Economics Online Tutor
This formula will always yield a negative number for a normal good.  This is due to the law of demand.
For a normal good, the price and quantity demanded will always move in opposite directions, due to a
downward-sloping demand curve.  If it does not yield a negative number, then it is not a normal good but
an inferior good.  Often, a normal good is assumed for purposes of economic analysis, and it will be
shown as the absolute value (the number without the negative sign).  This assumption is based on the
fact that the negative sign is irrelevant to the analysis.  The relationship is still negative, but the
negative sign is assumed to be there and is not shown.  There are exceptions, for example with a
demand equation, where the negative sign is important to the analysis.

For the remainder of this section,  in order to keep from repeating this relationship over and over,
assume that p.e.d. (or the price elasticity of demand), refers to the absolute value; forget about the
negative sign involved, unless it becomes relevant to the discussion.

You don’t really have to worry about memorizing this formula, but it helps to be able to recognize it when
you see it.  You do need to remember that the price elasticity of demand is a measurement of the relative
change in quantity to a given change in price, and that by using division to measure this comparison, a
higher number for a result will mean more responsiveness, or more sensitivity, of quantity to a price
change.

More responsive, or sensitive, means that the elasticity is higher.

Using division as a method of measurement highlights another important concept.  If the quantity
changes by the same percentage as the price change, then the answer will have a value of 1.  If the
quantity changes more than the price, the answer will have a value greater than 1.  If the quantity
changes less than the price change, the answer will have a value less than one.  This distinction is
important because for most types of analysis, the p.e.d., relative to 1, is more important than the actual
number itself.  In other words, the difference between a price elasticity of 3.5 and a price elasticity of 1.5
is not as important as the fact that each number is greater than 1.  This importance will be illustrated in
the section below about the effect of price elasticity of demand on total revenue.

The price elasticity of demand measurement (absolute value), as compared to 1, calls for some
terminology that you need to know:

If p.e.d. = 1, it is called unit elastic
If p.e.d. > 1, it is called elastic
If p.e.d. < 1, it is called inelastic

In other words, a unit elastic demand is when the quantity changes by the same percentage as the price
change.  An elastic demand is when the quantity changes by a larger percentage than the price change.
An inelastic demand is when the quantity changes by a smaller percentage than the price change.

You may encounter the extreme cases where either the price change or the quantity change is equal to
zero.  If there is no price change for any given range of quantities (the formula yields an answer that
divides the quantity change by zero, which is defined mathematically as infinity), then it is called perfectly
elastic.  If there is no quantity change for any given range of prices (the formula yields an answer that
divides zero by some number, which is defined mathematically as zero), then it is called perfectly
inelastic.

At this time, an example should be helpful.

Suppose that a company sells a product for \$2, and at this price the quantity sold is 100 units.  If the
company raised the price to \$3 it could sell 75 units.  What is the price elasticity of demand?

To arrive at the answer, start with the change in quantity.  The quantity sold will go from 100 units to 75
units.  A decrease of 25 units (100 - 75 = 25).  This would be a change, from the beginning units sold of
100, of 25/100, or 25%.

Now, figure the change in price, using the same method.  The price increased from \$2 to \$3, in increase
of \$1.  This would be a change, from the beginning price of \$2, of \$1/\$2, or 50%.

Now that you have the percentages, simply divide the quantity percentage by the price percentage, you
get:

25/50 = 0.5.  Always show this number as a fraction.  If rounding is necessary,  the answers could vary,
and the course instructor may set the rules for rounding.

In this example, the absolute value of the result, 0.5, is less than 1.  So using the terminology defined
above, this would be an inelastic demand.  The quantity changed by a lower percentage than the price
changed.

Perhaps another example, showing a result of an elastic, as opposed to an inelastic, answer would be
helpful.  Suppose you had a situation similar to the example above, where the original (beginning) price
is \$2, and the original (beginning) quantity sold is 100 units.  But now, suppose that in increase in the
price from \$2 to \$3 means that the quantity sold changes from 100 to 25.  Using the exact same method to
calculate the price elasticity of demand, you get:

The quantity sold will go from 100 units to 25 units.  A decrease of 75 units (100 - 25 = 75).  This would be a
change, from the beginning units sold of 100, of 75/100, or 75%.  The price change is exactly the same as
in the example above, so that percentage change is still 50%.  To get the price elasticity of demand, you
divide the percentage change in quantity by the percentage change in price, or in this case 75/50, or 1.5.
The price elasticity of demand in this case is greater than 1, since 1.5 > 1.  So using the terminology
defined above, this would be an elastic demand.  The quantity changed by a higher percentage than the
price changed.

DETERMINANTS OF THE PRICE ELASTICITY OF DEMAND:

AVAILABILITY OF SUBSTITUTES

DEGREE OF NECESSITY

SHARE OF BUDGET

TIME FRAME

To continue with the study of elasticity, click on one of the links
below:
 Price Elasticityof Demand
The price elasticity of demand is probably the first, and most common, type of
elasticity encountered in an economics class.  You should have an
understanding of the concepts behind elasticities in general, as used in
economics, before studying this section.  Reading the section titled
Elasticity
before proceeding with this page is recommended.  For cases where you are
required to use the midpoint formula, read this section first, but refer to the
section on the
midpoint formula to determine the answers to those questions.

The price elasticity of demand is a measure of responsiveness, or sensitivity,
of demand to a change in price.  If a business decides to raise the price of a
product, it will probably sell a lower quantity of that product, since for a normal
good the demand curve is downward-sloping.  Or if it decides to lower the
price, it will probably sell a higher quantity of that product.

The relative change in the quantity sold, compared to the change in price, is
the elasticity of demand.  [To understand the concepts behind the elasticity
formulas, so that you do not have to memorize the formula, read the section
titled
Elasticity.]  The price elasticity of demand is measured by taking the
percentage change in quantity and dividing by the percentage change in price.
It is shown mathematically by the formula:
 p.e.d. = %change in quantity / %change in price
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