Download Elasticity - Toronto District School Board

Elasticity
IB-SL Economics
Mr. Messere - CIA 4U7
Victoria Park S.S.
Outline
I. Introduction
II. Elasticity of Demand
A. Definition
B. Degrees of Elasticity of Demand
C. Relationship between Ed and Total Revenue
D. Determinants of Elasticity of Demand
III. Other Elasticities
A. Income Elasticity of Demand
B. Cross Price Elasticity of Demand
C. Elasticity of Supply
D. Determinants of Elasticity of Supply
Coffee Question
Consider the following:
• An economist was called in to consult for a coffee
shop that was losing money.
• One manager thought they needed to raise prices
in order to make more money on each coffee sold.
• The other manager thought that lowering prices
would make more money because a lot more
coffee could be sold.
Who was right?
Coffee Question
• The answer is - it depends. On what?
• If you lower the price - will the new sales
offset the loss in revenue on each coffee?
• If you raise your price - will the loss in sales
be offset by the increase in price of coffee?
• In other words, how much will the quantity
demanded change when price changes?
Demand
• We know, from the Law of Demand, that
price and quantity demanded are inversely
related.
• Now, we are going to get more specific in
defining that relationship
• We want to know just how much will
quantity demanded change when price
changes? That is what elasticity of demand
measures.
Elasticity of Demand
• Elasticity of Demand (Ed) measures the
responsiveness of the quantity demanded
(Qd) of a good to a change in its price (P).
Ed = % in Qd
(Note that  means “change”)
% in P
Ed = [(Q2-Q1)/Q1] ÷ [(P2-P1)/P1]
• Also note that the law of demand implies Ed is negative. We
will ignore the negative sign when discussing price elasticity
of demand.
Calculating Elasticity of Demand
• There are two methods for calculating
elasticity - point and arc methods.
• We will be examining the point method.
Point Elasticity
P
Consider the following Demand Curve:
6
5
2
1
0
D
2
3
6
7
Qd
Point Elasticity
P
A
6
5
B
…and let’s say we want to find
the Elasticity of Demand as we
move from point A to Point B...
2
1
0
D
2
3
6
7
Qd
Point Elasticity
• We know
• Ed = % in Qd or
% in P
Ed = [(Q2-Q1)/Q1] ÷ [(P2-P1)/P1]
• To calculate Ed from point A to B:
= [(3-2)/2]  [(5-6)/6]
= 1/2 ÷ -1/6
= 3 (since negative sign ignored)
• Calculate Ed from point C to D on the same curve
Point Elasticity
P
6
5
C
2
1
0
D
2
3
7
8
Qd
Point Elasticity
• Recall:
• Ed = % in Qd or Ed = [(Q2-Q1)/Q1] ÷ [(P2-P1)/P1]
% in P
• To calculate Ed from point C to D:
= [(8-7)/7]  [(1-2)/2]
= 1/7 ÷ -1/2
= 2/7 or 0.29 (since negative sign ignored)
Point Elasticity
• Note that Ed is different at different places along
the curve.
– Specifically, it gets smaller as you move down
the curve
• Note that elasticity and slope are NOT the same
thing.
• One last calculation - let’s find the elasticity of
demand going from point D to point C on the
same curve
Point Elasticity
• Recall:
• Ed = % in Qd or
% in P
Ed = [(Q2-Q1)/Q1] ÷ [(P2-P1)/P1]
• To calculate Ed from point D to C:
= [(7-8)/8]  [(2-1)/1]
= -1/8 ÷ 1
= 1/8 or 0.13 (since negative sign ignored)
How Do We Interpret Elasticity?
• The number we get from computing the
elasticity is a percentage - there are no units.
• We can read it as the percentage change in
quantity for a 1% change in price
How Do We Interpret Elasticity?
• Thus, if Ed = 2, that means on that part of
the demand curve, a 1% change in price will
cause a 2% change in quantity demanded.
• Or if we extrapolate, a 10% change in price
will cause a 20% change in quantity
demanded, and so on.
Degrees of Demand Elasticity
• Perfectly Inelastic Demand
• Ed = % in Qd
% in P
• Ed =
0
% in P
• Ed = 0
• No matter how much price changes,
consumers purchase the same amount of the
good.
> Example: Insulin
Elasticity
P
0
Perfectl
y
Inelastic
Demand
ED = 0
Qd
Degrees of Ed
• Inelastic Demand
• Ed = % in Qd
% in P
• Ed < 1 (in absolute value)
• % in Qd < % in P
• For every 1% change in P, Qd changes by
less than 1%
Elasticity
P
0
Relatively
Inelastic
Qd
Degrees of Ed
• Unitary Elastic Demand
• Ed = % in Qd
% in P
• Ed = 1 (in absolute value)
• % in Qd = % in P
• For every 1% change in P, Qd changes by
1% (in opposite direction)
Unitary Elastic Demand
P
Unitary
Elastic
0
QD
Degrees of Ed
• Elastic Demand
• Ed = % in Qd
% in P
• Ed > 1 (in absolute value)
• % in Qd > % in P
• For every 1% change in P, Qd changes by
more than 1% (in opposite direction)
Elasticity
P
Relatively
Elastic
0
Qd
Degrees of Ed
• Perfectly Elastic Demand
• Ed = % in Qd
% in P
• Ed = % in Qd
0
• Ed = infinity
• The price of the good never changes, no
matter how much consumers purchase of
the good.
Elasticity
P
Perfectl
y
Elastic
Demand
ED = œ
0
Qd
Generalizing about Elasticity
• Notice that the vertical (perfectly inelastic)
demand curve has an elasticity of zero and the flat
(perfectly elastic) demand curve has an elasticity
of infinity.
• As the demand curve goes from vertical to
horizontal the elasticity is going from 0 to infinity
• In other words, the flatter the demand curve, the
greater the elasticity or if the curve becomes more
vertical, then demand becomes more inelastic
The Coffee Problem
• Back to the Coffeehouse question - should
they raise or lower price?
• We said that depended on how much sales
will change when they change price
• In other words, it depends on the elasticity
Total Revenue & Elasticity
• Total Revenue = Price (p) x Quantity (q)
• The coffeehouse is interested in how TR
(total revenue) changes as p and q change
Total Revenue Calculation - Example
• Price $1
Qd = 100
• TR = $100
• Price $3
Qd = 90
• TR = $270
• Price $4
Qd = 50
• TR = $200
• Price $5
Qd = 30
• TR = $150
Total Revenue and Elasticity
• Let’s say demand is inelastic. Then if the coffeehouse
raises prices 10%, the sales will drop by less than 10%
• In other words, the gain in revenue from higher prices is
greater than the loss in revenue from lost sales.
Therefore, Total Revenue will rise
P
10%
TR
DCoffee
Qd
Total Revenue and Elasticity
• If they lowered prices, though, the loss of revenue
from higher prices would be greater than the gain
from increased sales, so Total Revenue will fall
P
10%
TR
DCoffee
Qd
Total Revenue and Elasticity
• Let’s say demand is elastic. Then if the coffeehouse raises
prices 10%, the sales will drop by more than 10%
• In other words, the gain in revenue from higher prices is
less than the loss in revenue from lost sales. Therefore, Total
Revenue will fall
P
10%
DCoffee
TR
Qd
Total Revenue and Elasticity
• If they lowered prices, though, the loss of revenue from
higher prices would be less than the gain in revenue from
increased sales, so Total Revenue will rise
P
10%
TR
DCoffee
Qd
Total Revenue and Demand
• So we can look at what happens to total
revenue as we move down a demand curve
• As we move down a demand curve we
know that demand is elastic and as we
lower price further demand becomes less
elastic until we hit unit elasticity, at which
point total revenue begins to fall and
demand becomes more inelastic
Total Revenue and Demand
$
ED = infinite
Elastic Ed >1
Unitary Elastic Ed = 1
Inelastic Ed < 1
ED = 0
$
Q
Ed = 1
Ed > 1
Ed < 1
Total Revenue
Q
Total Revenue Test
Elasticity of
Demand
Direction of Price
Change
Effect on Total
Revenue
Inelastic
Increase
Increase
Inelastic
Decrease
Decrease
Elastic
Increase
Decrease
Elastic
Decrease
Increase
Unitary
Any Change
Unchanged
Total Revenue Test
• If P and Total Revenue Move Together
• Demand is Inelastic
• If Qd and TR Move Together
• Demand is Elastic
• If changes in P or Qd Don’t Change TR
• Demand is Unitary Elastic
Determinants of Ed
Availability of Substitutes
• As there are more substitutes, demand is more
elastic
• With fewer substitutes, demand is more
inelastic
• Example:
• Coca-Cola has many substitutes and hence, demand is
very elastic
• Insulin has no substitutes for diabetic and hence,
demand is very inelastic.
Determinants of Ed
Percentage of Income Spent on Commodity
• The less expensive a good is as a fraction of
our total budget, the more inelastic the demand
for the good is (and vice versa).
• Example:
• Price of cars go up 10% (from $20,000 to $22,000)
• Price of toothpicks rise by 10% (from $2 to $2.20)
• Demand is more (elastic) affected by the price of cars
increasing vs. the increase in the price of toothpicks
(price inelastic).
Determinants of Ed
Time
• The longer the time frame is, the more elastic
the demand for a good is (and vice versa).
• Example - Price of Gasoline Increases
• Immediately: can’t do much, still need to get to work,
school, etc.
• Short-run: find a car pool, ride bike, public transit
• Long-run: next car you buy uses less gas.
Determinants of Ed
Nature of the Product - Necessities vs. Luxuries
• The more necessary a good is, the more inelastic
the demand for the good (and vice versa).
• Example: Insulin
Income Elasticity of Demand
• Income Elasticity of Demand (Ey) measures the responsiveness of quantity
demanded to changes in income (Y).
• Ey = % in Qd
% in Y
• Ey = ( Q/Q) ÷ ( Y/Y)
• Note that the negative sign is important!
Normal Goods
• Typically, if our income rises, we buy more
and vice versa. These types of goods are
called normal goods.
• EdY > 0 - normal good
Inferior Goods
• There are some goods we buy less of as our
income grows and more of as our income
falls.
• For instance, in university you’ll probably
eat Macaroni & Cheese. But when you get a
high paying job (as all V.P. grads do) you
will probably buy less Mac and Cheese.
• If a good’s elasticity is EdY < 0 it is an
inferior good
Cross Price Elasticity of Demand
• Another type of elasticity is the Cross Price
Elasticity. This measures how changes in
the price of one good can affect the quantity
demanded of another
• Cross Price Elasticity of Demand (EAPB) measures the responsiveness of quantity
demanded of good A when the price of good
B changes.
Cross Price Elasticity of Demand
• EAPB = % in Qd of Good A
%  in P of Good B
EAPB = (QA/QA ) (PB / PB)
• Note that the sign DOES matter for this
elasticity also!
Substitute Goods
• Consider Coke and Pepsi. If the price of
Coke goes up, what would you expect to
happen to the demand for Pepsi?
– It will rise, since people will buy less Coke and
more Pepsi. Thus the Demand for Pepsi will
rise.
• So the bottom of the elasticity fraction is
positive and top of the elasticity fraction is
positive.
Substitute Goods
This relationship is called substitutes and can
be seen when EA,B> 0.
Complement goods
• Consider Washing Machines and Dryers. If
the price of Washing Machines rises, what
would you expect to happen to the demand
for Dryers?
– It will fall, since people will buy less washers at
the new price, they will need less dryers.
• So the bottom of the elasticity fraction is
positive and top of the elasticity fraction is
negative.
Complement Goods
This relationship is called complements and
can be seen when EA,B < 0
Elasticity of Supply
• This is similar to price elasticity of demand,
except we substitute the word supply for
demand. It is measured the same and is
inelastic, elastic, and unit elastic.
• Elasticity of Supply (Es) - measures the
responsiveness of quantity supplied to
changes in price of the good.
Elasticity of Supply
Es = % in Qs
% in P
ES = (Q/Q) ÷ (P/P) or ES = [(Q2-Q1)/Q1]÷ [(P2-P1)/P1]
• Law of Supply tells us this number is
generally positive.
Determinants of Elasticity of Supply
• If supply is getting more (or less) elastic, we
are saying that the firms can change supply
in larger (or smaller) quantities when price
changes.
• Generally, anything that can affect a firm’s
ability to change production easily will
affect the elasticity of supply.
Determinants of Elasticity of Supply
• Time
– if time period very short, then an increase in
price does not significantly affect the quantity
offered for sale
– as the time period becomes longer, supply tends
to become more elastic
• sellers are able to respond more easily to changes in
the prices of their products
Determinants of Elasticity of Supply
• Storage Cost
– non-perishable goods (sunglasses) can be stored at
low costs and thus supply elasticity is greater than
perishable goods (vegetables) with high storage
costs
– with changes in price for non-perishable goods that
can be stored cheaply producers can release some
extra quantities when price rises and withdraw item
from market when price falls
– above option may not be possible with high storage
costs
Elasticity of Supply Cases
P
P
P
Perfectly Elastic
Supply
Unitary Elastic
Supply
Elastic Supply
Q
Q
P
Q
P
Inelastic
Supply
Q
Perfectly
Inelastic
Supply
Q
Examples of Elasticity of Supply
• To consider:
– How would the supply curve of NHL players
differ from the supply curve of bakers?
– What would the supply curve of Picasso
paintings look like?