This lesson on price elasticity of demand contains an explanation of elasticity, how to solve for both arc and point price elasticity of demand, its relation to total revenue, and the factors that influence the elasticity of demand for a product or service.

1. DEFINITION OF ELASTICITY
Think Back
Before starting this lesson, recallyour prior understanding of the Law of Demand.Thislaw basically tells us that the two variables price,
P and quantity, Q are correlated. If you change P, we can also predict that a change will also occur in Q. Specifically, the Law of Demand
states that price and quantity have an inverse or negativerelationship. This means that when the value of P increases, a change will also
occur in Q but in the opposite direction: a decrease in Q value will occur. In other words, when the price of a good increases, consumers
will want less quantity of that good. Conversely, when the price of a good decreases, consumers will want more quantity of that good.
Take note of this when studying elasticity.
You are probably alreadyfamiliar with the property of elasticity from your physics subject. Consider the following items:
You know from experience that the loom band on the left is more elastic than the baller band on the right. These items have different
elasticities.
Elasticityissimply the responsiveness of one variable to changes in another variable. By measuring elasticity we will learn whether one
variable is greatlyor only slightly affected by changes in another variable. In the case of the bands, the variables we ought to consider
are theamount of force applied on the object and the length the band stretches in response to the force. But in general, when
measuring elasticity we arebasically asking the question:
Will the value of A increase or decrease by a huge amount or only by a small amount when the value of B is changed?
This can be expressed mathematicallyusing the midpoint formula:
One application of theconcept of elasticitycan be on consumer demand. Specifically, we can measure PriceElasticity of Demand,which
is simply, a measure of how much Quantity Demanded changes in response to changes in Price. Knowing theLaw of Demandallows us
to predict the direction of the change (increase or decrease) but knowing Elasticity allows us to know the degreeof the changeas well
as the impact of price changes to our expenditure (if we areconsumers) or our sales (if we areentrepreneurs). Consider the following
scenarios:
Notice that when the price increased for cola and milk, both consumers decreased their quantity demanded for each product. The man
changed his QD from 4 to 0 while the woman changed her QD from 5 to 4. We could have predicted this outcome knowing the Law of
Demand alone. If you didn't know about elasticity you would straightawaythink this is bad because customers are buying less goods. But
did you know that for the seller of milk, increasing the price is actually a good strategy? When milk was being sold at 80 cents, the seller
earned $4 but when the milk sold for $2.4 each, the seller actually earned $9.6 even though the customer bought less than before. This
is because the increase in price offset the change in quantity demanded. Anyone with a knowledge of price elasticitycould have
predicted this outcome from the start.

2. SOLVING FOR ARC PRICE ELASTICITY OF DEMAND
Price Elasticity of Demand or PED is expressed mathematicallywith the percent change in quantity demanded as the numerator a nd the
percent change in price as the denominator:
By using the midpoint formula the arc elasticity is obtained or the value of PED across a rangeof prices. This helps us tell whether overall
the demand for a particular good is elastic or inelastic. (The significance of arc elasticitywill be made clearer when wecompare it to point
elasticity in Chapter 6.)
Try it! Last month,theprice of the cheapest pentel pens at Cang's Inc. was P6 a piece, and Sue was willing to buy a dozen. Today, the price
has gone up to P8 a piece, and Sue is now willing to buy only 10 pieces. What is Sue's price elasticity of demand?
To find Sue's price elasticity of demand, weneed to divide the percentagechange in quantity by the percentagechange in price. Use the
midpoint formula and try it yourself before moving on to see the solution.
Plug in the following given to the mid-point formula: Q1 = 12 Q2 = 10 P1 = 6 P2 = 8
Using the formula, we learnthat the elasticity coefficient of Kristylle's demand is 0.64. What does this mean? Well, solving is only the first
step. Now we will have to interpret our coefficient. On to the next chapter!
INTERPRETING THE PRICE ELASTICITY COEFFICIENT
When interpreting PED, there are five possible interpretations: perfectly inelastic, inelastic, unitary elastic, elastic, and perfectly elastic.
Here's what each one means:
Perfectly Inelastic Demand, ED = 0
No change in quantity demanded occurs whether price increases or decreases. The consumer's QD is always
the same, hence the verticaldemand curve. Very few goods would qualify as having perfectly inelastic demand
but an example could be life-saving drugs such as when a diabetic who badly needs insulin buys the prescribed
dosage even whenthe drug has become quite expensive. Since the product has no substitute and theconsumer
desperately needs it, he is a slave to the price.
Inelastic Demand, ED < 1 (less than one)
The percentage decrease in quantity is less (numerator) than the percentage increase in price (denominator).
You would end up with a fraction less than one since the denominator is greater than the numerator.
In our example from Chapter 2 the PED coefficient was 0.64 or in fraction form 7/11 which is less than 1. So
Sue's demand for pentel pens is inelastic. This means that Sue's quantity demanded decreased less than the
increase in price. This may be due to any of the following reasons:

3.  no close substitutes
 perceived as a necessity
 consumer has no time to look for substitutes
 price is just a small percentageof consumer's budget or
income
Unit Elastic Demand, ED = 1
The percent changein price and quantityareboth proportional or the sameso solving for PED yields a coefficient
of one.
The graph is a rectangular or equilateralhyperbola because all rectanglesunder the curve would yield the same
area. For example, the green rectangle would have the same area as the yellow rectangle. This has important
implications on revenue as you will learn in Chapter 5.
Elastic Demand
ED > 1 (greater than one)
graph:
The decreasein quantity demanded is greater thantheincrease in price so you willend up witha numerator that
is greater thanyour denominator, and since we use theabsolute value of theprice elasticitycoefficient, thevalue
would end up being greater than 1 (not negative).
For example, if the price of a branded shirt increased by 10% and this caused the shirt sales to drop by 20%, we can tell rig ht away that
thedemand for this branded shirt is elastic because thequantitydemanded for shirt changed more thanprice. Mathematically,bydividing
20% by 10%, we get a PED coefficient of 2, which is greater than 1.
Some reasons why a product may have elastic demand:
 has a lot of close substitutes
 perceived as a luxury
 consumer has theluxury of timeto decide on a purchase
 price is a huge percentage of consumer's budget or
income
Perfectly Elastic Demand
ED = ∞ (equal to infinity)
Very few goods would qualify as having perfectly elastic demand but an example could be products in perfectly
competitive marketswhich haveperfect substitutes. At a given price, consumers would buy as many units of the
product as they can (hence the horizontal demand curve) but if price increases, the seller may observe their
consumer demand shrink to zero.
How to Remember All That
Remember that the consumer is likea homie chained to a verticaldemand curve
when his demand is perfectly inelastic. Poor bruh. On the other hand, inelastic
demand is a wannabe. He idolizes his perfectly inelastic bro. He tries hard by
making his slope very steep but doesn't quite make it. As for the consumer with
perfectly elastic demand, he's a relaxed homie lying on a horizontal demand
curve 'coz he can buy as much as he wants. Elasticdemand is another wannabe. Who doesn't want to be a relaxed
homie? So he tries to make his slope as flat as possible but just doesn't cut it.
FACTORS THAT AFFECT PRICE ELASTICITY OF DEMAND
Availability of Substitutes
As we have learned from previous lessons, the Substitution Effect helps us predict that when the price of a good increases, consumers
will tend to switch to an alternativeor substitute. It makes sense then that a good with a lot of close substitutes (such as products in a
monopolistic market) will have a highly elastic demand. When the price of the good increases, people will decrease their quantity
demanded to a greater degreesince they areable to substitute the good for another product which gives them almost thesame
satisfaction. In fact, in a perfectly competitive market where products are perfect substitutes of each other, a good that increases its
price will experience a reduction of quantity demand to zero, since consumers can switch goods perfectly. The goods are completely the
same after all. Conversely, a good with no close substitutes will have highly inelastic demand. When the price of the good increases,
quantity demanded decreases to a lesser degreebecause consumers have no cheaper alternatives to switch to. They will likely reduce
their consumption in order to reduce spending, but not greatlyespecially if the good is a necessity.
Need or Want
If we think back to the Law of Economic Order it makes sense that goods which areconsidered needs will tend to have more inelastic
demand compared to wants. Consumers will prioritizenecessities first over luxuries.
Time
A student who needs to purchase a blue shirt for a class performance the following day and a student who needs the shirt at the end of
the month will have different price elasticities for a P500 shirt. This is because the student who needs the shirt at the end of the month
has the luxury of time to look for substitutes while the student who needs it thenext day does not.

4. Pricein relation to Budget/Income
Although a ball pen and an apartment may be considered by a student living awayfrom home as both necessities, the student may have
different price elasticities for each because of the difference in their share of her budget. For example, a ball pen typically costs P5 while
apartment rent typically costs P2500. If both record a 50% increase in price, the ball pen will now cost P7.50 while the apartment will
now cost P3750. For a student who has a monthly allowance of P5000, the new rent will takeup 75% of her budget. On the other hand
the new ball pen price is only 0.15% of her budget. Having this understanding, we can predict that the student will likely start scouting
for a new apartment but will readily buy the ball pen.
RELATING ELASTICITY TO TOTAL REVENUE
Think Back
Remember that totalrevenue is derived by multiplying the number of items sold times the unit price, expressed in the formula TR = PxQ.
Price and Quantity arethe two variables we examine to arriveat a measure of the Price Elasticity of Demand. These two variables, P and
Q, arealso important in measuring Revenue. From a consumer's standpoint, Revenue is the total value of consumer expenditure at a
given price. From a producer's point of view, Revenue is the total value of sales at a given price. Consumer Expenditure and Total
Revenue are reallyjust two sides of the same coin. So when you faceproblems mentioning either of the two, you now know they really
mean the same thing.
Changein TotalRevenue can be derived using the following formula:
For example, if theprice of a good increases by 3% and the quantity demanded decreases by 10% wecan write this algebraically:
%Δ(PQ) = 3% + (-10%) %Δ(PQ) = -7%
Try it!
The price of rice per sack in the market increases by 15%
and quantity demanded decreases by 10%.
The price of bread in BreadLumpincreases by 10% and
quantity demanded decreases by 5%.
The price of a plain shirt in Robinson's Department Store
increases by 10% causing sales to decrease by 20%.
The cost of ice cream per gallon increases by 5% while
sales declined by 15%.
Use the formula to find out the impact of the above
changes on the supplier's totalrevenue (or consumer's
expenditure). We can gain even more insight into this by comparing total revenue with the price elasticity of demand for these goods.
Notice that for goods with inelastic PED, increasing the price resulted in an overall increase in their total revenue despite consumers
reducing their quantity demanded. Recall now that TR = P x Q which tells us that totalrevenue is dependent on both price and quantity.
If reduction in quantity demanded is less compared to the increase in price, the greater increase in price would offset the decrease in
quantity demanded resulting in higher TR for goods with inelastic PED. On the other hand, for goods with elastic PED, increasing the
price results in an overall decrease in the total revenue as the price increase would not be enough to offset the bigger decrease in
quantity demanded.
In Summary

5. SOLVING FOR POINT PRICE ELASTICITY OF DEMAND
Observe the following graphof a linear demand curve:
If we solve for the PED between 0 to 9 pesos, we get:
Under absolute value PEDis1/3 whichislessthan1. Thistellsusthat below
the midpointof the curve,consumerdemandisinelastic.
Now let's try solving for PED between 9 to 18 pesos. We get:
Under absolute value PED is 3 which is greater than1.
Above the midpoint of thecurve, consumer demand is
elastic. What is going on?
What this shows us is that at any point on the demand
curve, elasticityvalues differ. The lower end of the curve
closer to the x-axis will tend to have relatively(in
comparison) more inelastic demand while the upper end of
the curve closer to the y-axis will tend to have relatively
more elastic demand.
This makes sense because as we have learned in the
previous chapters, the higher the percentageof price relativeto the consumer's budget, the more elastic demand will be.
However, if we solve for the PED using the points when price is at its lowest (0 pesos) and at its highest (18 pesos) using the midpoint
formula, we get:
This indicates that the linear demand curve shown above
has unitary elasticity overall. This is also because we
basically got the price elasticity value at the midpoint of
the linear demand curve (9, 9).
So far, we have obtained our PED using themidpoint
method, and through the above example we have seen its
usefulness in determining PED across a rangeof prices.
However, there may be times when what is given is only
one point and the demand function. In cases like this, a
slightly different formula can be used to find the point
price elasticity of demand.
POINT ELASTICITY FORMULA
Try it!
Jefprill's demand for broccoli is given by QD = 40 – 2P. Jefprill buys Q = 5 units of broccoli.
What is his price elasticity of demand at this level of quantity?
Using the point elasticity formula, we have the following: