Elasticity and its application

In this chapter,
look for the answers to these questions:
What is elasticity? What kinds of issues can elasticity help us understand?
What is the price elasticity of demand?
How is it related to the demand curve?
How is it related to revenue & expenditure?
What is the price elasticity of supply?
How is it related to the supply curve?
What are the income and cross-price elasticities of demand?

You design websites for local businesses.
You charge $200 per website,
and currently sell 12 websites per month.
Your costs are rising
(including the opportunity cost of your time),
so you consider raising the price to $250.
The law of demand says that you won’t sell as many websites if you raise your price.
How many fewer websites? How much will your revenue fall, or might it increase?
A scenario…

ELASTICITY AND ITS APPLICATION
Elasticity
Basic idea:
Elasticity measures how much one variable responds to changes in another variable.
One type of elasticity measures how much demand for your websites will fall if you raise your price.
Definition:
Elasticity is a numerical measure of the responsiveness of Qd or Qs to one of its determinants.

ELASTICITY AND ITS APPLICATION
Price Elasticity of Demand
Price elasticity of demand measures how much Qd responds to a change in P.
Loosely speaking, it measures the price-sensitivity of buyers’ demand.

ELASTICITY AND ITS APPLICATION
Price Elasticity of Demand
Price elasticity
of demand equals
P rises by 10%
Q falls by 15%
Example:

ELASTICITY AND ITS APPLICATION
Price Elasticity of Demand
Along a D curve, P and Q move in opposite directions, which would make price elasticity negative.
We will drop the minus sign and report all price elasticities as
positive numbers.

ELASTICITY AND ITS APPLICATION
Calculating Percentage Changes
Demand for your websites
Standard method
of computing the percentage (%) change:
Going from A to B,
the % change in P equals
($250–$200)/$200 = 25%

ELASTICITY AND ITS APPLICATION
Calculating Percentage Changes
Demand for your websites
Problem:
The standard method gives different answers depending on where you start.
From A to B,
P rises 25%, Q falls 33%,
elasticity = 33/25 = 1.33
From B to A,
P falls 20%, Q rises 50%, elasticity = 50/20 = 2.50

ELASTICITY AND ITS APPLICATION
Calculating Percentage Changes
So, we instead use the midpoint method:
The midpoint is the number halfway between the start & end values, the average of those values.
It doesn’t matter which value you use as the “start” and which as the “end” – you get the same answer either way!

ELASTICITY AND ITS APPLICATION
Calculating Percentage Changes
Using the midpoint method, the % change in P equals
The % change in Q equals
The price elasticity of demand equals

A C T I V E L E A R N I N G 1
Calculate an elasticity
Use the following
information to
calculate the
price elasticity
of demand
for hotel rooms:
if P = $70, Qd = 5000
if P = $90, Qd = 3000

A C T I V E L E A R N I N G 1
Answers
Use midpoint method to calculate
% change in Qd
(5000 – 3000)/4000 = 50%
% change in P
($90 – $70)/$80 = 25%
The price elasticity of demand equals

ELASTICITY AND ITS APPLICATION
What determines price elasticity?
To learn the determinants of price elasticity,
we look at a series of examples.
Each compares two common goods.
In each example:
Suppose the prices of both goods rise by 20%.
The good for which Qd falls the most (in percent) has the highest price elasticity of demand.
Which good is it? Why?
What lesson does the example teach us about the determinants of the price elasticity of demand?

ELASTICITY AND ITS APPLICATION
EXAMPLE 1:
Breakfast cereal vs. Sunscreen
The prices of both of these goods rise by 20%.
For which good does Qd drop the most? Why?
Breakfast cereal has close substitutes
(e.g., pancakes, Eggo waffles, leftover pizza),
so buyers can easily switch if the price rises.
Sunscreen has no close substitutes,
so consumers would probably not
buy much less if its price rises.
Lesson: Price elasticity is higher when close substitutes are available.

ELASTICITY AND ITS APPLICATION
EXAMPLE 2:
“Blue Jeans” vs. “Clothing”
The prices of both goods rise by 20%.
For which good does Qd drop the most? Why?
For a narrowly defined good such as
blue jeans, there are many substitutes
(khakis, shorts, Speedos).
There are fewer substitutes available for broadly defined goods.
(There aren’t too many substitutes for clothing,
other than living in a nudist colony.)
Lesson: Price elasticity is higher for narrowly defined goods than broadly defined ones.

ELASTICITY AND ITS APPLICATION
EXAMPLE 3:
Insulin vs. Caribbean Cruises
The prices of both of these goods rise by 20%.
For which good does Qd drop the most? Why?
To millions of diabetics, insulin is a necessity.
A rise in its price would cause little or no decrease in demand.
A cruise is a luxury. If the price rises,
some people will forego it.
Lesson: Price elasticity is higher for luxuries than for necessities.

ELASTICITY AND ITS APPLICATION
EXAMPLE 4:
Gasoline in the Short Run vs. Gasoline in the Long Run
The price of gasoline rises 20%. Does Qd drop more in the short run or the long run? Why?
There’s not much people can do in the
short run, other than ride the bus or carpool.
In the long run, people can buy smaller cars
or live closer to where they work.
Lesson: Price elasticity is higher in the
long run than the short run.

ELASTICITY AND ITS APPLICATION
The Determinants of Price Elasticity:
A Summary
The price elasticity of demand depends on:
the extent to which close substitutes are available
whether the good is a necessity or a luxury
how broadly or narrowly the good is defined
the time horizon – elasticity is higher in the long run than the short run

ELASTICITY AND ITS APPLICATION
The Variety of Demand Curves
The price elasticity of demand is closely related to the slope of the demand curve.
Rule of thumb:
The flatter the curve, the bigger the elasticity.
The steeper the curve, the smaller the elasticity.
Five different classifications of D curves.…

ELASTICITY AND ITS APPLICATION
“Perfectly inelastic demand” (one extreme case)
P falls by 10%
Q changes
by 0%
0%
10%
= 0
Consumers’
price sensitivity:
D curve:
Elasticity:
vertical
none
0

ELASTICITY AND ITS APPLICATION
“Inelastic demand”
Q rises less than 10%
< 10%
10%
< 1
P falls by 10%
Consumers’
price sensitivity:
D curve:
Elasticity:
relatively steep
relatively low
< 1

ELASTICITY AND ITS APPLICATION
“Unit elastic demand”
Q rises by 10%
10%
10%
= 1
P falls by 10%
Consumers’
price sensitivity:
Elasticity:
intermediate
1
D curve:
intermediate slope

ELASTICITY AND ITS APPLICATION
“Elastic demand”
Q rises more than 10%
> 10%
10%
> 1
P falls by 10%
Consumers’
price sensitivity:
D curve:
Elasticity:
relatively flat
relatively high
> 1

ELASTICITY AND ITS APPLICATION
“Perfectly elastic demand” (the other extreme)
P1
P changes by 0%
Q changes
by any %
any %
0%
= infinity
P2 =
Consumers’
price sensitivity:
D curve:
Elasticity:
infinity
horizontal
extreme

ELASTICITY AND ITS APPLICATION
Elasticity of a Linear Demand Curve
The slope
of a linear demand curve is constant,
but its elasticity
is not.

ELASTICITY AND ITS APPLICATION
Price Elasticity and Total Revenue
Continuing our scenario, if you raise your price
from $200 to $250, would your revenue rise or fall?
Revenue = P x Q
A price increase has two effects on revenue:
Higher P means more revenue on each unit
you sell.
But you sell fewer units (lower Q),
due to Law of Demand.
Which of these two effects is bigger?
It depends on the price elasticity of demand.

ELASTICITY AND ITS APPLICATION
Price Elasticity and Total Revenue
If demand is elastic, then
price elast. of demand > 1
% change in Q > % change in P
The fall in revenue from lower Q is greater
than the increase in revenue from higher P,
so revenue falls.
Revenue = P x Q

ELASTICITY AND ITS APPLICATION
Price Elasticity and Total Revenue
Elastic demand
(elasticity = 1.8)
When D is elastic,
a price increase
causes revenue to fall.
lost revenue due to lower Q
increased revenue due to higher P
Demand for your websites

ELASTICITY AND ITS APPLICATION
Price Elasticity and Total Revenue
If demand is inelastic, then
price elast. of demand < 1
% change in Q < % change in P
The fall in revenue from lower Q is smaller
than the increase in revenue from higher P,
so revenue rises.
In our example, suppose that Q only falls to 10 (instead of 8) when you raise your price to $250.
Revenue = P x Q

ELASTICITY AND ITS APPLICATION
Price Elasticity and Total Revenue
Now, demand is inelastic: elasticity = 0.82
When D is inelastic,
a price increase
causes revenue to rise.
lost revenue due to lower Q
increased revenue due to higher P
Demand for your websites

A. Pharmacies raise the price of insulin by 10%. Does total expenditure on insulin rise or fall?
B. As a result of a fare war, the price of a luxury cruise falls 20%.
Does luxury cruise companies’ total revenue
rise or fall?
A C T I V E L E A R N I N G 2
Elasticity and expenditure/revenue

A C T I V E L E A R N I N G 2
Answers
A. Pharmacies raise the price of insulin by 10%. Does total expenditure on insulin rise or fall?
Expenditure = P x Q
Since demand is inelastic, Q will fall less
than 10%, so expenditure rises.

A C T I V E L E A R N I N G 2
Answers
B. As a result of a fare war, the price of a luxury cruise falls 20%.
Does luxury cruise companies’ total revenue
rise or fall?
Revenue = P x Q
The fall in P reduces revenue,
but Q increases, which increases revenue. Which effect is bigger?
Since demand is elastic, Q will increase more than 20%, so revenue rises.

ELASTICITY AND ITS APPLICATION
APPLICATION: Does Drug Interdiction Increase or Decrease Drug-Related Crime?
One side effect of illegal drug use is crime: Users often turn to crime to finance their habit.
We examine two policies designed to reduce illegal drug use and see what effects they have on drug-related crime.
For simplicity, we assume the total dollar value of drug-related crime equals total expenditure
on drugs.
Demand for illegal drugs is inelastic, due to addiction issues.

ELASTICITY AND ITS APPLICATION
Policy 1: Interdiction
Interdiction reduces the supply of drugs.
Since demand for drugs is inelastic,
P rises propor-tionally more than Q falls.
Result: an increase in
total spending on drugs, and in drug-related crime

ELASTICITY AND ITS APPLICATION
Policy 2: Education
Education reduces the demand for drugs.
P and Q fall.
Result:
A decrease in total spending on drugs, and in drug-related crime.

ELASTICITY AND ITS APPLICATION
Price Elasticity of Supply
Price elasticity of supply measures how much Qs responds to a change in P.
Loosely speaking, it measures sellers’
price-sensitivity.
Again, use the midpoint method to compute the percentage changes.

ELASTICITY AND ITS APPLICATION
Price Elasticity of Supply
Price
elasticity
of supply equals
P rises by 8%
Q rises by 16%
Example:

ELASTICITY AND ITS APPLICATION
The Variety of Supply Curves
The slope of the supply curve is closely related to price elasticity of supply.
Rule of thumb:
The flatter the curve, the bigger the elasticity.
The steeper the curve, the smaller the elasticity.
Five different classifications.…

ELASTICITY AND ITS APPLICATION
“Perfectly inelastic” (one extreme)
Q1
P1
Q changes
by 0%
0%
10%
= 0
P rises by 10%
Sellers’
price sensitivity:
S curve:
Elasticity:
vertical
none
0

ELASTICITY AND ITS APPLICATION
“Inelastic”
Q1
P1
Q rises less than 10%
< 10%
10%
< 1
P rises by 10%
Sellers’
price sensitivity:
S curve:
Elasticity:
relatively steep
relatively low
< 1

ELASTICITY AND ITS APPLICATION
“Unit elastic”
Q1
P1
Q rises
by 10%
10%
10%
= 1
P rises by 10%
Sellers’ price sensitivity:
S curve:
Elasticity:
intermediate slope
intermediate
= 1

ELASTICITY AND ITS APPLICATION
“Elastic”
Q1
P1
Q rises more than 10%
> 10%
10%
> 1
P rises by 10%
Sellers’
price sensitivity:
S curve:
Elasticity:
relatively flat
relatively high
> 1

ELASTICITY AND ITS APPLICATION
“Perfectly elastic” (the other extreme)
P1
P changes by 0%
Q changes by any %
any %
0%
= infinity
P2 =
Sellers’
price sensitivity:
S curve:
Elasticity:
horizontal
extreme
infinity

ELASTICITY AND ITS APPLICATION
The Determinants of Supply Elasticity
The more easily sellers can change the quantity they produce, the greater the price elasticity of supply.
Example: Supply of beachfront property is harder to vary and thus less elastic than
supply of new cars.
For many goods, price elasticity of supply
is greater in the long run than in the short run,
because firms can build new factories,
or new firms may be able to enter the market.

A C T I V E L E A R N I N G 3
Elasticity and changes in equilibrium
The supply of beachfront property is inelastic. The supply of new cars is elastic.
Suppose population growth causes
demand for both goods to double
(at each price, Qd doubles).
For which product will P change the most?
For which product will Q change the most?

A C T I V E L E A R N I N G 3
Answers
Beachfront property (inelastic supply):
When supply
is inelastic,
an increase in demand has a bigger impact on price than on quantity.

A C T I V E L E A R N I N G 3
Answers
New cars
(elastic supply):
When supply
is elastic,
an increase in demand has a bigger impact on quantity than on price.

ELASTICITY AND ITS APPLICATION
How the Price Elasticity of Supply Can Vary
Supply often becomes
less elastic
as Q rises,
due to capacity limits.
elasticity > 1
elasticity < 1

ELASTICITY AND ITS APPLICATION
Other Elasticities
Income elasticity of demand: measures the response of Qd to a change in consumer income
Recall from Chapter 4: An increase in income causes an increase in demand for a normal good.
Hence, for normal goods, income elasticity > 0.
For inferior goods, income elasticity < 0.

ELASTICITY AND ITS APPLICATION
Other Elasticities
Cross-price elasticity of demand:
measures the response of demand for one good to changes in the price of another good
For substitutes, cross-price elasticity > 0
(e.g., an increase in price of beef causes an increase in demand for chicken)
For complements, cross-price elasticity < 0
(e.g., an increase in price of computers causes decrease in demand for software)

ELASTICITY AND ITS APPLICATION
Cross-Price Elasticities in the News
“As Gas Costs Soar, Buyers Flock to Small Cars”
-New York Times, 5/2/2008
“Gas Prices Drive Students to Online Courses”
-Chronicle of Higher Education, 7/8/2008
“Gas prices knock bicycle sales, repairs into higher gear” -Associated Press, 5/11/2008
“Camel demand soars in India”
(as a substitute for “gas-guzzling tractors”) -Financial Times, 5/2/2008
“High gas prices drive farmer to switch to mules”
-Associated Press, 5/21/2008

CHAPTER SUMMARY
Elasticity measures the responsiveness of
Qd or Qs to one of its determinants.
Price elasticity of demand equals percentage change in Qd divided by percentage change in P.
When it’s less than one, demand is “inelastic.” When greater than one, demand is “elastic.”
When demand is inelastic, total revenue rises when price rises. When demand is elastic, total revenue falls when price rises.

CHAPTER SUMMARY
Demand is less elastic in the short run,
for necessities, for broadly defined goods,
or for goods with few close substitutes.
Price elasticity of supply equals percentage change in Qs divided by percentage change in P.
When it’s less than one, supply is “inelastic.” When greater than one, supply is “elastic.”
Price elasticity of supply is greater in the long run than in the short run.