The elasticity of Demand: Concept, Types, and Importance
Concept of
Elasticity of Demand:
The law of demand indicates the direction of
change in quantity demanded to a change in price.
It states that when the price falls, demand
rises. But how much the quantity demanded rises (or falls) following a certain
fall (or rise) in prices cannot be known from the law of demand. That is to
say, how much quantity demanded changes following a change in the price of a
commodity can be known from the concept of elasticity of demand.
In Fig. 2.41, we have drawn two demand curves for good X and good Y.
Both these curves are negative sloping. Let us assume that the prices of both goods
X and Y are PX1 and PY1 (note that PX1 = PY1). At price OPX1, a consumer
demands OX1, and, at price OPY1, OY1 is demanded.
 |
| Response to product demand |
Now if prices of both X and Y decline by an identical amount to OPX2 and OPY2, the quantity
demanded for X and Y rises from OX1 to OX2 and from OY1 to OY2, respectively. But the change in quantity demanded good X is greater than the change in quantity demanded good Y. This
means that good X is more sensitive or responsive to a change in its price than
good Y. This is called elasticity of demand.
By elasticity of demand, we normally mean
price elasticity of demand. (Price) the elasticity of demand measures the degree of
responsiveness of quantity demanded following a change in own price of the
commodity, holding money income and prices of related goods constant.
(Price) the elasticity of demand is the relative
difference in the dependent variable (here, quantity) divided by the relative
difference in the independent variable (here, price). Alternatively, it is defined
as the absolute value of the ratio of percentage change in price. Thus, the
elasticity of demand is a relative concept.
The formula for calculating the elasticity of demand is:
EP = proportional changes in quantity
demanded/proportional changes in price
= % changes in quantity demanded/changes in
price
EP = |∆Q/Q/∆P/P|= |∆Q/∆P.P/Q|
The vertical lines in the formula denote that we take the absolute value
of the ratio and ∆P and ∆Q denote the changes in price and quantity. Since both
price and quantity move in opposite directions, EP must always
be a negative number. Normally, we drop the negative sign and take the absolute
value of EP by taking ‘mod’ (or use the negative sign by dropping vertical lines).
Or absolute value, denoted by ||, turns the negative number into a
positive one. Thus, EP = |- 5%/2%| = 2.51 = 2.5.
Price elasticity is a pure number, independent of units of measure. The percentage
will be the same whether we measure the quantity demanded in numbers or kilograms
or liters.
Types
of Own (Price) Elasticity of Demand:
For all types of commodities, the rate of
change of quantity demanded to a change in own price is not uniform. For some
commodities, demand is said to be more responsive to price changes compared to
other commodities. That is why there are various types of elasticities of
demand.
They are of the following five types:
(1) Elastic Demand (EP > 1):
Demand is said to be elastic if the change in
price causes a more than proportionate change in quantity demanded. A 10 p.c.
change in price causes quantity demanded to change by more than 10 p.c. In
other words, if E is greater than one, demand is said to be elastic (Fig. 2.42).
 |
| Elasticity of demand |
EP = 1,000/1,000 ÷ 20/160 = 1,000/20 .160/1,000 =
8
Since the elasticity of demand for gold is
greater than one, gold is a luxury item.
(2)
Inelastic Demand (EP < 1):
When the change in price causes a less than proportionate change in
quantity demanded, demand is inelastic. A 10 p.c. cut in price may cause
quantity demanded to fall by, say, 1 p.c. Thus, demand is said to be inelastic
(Ep< 1), shown in Fig. 2.43. Usually, demand is
inelastic for necessary goods.
 |
| Inelastic Demand |
EP = 400/160 ÷ 20/40 = 400/20. 40/1,600 = 0.5
Thus, wheat has an inelastic demand since EP <
1 and wheat is a necessary article.
(3)
Unit elasticity of Demand (EP = 1):
When the change in price causes the same proportionate change in
quantity demanded, demand has unit elasticity. A 10 p.c. the decline in price will
lead to an exactly 10 p.c. increase in quantity demanded. Then EP = 1 (Fig. 2.44).
 |
| Unitary Elastic Demand |
Suppose that the price of a commodity declines
from Rs. 200 to Rs. 100 per kilogram. As a result, demand for that commodity
rises from 400 kilograms to 800 kilograms. Thus,
EP = 400/400 ÷ 100/100 = 400/100. 100/400 = 1
(4)
Perfectly Elastic Demand (EP = ∞)
When a slight change in price causes a great
change in quantity demanded, the value of elasticity of demand tends to be
infinity, and demand is said to be infinite or perfectly elastic. In this case,
the demand curve (DD,) becomes parallel to the horizontal axis (Fig. 2.45).
Under a perfectly competitive market, the demand curve for a product of an
individual firm becomes perfectly elastic.
 |
| Perfectly Elastic Demand |
If the quantity demanded becomes completely
unresponsive to price changes, the coefficient tends to be zero. In this case,
whatever the price, even if it is zero, the quantity demanded will remain fixed at
a particular level. The demand curve, thus, becomes parallel to the vertical
axis (Fig. 2.46) and demand is said to be completely (perfectly) inelastic.
 |
| Perfectly Inelastic demand |
(5) Measurement of
Elasticity of Demand:
There
are three methods of measuring the elasticity of demand. These are:
(a) Total outlay (revenue) method
(b) Point elasticity method
(c) Arc elasticity method
All
these methods are described below:
1.
Elasticity and Total Revenue or Outlay Method:
Marshall offered the method of total revenue
or total outlay for estimating the elasticity of demand. What the sellers receive
from the sale of commodities is called total expenditure or outlay of buyers.
There is no difference between total revenue and total outlay since what is
spent by the buyers is received as income by the sellers.
Thus, total outlay/revenue is the price
multiplied by the number of purchases, i.e., TR = P × Q. Here we want to measure
how much total outlay changes following a change in price. It depends upon the
elasticity of demand.
(a) Elastic Demand:
Suppose price declines (rises). As a result,
total expenditure rises (falls). Under the circumstance, the value of
elasticity of demand becomes greater than one. In Fig. 2.47, we have drawn a
demand curve having a value of greater than one.
 |
| Elastic Demand |
At a price OP, OA is demanded. Thus, the total expenditure equals OP ×
OA = rectangle OPBA. As the price drops to OP1, the quantity
demanded rises to OA1. Now, the total expenditure
becomes OP1 × OA1 = rectangle
OP1B1A1.
Since rectangle OP1B1A1 >
rectangle OPBA, demand is said to be elastic. Remember: When price and total
outlay move in opposite directions, demand for the product becomes elastic.
(b) Inelastic Demand:
If the total outlay falls when the price falls, or if the total outlay rises
when the price rises, then demand is said to be inelastic (i.e., Ep< 1). In Fig. 2.48, the initial total outlay is OP1 × OA1 = rectangle
OPBA. Now, if the price falls, the total outlay becomes OP1 ×
OA1 = rectangle OP1B1A1. Fig. 2.48
suggests that the rectangle OPBA is larger than the rectangle OP1B1A1. Hence, demand is inelastic.
 |
| Inelastic Demand |
(c) Unit Elasticity:
Irrespective of variations in demand and price, if the total outlay does
not change, then demand is unit elastic (i.e., Ep = 1). In
Fig. 2.49, we see that at price OP, the total outlay is rectangle OPBA. When the price
declines to OP, the total outlay becomes the area OP1B1A1.
 |
| Unitary Elastic Demand |
Since rectangle OPBA = rectangle OP1B1A1, demand is said
to have a unitary elasticity. The demand curve then looks like a rectangular
hyperbola since the area of all the rectangles formed by the demand curve is
always the same.
(d) Perfectly Elastic Demand:
In this case, at a particular price, any amount is demanded. Fig. 2.45
suggests that at a price OD, the quantity demanded may be OA or OA1 or any amount. More revenue is earned at OA1 than at OA, although the price is kept fixed.
(e) Perfectly Inelastic Demand:
Fig. 2.46 tells us that as price rises,
revenue rises. The vertical straight line demand curve says that whatever the
price, the quantity demanded remains the same.
These relations between elasticity of demand and total outlay (P ×
Q = TR) may be presented here in a tabular form:
 |
| Elasticity and TR |
The relationship between elasticity and total
outlay can also be explained in terms of Fig. 2.50 where we measure the price of
the commodity on the vertical axis and the total outlay on the horizontal axis.
Here ABCD is the total outlay curve.
 |
| Total Outlay curve Elasticity of demand |
In segment
AB, demand is inelastic (Ep< 1), because the price and total outlay move in the same direction. Demand is said to be elastic
(Ep> 1) in the region CD since price and total
outlay move in the opposite direction. A total outlay remains invariant when price
changes in the region BC and demand are unitary elastic.
(6) 2. Point Elasticity Method of Measurement:
When the change in price is infinitesimally
small, the Marshallian method may not provide an accurate estimate of the elasticity of
demand. In that case, a geometrical method may be employed. This method aims at
measuring the elasticity of demand at a particular point on a demand curve.
So long, we tried to calculate the elasticity
over a certain area or segment of a demand curve and the terms elastic, inelastic
and unit elastic had been applied to the whole demand curve. However, such is
not true. It may happen that the demand for a product can be elastic in one
price range and inelastic in another.
In fact, the degree of elasticity varies from
one price range to another. So, it is better to calculate elasticity at a
particular point on a demand curve to have an accurate estimate. This is
explained in terms of Fig. 2.51. (Exam studies)
 |
| Point Elasticity |
The demand curve is DD1. To measure the elasticity of demand at point E, we have drawn a straight line CF tangent to DD1 at point E. Points E and H are very close to
each other. As the price declines from OP1 to OP2, the quantity demanded rises from OM1 to OM2.
The
formula for the elasticity of demand is:
EP = ∆Q/Q ÷ ∆P/P
The
slope of the demand curve is:
∆P/∆Q = M1E /M1F
... ∆Q/∆P = M1F /M1E
The
second component of the elasticity formula is:
P/Q = M1E /OM1
... EP = ∆Q/∆P.
P/Q = M1F/M1E. M1E/OM1= M1F/OM1
Note
that EM1F, CP1E, and COF are similar triangles, the
elasticity of demand curve DD1 at point E can be measured as:
... EP = M1F/OM1 = P1O/P1 = EF/EC
Thus, the elasticity of demand at point E on a curvilinear demand curve DD1 is approximately equal to
EF/EC = lower segment of the demand
curve/upper segment of the demand curve
On the basis of this method of measurement,
one can estimate the elasticity of demand on a linear demand curve, shown in Fig.
2.52.
 |
| The elasticity of Demand (O-∞ ) |
Here, DD1 is a linear demand curve. The elasticity of demand varies from point to point on a demand curve. At point P, the elasticity of demand is PD1/PD. As the
distance between PD1 and PD is the same, it is
unit elastic (i.e., Ep = 1). As we move downwards
along the curve DD1 from the mid-point, say
point P2, elasticity declines. At P2 it is, inelastic (i.e., 0 < Ep< 1) since P2D1< P2D.
At point D1, elasticity is zero since 0/DD1is equal to zero. Further, as we move upwards from
the mid-point, elasticity increases. At P1, it is elastic
(i.e., 1 < Ep< ∞) since P1D1> P1D. On the other hand, at point D, it is infinite
since DD1/0 is equal to infinity. Thus, at lower prices it is
inelastic, and at higher prices it is elastic.
Thus, the elasticity of demand on a straight line demand curve varies from
zero to infinity (0 ≤ Ep ≤ ∞).
3.
Arc Elasticity Method:
For very small movements in price and
quantity, the point elasticity method is an appropriate one. In other words, the point
elasticity method measures (price) elasticity of demand at a particular point
on the demand curve. However, if the price change is somewhat of a larger magnitude
then the geometrical method may give a misleading estimate.
To avoid this problem, elasticity is measured
over an arc of the demand curve. In other words, when we intend to estimate
(price) the elasticity of demand over some portion (i.e., the arc) of the demand
curve, we then have the arc elasticity method. Sometimes we know two prices and two
quantities.
Under the circumstance, the point elasticity
method may not provide a good estimate. What is required in this case is the
average elasticity of two prices and two quantities. This is called ‘arc’
elasticity because it measures the average elasticity on an arc of a demand
curve.
Suppose we have the following information about two prices and
quantities:
 |
| Information about two prices and quantities |
Here changes in both price and quantity are much larger. Using old
price (P1) and old quantity (Q1), one finds the value of
elasticity of demand as:
EP = ∆Q /∆P. P1/Q1 = – 400/100. 60/400 = -6.0
When new price (P2) and new
quantity (Q2) are taken into account, the coefficient becomes
EP = ∆Q /∆P. P2/Q2 = – 400/100. 50/800 = -2.5
Thus, estimation of elasticity in accordance
with the formula for the point elasticity method gives vastly different results. In
other words, since the elasticity of demand varies depending on the base, one
should consider the average price and average quantity demanded to calculate the elasticity of demand.
That is to say, we want to measure average elasticity over an arc
of the demand curve (i.e., mid-point or average, price, and quantity):
In terms of
Fig. 2.53, we want to compute the arc price elasticity of demand over the arc AB of
the demand curve DD1. In other words, we want to
measure elasticity between points A and B. The above formula measures arc
elasticity over the straight line AB.
 |
| Arc Elasticity |
To do so, we
have to take the average prices (OP and OP1) and the average quantities (OM and OM1). Greater the convexity of the
demand curve between A and B, one obtains an almost perfect estimate of
elasticity. Or greater the concavity of the demand curve between points A and
B, the poorer the approximation of measurement of arc elasticity.
As we go on making the price change smaller
and smaller, the arc of the demand curve may vanish or converge to a point. So,
as a special case of arc elasticity, the concept of point elasticity becomes
relevant.
Factors Determining Elasticity
of Demand:
There
are various factors on which elasticity of demand depends:
(a) Nature of the Commodity:
In the first place, it depends on the nature
of the commodity. Commodities that are supposed to be essential or critical to
our daily lives must have inelastic demand since the price change of these
items does not bring about a greater change in the quantity demanded.
But, luxury goods have an elastic demand.
Demand for these goods can be quickly reduced when their prices rise. When their
prices fall, consumers demand these goods in larger quantities. However,
whether a particular commodity is a necessity or a luxury depends on the income,
tastes, and preferences of the consumer.
A particular good may be necessary to someone
having an inelastic demand. The same commodity may be elastic to another consumer.
For instance, owning a TV may be a luxury item for a low-income person. But the
same may be bought as an essential item by a rich person.
(b)
Availability of Substitutes:
Secondly, commodities having a large number of
substitutes must have an elastic demand. Some products, such as Horlicks,
Complan, Viva, Maltova, Milo, etc., have quite a large number of close
substitutes. A change in the price of, say, Horlicks—the prices of other
substitutes remaining constant—will lead a consumer to substitute one beverage
for another.
If the price of Horlicks goes down, buyers
will demand more of it and less of its substitutes. Conversely, demand is
fairly inelastic in the case of those commodities which do not have a large
number of substitutes.
(c)
Extent of Uses:
Thirdly, there are some commodities that can
be used for a variety of purposes. For example, electricity. If the price per unit
of electricity consumed falls, people will reduce their consumption of its
substitutes (e.g., coal, gas, etc.) and increase the consumption of
electricity.
The coefficient of price elasticity of demand, in this case, must be greater than one. On the other hand, when a commodity is used
only for one or two purposes, a price change will have less effect on its
quantity demanded and, therefore, demand will be inelastic.
(d)
Habit Good:
Fourthly, there are some commodities consumed
out of habits and conventions— they have an elastic demand. Even in the face of
rising prices of those commodities or falling income, people will consume those
(such as cigarettes).
For this reason, price elasticity, as well as income elasticity of demand for this type of commodity, is inelastic. Further,
gold ornaments are used in the marriage ceremony rather out of the convention,
though gold prices are rising. When gold is used in this way, its demand
becomes inelastic.
(e)
Time Dimension:
Fifthly, the shorter the time, the lower will be the
elasticity of demand. This is because in the short run satisfactory substitutes
for a product may not be available. Thus, demand for a product in the short run
usually becomes inelastic. Such a commodity will be elastic in the long run
when close substitutes may be produced.
Thus, the response of quantity demanded to a
change in price will tend to be greater (smaller), the longer (shorter) the time span considered. In the long run, there is enough time for adjustments to
be made following a change in price.
(f)
The Importance of being Unimportant:
Sixthly, people often pay little attention to
the price of a product if it constitutes a relatively small part of their
budget. For example, if the fire of railway ticket of a tourist who travels by
rail once a year is increased from Rs. 125 to Rs. 135, then he may not
postpone his journey. This means he is unresponsive to such price hikes and his
demand is inelastic. This is called ‘the importance of being unimportant.
(g)
Durability:
Finally, durable commodities have an elastic
demand. If the price of these goods rises, people will spend less on these
goods. On the other hand, following a fall in the price of durable commodities
(e.g., refrigerators), people demand more of them. In the case of non-durable
commodities, demand is elastic.
Importance
of the Concept of Elasticity of Demand:
The concept of elasticity of demand has both
theoretical and practical value.
The concept may be used in understanding as well as tackling
various economic problems:
(a)
Price Determination:
Use of the concept of elasticity of demand is
required in the price determination of a commodity under different market
conditions. Under perfect competition, in the short run in which supply is absolutely
inelastic price depends upon the elasticity of demand.
If demand suddenly falls—supply remaining
fixed—prices will fall, and, if demand suddenly rises, prices will rise as
output cannot be increased. Again, the stability of prices also depends on the
elasticity of demand and elasticity of supply. If either the demand or the
supply is elastic, fluctuations in prices will be within narrow limits.
Further, if the demand for an agricultural
commodity is inelastic, increased production may spell disaster to the economic
condition of farmers. So the government can adopt measures to save the plight
of the farmers.
A monopoly seller must have knowledge
relating to the elasticity of demand for his product while determining the
price of his commodity.
A monopolist will produce a commodity in the
range of his demand curve where demand is said to be elastic. He will never
produce in the range of the demand curve where demand is inelastic. Obviously, the price determination of the monopoly product will be governed by the elasticity
of demand.
(b)
Wage Determination:
The concept of elasticity of demand is
employed in wage determination. Wages, in modern days, are determined through
the process of collective bargaining. Trade unions will be successful in raising
the wage rate provided labor demand is deemed to be inelastic. This is because
of fact that the degree of substitution between labor and other labor
substituting inputs is less.
Trade union becomes cautious in demanding
higher wage rates when the demand for labor is said to be elastic. Under the
circumstance, the employer may be forced to employ more machines (assumed to be
a cheaper input) than labor.
Anyway, this concept may be employed in analyzing
the problems connected with changes in the conditions of supply. Economists are
interested in knowing the effect on employment in the software industry
following a rise in the wages of workers engaged in this industry. We can
answer this question in terms of Fig. 2.60.
 |
| Demand for and Supply of Computer |
Here DD is a
rather inelastic demand curve whereas demand curve D1D1 is an
elastic one. Both these demand curves intersect the supply curve, SS, at point
E. Thus the equilibrium price is OP and the equilibrium quantity demanded and
supplied is OC.
Let there be an increase in the wages of workers in the computer
industry. Consequently, the supply curve for computers will shift left to S1S1 and the
price will rise to OP2 if the demand curve is assumed
to be DD and to OP1 if the demand curve is D1D1. However, output
contracts more in the case of elastic demand (from OC to OC1). If demand is inelastic, the output will shrink less
(from OC to OC2).
“The general rule is that where demand is elastic, a change in
supply will cause the quantity sold to change rather than price; where demand
is inelastic, price changes rather than the quantity sold. Thus, the trade union
will find it more difficult to obtain a wage increase for its members without
creating unemployment where the elasticity of demand for the product made is
high.” (Jack
Harvey)
(c)
Policy Determination:
The concept of elasticity of demand is of
great importance to a finance minister. While imposing taxes or raising the
existing tax rates, the finance minister must have sufficient knowledge of the
elasticity of demand for the taxed commodity.
If the demand for the product is inelastic,
the purpose of the tax—say revenue-earning—will be served. That is why taxes
are mostly imposed or rates of taxes are raised in the case of commodities
having inelastic demand.
Again, the concept may be used in the
determination of the incidence of a tax. It is easier to shift the burden of taxes
onto the consumers if the product demand is assumed to be inelastic. Further,
whether exportable or importable be taxed or not, the concept of elasticity may
be of great use.
(d)
Exchange Rate Determination:
In international trade too, the concept may
be employed. For instance, as far as exchange rate (i.e., the rate at which one
currency is exchanged for another currency) determination is concerned, the
concept of elasticity of demand is of great importance.
The concept of elasticity of demand is used
to justify whether the devaluation of a currency is the right step in curbing the balance
of payment problems of a country. Devaluation is expected to correct the
balance of payments disequilibrium if the sum of the elasticities of demand for
export and import exceeds unity.
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