
2. The less a good is a necessity, the more elastic its demand curve. Necessities tend to have fewer
substitutes than do luxuries.
3. As the definition of a good becomes more specific, demand becomes more elastic.
a. If the good you are talking about is broadly defined (say, transportation) there are not many
substitutes and demand will be inelastic.
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Elasticity of Demand
b. If the definition of a good is narrowed, say to transportation by bus, there are more substitutes.
4. Demand for goods that represent a large proportion of one’s budget are more elastic than demand for
goods that represent a small proportion of one’s budget.
a. Goods that cost very little relative to your total expenditures are not worth spending a lot of time
figuring out if there is a good substitute.
b. It is worth spending a lot of time looking for substitutes for goods that take a large portion of
one’s income.
Price Elasticity of Demand and Total Revenue
A. Knowing price elasticity of demand tells suppliers how their total revenue (total quantity sold multiplied
by price of good) will change if their price changes (Chapter Objective 4). See Figures 6-5 and 6-6.
1. If D is elastic (D > 1), a rise in price lowers total revenue. (Price and total revenue move in opposite
directions.) This occurs at prices above the point where demand is unit elastic.
2. If D is unit elastic (D = 1), a rise in price leaves total revenue unchanged.
3. If D is inelastic (D < 1), a rise in price increases total revenue. (Price and total revenue move in the
same direction.) This occurs at prices below the point where demand is unit elastic.
B. Elasticity of individual and market demand.
1. Market demand elasticity is influenced both by how many people drop out totally and by how much
an existing consumer marginally changes his or her quantity demanded.
2. If a firm can somehow separate the people with less elastic demand from those with more elastic
demand, it can charge more to the individuals with inelastic demand and less to individuals with
elastic demands. Economists call this price discrimination.
3. Examples of price discrimination include:
a. Airlines’ Saturday stay-over specials.
b. The phenomenon of haggeling over the price of new cars.
c. The almost-continual-sale phenomenon.
Price Teasers
Rank the following items in ascending order of their own-price elasticity of demand.
Hair cut, beer, wine, toothpick, newspaper, football game, airline travel and salt.
Football and Season Ticket Holders
The University of Erewhon has just lowered the price of its season football tickets from $350.00 to $300.00. s a
result, there was an increase in the number of season ticket purchased from 43,000 to 47,000. Calculate the
price elasticity of demand for season tickets. (ANS: =0.58).
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Elasticity of Demand
Do you believe in Ice Cream Marketing Experts?
The marketing people at Ben and Jerry’s Ice Cream Company in the Gonish believe that if they lower the price
of Cheery Garcia flavour ice cream by 25 percent, the quantity sold will increase by 5 percent.
- Calculate the price elasticity of demand for Cheery Garcia flavour ice cream.
- If the marketing people are correct in their belief, then what happens to total revenue from Cheery Garcia
ice cream if they lower the price?
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Elasticity of Demand
II.. Other Elasticity Concepts
Cross-Price Elasticities: Exz
Example 3:
Exz = Percentage change in quantity demanded of good X
Percentage change in the price of good Z
Ed 
0
Q d
0 P
0
0
Q

P
Qave
Pave
1. Substitutes are goods that can be used in place of another good. When the price of a good goes up,
the demand for the substitute good also goes up.
2. Complements are goods that are used in conjunction with other goods. A fall in the price of a good
will increase the demand for its complement. The cross-price elasticity of complements is negative.
(a) Suppose the price of good z increases from $1.50 to $1.80 and the quantity demanded of good
X falls from 60 to 35 units per period. (a) Calculate the cross-price elasticity of demand for good
X with respect to good Z. (b) How will you describe the relationship between the two goods? (c)
Illustrate your answer your graphs.
Information
Po,z = 1.5, P1,z = 1.8
Q0,x = 60, Q1,x = 35
P1- Po = ΔP =
Q1-Q0 = ΔQ =
Pave =
Qave =
Q
Qave
Q d
Ed 

0 P
P
0
Pave
0
This means that
A 1% fall in price of Z => a
A 10% fall in price of Z => a
A 5% rise in price of Z =:> a
0
? (increase/decrease ?) in quantity demanded of X
? (increase/decrease ?) in quantity demanded of X
? (increase/decrease ?) in quantity demanded of X
(b) Goods X and Z are (substitutes/ complements/ unrelated ?)
Px
Qx
Pz
Qz
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Elasticity of Demand
(b) Suppose the price of good z increases from $1.50 to $1.80 and the quantity demanded of good X rises from
35 to 60 units per period. (a) Calculate the cross-price elasticity of demand for good X with respect to good Z.
(b) How will you describe the relationship between the two goods? (c) Illustrate your answer your graphs.
The Demand for Alcoholic Beverages in Nova Scotia:
Elasticities & Public Policy-Making. In their study of the demand for Alcoholic beverages in Nova Scotia
(1972-1991) AmoakoTuffour and LeBlanc (Atlantic Canada Economic Papers, 1996) found the following
own-and cross-price elasticities of demand for beer, wine and spirits:
Own-Price Elasticities
Cross-Price Elasticities
Beer
Wine
Spirits
BW
BS
SW
Before
1984
-0.8
-1.5
-0.8
0.2
-0.3
-0.2
After
1984
-0.5
-0.9
-0.7
-0.4
-1.0
2.4
May 1984 marked the beginning of the province-wide Drinking and Driving Campaign, with the slogan "If You
Drink, Don't Drive".
(a) What can you say about Nova Scotians demand for alcoholic beverages since 1972?
(b) On the basis of the cross-price elasticities, what is the relationship between beer and wine? between beer
and spirits? and between spirits and wine before and after 1984? Are you surprised by any of these results?
Why or why not?
(c) On the basis of the results, can taxes stop people from drinking? Explain your response.
III. Income elasticity of demand
A. Income elasticity of demand are (1) income elasticity of demand and (2) cross-price elasticity of demand.
1. Income elasticity of demand () is defined as the percentage change in demand divided by the
percentage change in income It tells us the responsiveness of demand to changes in income. Put
another way:
Income Elasticity of demand 
Percentage change in quantity demanded
Percentage change in income
2. An increase in income generally increases one’s consumption of almost all goods, although the
increase may be greater for some goods than for others.
a. Normal goods — those whose consumption increases with an increase in income — have income
elasticities greater than zero. Normal goods are divided into luxuries and necessities. Luxuries
are goods that have an income elasticity greater than one. Their percentage increase is greater
than the percentage increase in income. Shoes are a necessity — a good that has an income
elasticity of less than 1. The consumption of a necessity rises by a smaller proportion than the rise
in income.
b. Inferior goods — those whose consumption decreases as income increases — have income
elasticities of less than zero. Powdered milk is an example of an inferior good.
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Elasticity of Demand
IV. Price Elasticity of Supply.
A. The price elasticity of supply is the percentage change in quantity supplied divided by the percentage
change in price. Put another way:
S 
Percentage change in quantity supplied
Percentage change in price
B. Factors affecting substitution and supply.
1. The longer the time period considered, the more elastic the supply. The reasoning is the same as for
demand — in the long run there are more options for change so it is easier (less costly) for suppliers
to change into the production of another good.
2. Economists distinguish three time periods relevant to supply:
a. In the instantaneous period, quantity supplied is fixed so the elasticity of supply is perfectly
inelastic. This supply is sometimes called the momentary supply
b. In the short run, some substitution is possible, so the short-run supply curve is somewhat elastic.
c. In the long run, significant substitution is possible; the supply curve becomes very elastic.
3. One additional factor to consider: many supplied goods are produced, so we must take into account
how easy it is to substitute for existing goods by producing more of those same goods.
C. How substitution factors affect specific decisions.
1. An example of a 10-cent gas tax increase in Windsor, Ontario and the nation:
a. In the short run the demand for gasoline would be less elastic than in the long run.
b. In the long run, motorists would switch to fuel-efficient cars.
c. Although gasoline is considered a necessity, it is only a small part of what it costs to drive, thus
demand would probably be inelastic.
d. For the entire country, demand would be inelastic, but for Windsor, it would be very elastic since
there are many alternative choices of transportation. For example, some may switch to an
alternative form of transportation, while others would go to neighbouring areas to buy gasoline.
2. Smaller geographic areas have more elastic demands which limits how highly local governments can
tax goods relative to their neighbouring localities.
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