— We have seen in chapter three how a change in the price of the good results in change in quantity demanded of that good in the opposite direction (movement along the same demand curve); and how a change in income results in a change in quantity demanded at every price. The same thing is said about the changes in the price of related goods and other non-price determinants.
— The question is now how to measure the magnitude of each change in quantity demanded or supplied as a response to a change in one of the independent variables. The same argument can be applied to the quantity supplied.
— In order to have a better picture of the degree of responsiveness of quantity to a change in one of the independent variable we have to understand the concept of elasticity.
— Elasticity is a measurement of the degree of responsiveness of the dependent variable to changes in any of the independent variables.
— In general elasticity is the percentage change in one variable in response to a percentage change in another variable.
Elasticity =
% ∆ dependent V ariable
% ∆ I ndependent Variable
=
% ∆ Y
% ∆ X
= Elasticity Coefficien t
— Elasticity coefficient includes a sign and a size. We need to interpret the sign and the size of the coefficient.
— Sign shows the direction of the relationship between the two variables. A positive sign shows a direct relationship while a negative sign shows an inverse relationship between the two variables.
Page 1 of 34

— Size illustrates the magnitude of this relationship. In other words, it shows how large the response of the dependent variable to the change in the independent variable.
— Large elasticity coefficient means that a small change in the independent variable will result in a large change in the dependent variable (the opposite is true).
— Elasticity coefficient is a unit-free measure because in calculating the elasticity we use the percentage change rather than the change to avoid the difficulty of comparing different measurement units, and the percentages cancel out.
— Changing the units of measurement of price or quantity leave the elasticity value the same
— Elasticity is an important concept in economic theory. It is used to measure the response of different variables to changes in prices, incomes, costs, etc.
— In addition to price and income elasticities of demand, you may estimate the elasticity with respect to any of the other variables like advertisement and weather conditions. You may even measure the elasticity of production to various inputs or the elasticity of your grades in managerial economics to hours of study.
— This chapter covers some of the important types of elasticities.
Page 2 of 34

d
:
— In the previous chapter we have discussed the movement of the quantity demanded along a given demand curve as a result of change in the price of the good. The direction of the movements reflects the law of demand that shows an inverse (negative) relationship between P and Q d
; the lower the price the greater the quantity demanded.
— When supply increases while demand stays
S 0
P constant, the equilibrium price falls and the equilibrium quantity increases. But does the price fall by a large amount or a little?
And does the quantity increase by large
P 0
P 2
P 1
S 1
D 2 amount or a little? The answer depends on Q 0 Q 2
D
Q 1
1
Q
the responsiveness of quantity demanded to a change in price.
— We are now going to discuss the question of how sensitive the change in quantity demanded is to a change in price. The response of a change in quantity demanded to a change in price is measured by the price elasticity of demand.
— Price elasticity of demand (E d
) is an economic measure that is used to measures the degree of responsiveness of the quantity demanded of a good to a change in its price, when all other influences on buyers’ plans remain the same.
— The price elasticity of demand is calculated by dividing the percentage change in quantity demanded by the percentage change in price.
E d
=
% ∆ Q
% ∆ P d =
∆ Q d
∆ P
/ Q
/ P d
— Example:
Suppose P
1
= 7, P
2
= 8, Q
1
= 11, Q
2
= 10, then
If P from 8 to7, E d
= -0.8
If P from 7 to 8, E d
= -0.64
— You can see that the value of E d
is different depending on direction of change in
P even with the same magnitude.
Page 3 of 34

— To solve this problem we use Arc elasticity
— The arc elasticity of demand is measured over a discrete interval of a demand
(or a supply) curve.
— To calculate the price elasticity of demand (E d
): We express the change in price as a percentage of the average price— the average of the initial and new price, and we express the change in the quantity demanded as a percentage of the average quantity demanded—the average of the initial and new quantity.
— By using the average price and average quantity , we get the same elasticity value regardless of whether the price rises or falls.
E d
=
=
%
%
Q
Q
2
2
∆ Q
∆ P d
−
+
Q
1
Q
1
=
×
∆ Q d
Q avg
∆ P
P avg
P
P
2
2
=
+
−
P
1
P
1
( Q
Q
2
( P
2
P
2
+
2
+
−
Q
Q
1
1
) /
− P
1
P
1
) / 2
2
=
Q
P
2
2
−
−
Q
P
1
1
=
×
P
2
Q
2
Q
2
Q
2
P
2
P
2
− Q
1
+
−
Q
1
P
1
+ P
1
+
+
P
1
Q
1
= −
Where,
Q
1
= the original (the old) quantity demanded, Q
2
= the new quantity demanded
P
1
= the original (the old) price, P
2
= the new price
Q avg
= the average quantity, P avg
= the average price
— The formula yields a negative value, because price and quantity move in opposite directions (law of demand). But it is the magnitude, or absolute value, of the measure that reveals how responsive the quantity change has been to a price change. Thus, we ignore the minus (negative) sign and use the absolute value because it simply represents the negative relationship between P and Q d
— Example:
Suppose P
1
= 7, P
2
= 8, Q
1
= 11, Q
2
= 10, then
E d
=
10
10
−
+
11
11
÷
2
8
8
−
+
7
7
2
= − 0 .
71
Now how to interpret the elasticity coefficient? What E d
= - 0.71 means?
Page 4 of 34

It means that if the price of the good increases (decreases) by 1% the quantity demanded of the good decreases (increases) by 0.71%
— Example:
Price($) Q d
(bushels of Wheat)
8 20
40
60
80
What is the E d if P increases from 6 to 7?
E d
=
40
60
−
+
60
40
×
7
7
+
−
6
6
= − 2 .
6
A 1% increase in P would result in a 2.6% decrease in Q d
— Example:
If a rightward shift in the supply curve leads to an increase in Q d
by 10 % as a result of a decrease in P by 5%. a. Calculate E d
.
E d
=
%
%
∆ Q
∆ P d =
10
− 5
= − 2 b. Interpret E d
E d
= 2 means that a decrease in P by 1% results in an increase in Q d
by 2% c. What would be the increase in Q d
if P decreases by 4%?
Since E d
=
%
%
∆ Q
∆ P d , then % ∆ Q d
= (
E d
) ( % ∆ P ) = (-2) (-4%) = + 8 %,
Thus, a decrease in P by 4% results in an increase in Q d
by 8% d. What would be the decrease in P if Q d
increases by 6%
Since E d
=
%
%
∆ Q
∆ P d , then
%
∆
P
=
% ∆ Q d
E d
=
6 %
− 2
= − 3 % ,
Thus, if Q d
increases by 6%, P decreases by 2%
— However, if we want to measure E d
at a single point rather than between two points we should use point elasticity of demand
Page 5 of 34

— The point elasticity of demand measured at a given point of a demand (or a supply) curve. It is the price elasticity for small changes in the price or for changes around a point on the demand curve.
ε d
=
% ∆ Q d
% ∆ P
= dQ d
Q dP
P
= dQ dP
×
P
Q
— The point elasticity of a linear demand function can be expressed as:
ε d
=
∆ Q
∆ P
×
P
Q
— Notice that the first term of the last formula is nothing but the slope of the demand function with respect to the price.
— Having this fact in mind you will easily remember that:
1. The value of the elasticity; varies along a linear demand curve, as P/Q change even though, the slope is constant.
2. The value of the elasticity varies along a nonlinear demand curve as both terms in the above equation varies from as we move along a nonlinear demand curve.
3. The value of the elasticity is constant along the demand curve only in the case of an exponential function in the form:
Q d
= aP -b , where the price elasticity of demand equals –b, which can be proved as follows:
ε d
= dQ dP
×
P
Q
= − baP − b − 1 ×
P aP − b
= − b
— This type of nonlinear equations can be expressed in linear form using logarithm log Q = log a – b (log P)
— Example:
Calculate the elasticity of demand using the following equation:
Q d
= 50P -3 ,
Page 6 of 34

ε d
= dQ dP
×
P
Q
= − 150 ( P − 4 ) ×
P
50 P − 3
=
− 150
P 4
×
P × P
50
3
=
− 150
50
P 4
×
P 4
= − 3
— Example:
Given Q d
= 2000 - 20P, Find ε d
when P=70 d
= 2000 – 20(70) = 2000 – 1400 = 600
ε d
= dQ dP
×
P
Q
= ( − 20 ) ×
70
600
= − 2 .
33
— Example:
If Q d
=200 - 300P + 120I + 65T – 250P c
+ 400P s
, and if I=10, T=60, P c
=15, P s j
=10, Find: a. E d
for the price range $10 and $11 b. Ε d
at P =$10
Q d
= 200 - 300P + 120(10) + 65(60) – 250(15) + 400(10)
= 200 - 300P + 1200 + 3900 – 3750 + 4000
Q d
= 5550 – 300P a. E d
for the price range $10 and $11 (Arc Elasticity)
At P=10, Q d
= 5550 – 300(10) = 2550
At P=11, Q d
= 5550 – 300(11) = 2250
E d
=
2250 − 2550
11 − 10
×
11 + 10
2250 + 2550
= − 1 .
31 b. Ε d
at P =$10 (Point Elasticity)
ε d
= dQ dP
×
P
Q
= ( − 300 ) ×
10
2550
= − 1 .
2
— Example:
Assume a company sells 10,000 units of its output at price of $100.
Suppose competitors decrease their price and as a result the company’s sale decrease to 8,000 units. E d
in this price-quantity range is -2. What must be the price if the company wants to sell the same number of units before its competitors decrease their price?
Using E d
=
Q
2
P
2
−
−
Q
1
P
1
×
P
2
Q
2
+
+
P
1
Q
1
= − 2
Page 7 of 34

Q
1
=8000, Q
2
= 10000, P
1
= 100, P
2
=?
−
=
2 =
10 , 000
P
2
−
− 8 , 000
100
(
2 , 000 ( P
2
P
2
− 100
+ 100 )
)( 18 , 000 )
×
=
P
2
10 , 000
+
+
2
18 ,
, 000
100
P
000 P
2
2
8 , 000
=
(
( 10
P
2
, 000
−
−
100
8 , 000
)( 10 ,
)( P
000
2
+
+ 200 , 000
− 1 , 800 , 000
+ 100 )
8 , 000 )
For simplification, divide numerator and denominator of left-hand side by 1000
− 2 =
2 P
2
18 P
2
+
−
200
1 , 800
− 2 ( 18 P
2
− 1800 ) = 2 P
2
+ 200
-36P
2
+ 3600 = 2P
2
+ 200
-38P
2
= -3400
P
2
= -3400/-38 = 89.5
TR
1
= 100 X 8,000 = 800,000
TR
2
= 89.5 X 10,000 = 895,000
Since TR
2
> TR
1
Ö TR Ö it is good to cut price but π is not known since we do not the TC
— Example:
A 50% decrease in the price of salt caused the quantity demanded to increase by10%. Calculate the price elasticity of demand for salt, explain the meaning of your result and tell if the demand for salt is elastic or inelastic?
E d
= 10/50 = 0.20 which means a10% change in price results in a 2% Change in the quantity demanded in the opposite direction.
— Example:
Q d
= 50 – P 3 , is the demand curve equation for apple, calculate the price elasticity of demand when P =3 and Q = 9.
ε d
= dQ dP
×
P
Q
= − 3 ( 3 2 ) ×
3
9
= − 27 ×
1
3
= − 9
Page 8 of 34

— Using absolute value of E d
, we differentiate between five categories of elasticity that range between zero and infinity.
1. Relatively Elastic Demand (E d
> 1)
If E d
=
% ∆ Q
% ∆ P d > 1 ⇒ % ∆ Q d
> % ∆ P ⇒ demand is elastic.
Consumers are very responsive to changes in P. Demand curve is flatter ⇒ 1% change in P results in a more than 1% change in Q d
(in the opposite direction).
(if E d
= 2 that means if P by 1% Qd by 2%.)
Examples of elastic goods: cars, furniture, vacations, etc.
2. Relatively Inelastic Demand (E d
< 1)
If E d
=
% ∆ Q
% ∆ P d < 1 ⇒ % ∆ Q d
< % ∆ P ⇒ demand is inelastic.
Consumers are not very responsive to changes in P. Demand Curve is steeper ⇒ 1% (or ) in P results in a less than 1%
Examples of inelastic goods: medicine, food, etc.
— If the price elasticity is between 0 and 1, demand is inelastic.
(or ) in Qd (if E d
= 0.70 that means if P by 1% Q d
by 0.7%.) or (if P by
10% Q d
by 7%.)
P
More Elastic
More Inelastic
Q d
Page 9 of 34

3. Unitary Elastic Demand (E d
= 1)
If E d
=
% ∆ Q
% ∆ P d = 1 ⇒ % ∆ Q d
= % ∆ P ⇒ demand is
P unit-elastic
1% in P results in a 1% in Q d
4. Perfectly Elastic Demand (E d
= ∞ )
If E d
=
% ∆ Q
% ∆ P d =
⇒ demand is perfectly elastic
P
0
S 1
D
S 2
Q d
D
⇒ horizontal demand curve ⇒ the same price is
P charged regardless of Q d
(perfect competition).
Any price increase would cause demand Q d to fall to zero. Shifts in supply curve results in no change in price. Examples: identical products sold side by side, agricultural products.
5. Perfectly Inelastic Demand (E d
= 0)
If E d
=
% ∆ Q d
% ∆ P
= 0 ⇒ demand is perfectly inelastic
⇒ a vertical demand curve ⇒ demand is
P
D
S 1
S 2 completely inelastic. Q d
remains the same regardless of any change in price. Shifts in supply Q d
Q d curve results in no change in Q d
. Examples: medicine of heart diseases or diabetes such as insulin A good with a vertical demand curve has a demand with zero elasticity.
— We conclude from the five categories above that the more flatter is the demand curve the more elastic is the demand and the more steeper is the demand curve the more inelastic is the demand
Page 10 of 34

Elasticity along straight line demand curve
— Elasticity of demand (E d
) is not the slope of the demand curve.
Slope =
∆ P
∆ Q d
,
Elasticity: E d
=
%
%
∆ Q
∆ P d
— For a straight-line (linear) demand curve the slope is constant (i.e., the slope is the same at every point along the curve). It is equal to the change in price over the change in quantity demanded.
— Although the slope is constant, price elasticity varies along a linear demand curve.
P
E d
= ∞
E d
> 1
E d
=1
E
E d d
< 1
= 0
Q
— The following equation shows the relationship between the elasticity and the slope of a straight line demand curve
E d
=
%
%
∆ Q
∆ P d =
∆ Q d
∆ P
/ Q
/ P d =
∆ Q d
Q d
×
P
∆ P
=
∆ Q
∆ P d ×
P
Q d
=
1 slope
×
P
Q d
Since the slope of straight-line demand curve is constant,
1 slope
is also constant Ö elasticity varies as a result of variation of
P
Q d
; i.e. straight-line demand curve elasticity depends on the values of Q d
and P
Page 11 of 34

1. When P = 0, E d
= 0 (perfectly inelastic)
2. When Q = 0, E d
= ∞ (perfectly elastic)
3. E d
increases as we move upward along a straight-line demand curve (from the inelastic range to the elastic one) (as P ↑ and Q ↓ )
4. E d
decreases as we move downward along the straight-line demand curve
(as P ↓ and Q ↑ ).
— Thus, along downward sloping demand curve, demand is elastic when price is high, inelastic when price is low and unit-elastic at the midpoint of the demand curve.
d
— Managers of profit maximizing firms are usually concern with the best pricing strategy.
— There is a relationship between the price elasticity of demand and revenue received.
— Total revenue (TR) equals the total amount of money a firm receives from the sales of its product
— TR = P X Q.
— TR is affected by changes in both P and Q d
. But as we know by now the law of demand implies that an increase in P will result in a decrease in Q d.
— Thus, an increase in P may or may not lead to greater TR. This depends on which effect is the largest, price effect or the effect of quantity demanded.
— The size of the price elasticity of demand coefficient, tells us which of these two effects is largest. o
If demand is elastic (E d
>1) ⇒ % ∆ Q d
> % ∆ P
ƒ 10 ↑ in P results in more than 10 % ↓ in sales ⇒ TR ↓
ƒ 10 ↓ in P results in more than 10 % ↑ in sales ⇒ TR ↑ o
If demand is inelastic (E d
<1) ⇒ % ∆ Q d
< % ∆ P
ƒ 10 ↑ in P results in less than 10 % ↓ in sales ⇒ TR ↑
Page 12 of 34

ƒ 10 ↓ in P results in less than 10 % ↑ in sales ⇒ TR ↓ o
If demand is unit elastic (E d
=1) ⇒ % ∆ Q d
= % ∆ P
ƒ 10 ↑ in P results in 10 % ↓ in sales ⇒ TR does not change
ƒ 10 ↓ in P results in 10 % ↑ in sales ⇒ TR does not change
P
E>1
↑ ↓
TR
↓ ↑
E<1
↑
E = 1
-
↓ -
— The rises or falls in TR as price increases (or decreases) depend on E d
. Hence,
TR varies along a linear downward sloping demand curve.
— In order to increase total revenues, the manager should increase prices of products that have inelastic demands, and should reduce prices of products that have elastic demands.
Graphical Illustration of the relationship between TR, P, MR, and E d
— When the price is equal to zero, as it is where demand intersects the quantity axis, or when the quantity demanded equals zero, as it is when the demand intersects the price axis, total revenue must equal zero. Thus, when a firm either sells none of its goods or sells its good for a zero price, they bring in zero revenue.
— If the firm moves away from either of these intersection points then their total revenue must increase. Total revenue continues to rise as the firm moves away from the intersections until it reaches a maximum at the midpoint.
— For a price increase, total revenue rises when demand is inelastic and falls when demand is elastic.
— With a linear DC, TR increases and then decreases when P increases (or when
P decreases)
— To max TR, set price at unitary elastic price
Page 13 of 34

— Marginal revenue is the revenue generated by selling one additional unit of the product
— It is the change in total revenue resulting from changing quantity by one unit.
MR =
∆ TR
∆ Q
— For a straight-line demand curve the marginal revenue curve is twice as steep as the demand.
— To sell more, often price must decline, so MR is often less than the price.
— When E
P
= ∞ . MR = P.
— At the point where marginal revenue crosses the X-axis, the demand curve is unitary elastic and total revenue reaches a maximum.
— A product maximizing manager will expand product as long as the additional unit produced adds more to TR than adding to TC; i.e., expand production as long as MR > MC and M π is positive.
— The optimal production reached when MR = MC and M π = 0
— Units produced over and above the optimal level will have negative M π because for these units MR < MC
— When TR is maximized, MR = 0 and MC (positive value) is definitely greater than MR.
— The conclusion here is that if the manager maximizes TR the firm will make less than max profit.
E d
Demand MR P TR
E d
>1 Elastic MR >0
E d
< 1 Inelastic MR < 0
E d
= 1 Unit elastic MR = 0 - Max.
Page 14 of 34

∞
P
E d
> 1
P *
0
TR
E d
= 1
MR
E d
< 1
0
Q
E > 1;
MR > 0
E = 1;
MR=0
E < 1;
MR< 0
TR
0
Q *
— The above graph shows that:
Q o
E d
>1 ⇒ Demand elastic ⇒ MR>0 ⇒ P and TR move in the opposite direction (negative relationship) o
E d
< 1 ⇒ Demand inelastic ⇒ MR < 0 ⇒ P and TR move in the same direction (positive relationship) o
E d
= 1 ⇒ Demand unit elastic ⇒ MR = 0 ⇒ TR is maximum
— Example:
If a company wants to ↑ its TR when E d
= 0.75, it should ↑ P
— Example:
If a company wants to ↑ its TR when E d
= 1.5, it should ↓ P
Page 15 of 34

— Example:
If E d
= 1, an ↑ in P by 15%, ⇒ Q d
↓ by 15%, ⇒ TR will not change
— Example:
Given Q d
= 20 – 2P,
Find the price range for which a. D is elastic b. D is inelastic c. D is unit elastic d. If the firm increases P to $7, is TR increasing or decreasing?
Answer:
Q d
= 20 – 2P ⇒ P = 10 – 0.5Q
0.5Q
2
MR = 10 –Q
When MR = 0, 10 – Q =0 ⇒ Q = 10 and P = 10 – 0.5(10) = 5
At this P and Q, E d
= 1 a. D is elastic for price range above 5 (or Q less than 10) b. D is inelastic for price range below 5 (or Q above 10) c. D is unit elastic at P = 5 and Q = 10 d. If the firm chooses to increase the price to $7 and 7 is in the elastic part,
TR will be decreasing
— Example:
Given Q d
= 150 – 10P, find Q and P at which ε d
= -1
Since Q d
= 150 – 10P ⇒ P = (150/10) – (1/10) Q = 15 – 0.1Q ⇒
TR = 15Q – 0.1Q
2
MR = dTR/dQ = 15 – 0.2Q
(Note that the slope of MR equation is twice the slope of the inverse demand equation).
TR reaches maximum when MR = 0 (Q that max TR is the same as Q that makes MR= 0
Set MR =0 ⇒ 15 – 0.2Q = 0 ⇒ Q =15/0.2= 75 and P = 15 – 0.1(75) = 7.5
Page 16 of 34

So, at Q=75 and P=7.5
MR = 0 and ε d
= dQ dP
×
P
Q
= ( − 10 )
⎛
⎝
7 .
5
75
=
− 75
75
= − 1 Ö TR is maximized
— Find P and Q at which E d
>1 and E d
<1
E d
>1 at P > 7.5, and Q < 75
E d
<1 at P < 7.5, and Q > 75
— Example:
E d
10 1 10 --- --
5 6 30 0 1.00
E d
> 1 (elastic demand
E d
= 1 (unitary elastic), TR is max and MR is zero
E d
< 1 (inelastic demand
— Exercise:
From the graph to the right a. calculate E d b. When P increases what would happen to TR?
E d
= 1 and TR remains the same.
The area (0-5-a-20) = the area (0-4-b-25)
Page 17 of 34
P
5
4
0
2 a b
2
D
Q

MR and Elasticity
— The relationship between Marginal Revenue (MR), price (P), and price the elasticity of demand (E d
), can be stated using the formula:
MR = P
⎣
⎢
⎡
1 +
⎝
⎜⎜
⎛ 1
ε d
⎠
⎟⎟
⎞
⎦
⎥
⎤
— Clearly the equation shows that if E d
< -1, MR must be positive: if E d
> -1, MR must be negative; and if E d
= -1, MR must be zero.
— To proof the relationship between MR and E d
, (for your information only)
We know that TR = P X Q
MR = dTR dQ
= d dQ
( PXQ ) = PX dQ dQ
Multiply the second term by P/P
+ Q dP dQ
= P + Q dP dQ
MR = p +
P
P
XQ dP dQ
But
= P ( 1 +
1
P
XQ dP dQ
) = P ( 1 +
Q
P
X dP dQ
)
ε d
=
So ,
1
ε d dQ dP
=
X
P
Q dP dQ
X
Q
P
Thus , MR = P (1 +
1
ε d
)
— If P = 20 and ε d
= -4 find MR
MR = 20
⎣
⎢
⎡
1 +
⎝
⎜
⎛
−
1
4 ⎠
⎟
⎞
⎦
⎥
⎤
MR = 20 (1 - 0.25)
= 20 (0.75) = 15
Page 18 of 34

— Demand for some goods and services is elastic whereas for other goods and services is inelastic.
— Elasticity does not only differ from one good to another but also it may differ for a particular product at different prices.
— The elasticity of demand is computed between points on a given demand curve.
Hence, the price elasticity of demand is influenced by all determinants of demand.
— We can summarize the main factors that affect E d
as:
1. Availability and closeness of Substitutes
— When a large number of substitutes are available, consumers respond to a higher price of a good by buying more of the substitute goods and less of the relatively more expensive one. So, we would expect a relatively high price elasticity of demand for goods or services with many close substitutes, but would expect a relatively inelastic demand for goods with few close substitutes.
— Example:
Dell computer, for example, has many substitutes. So its price elasticity of demand is highly elastic because the consumers can easily shift to the other substitutes if the price of Dell computer increases
— Example:
Pepsi and Coke are very close substitutes. So, the availability of Pepsi makes the price elasticity of demand of Coke very high. Any increase in the price of
Coke will result in a huge shift of consumers to Pepsi’s purchase.
— Furthermore, the broader the definition of the good, the lower the elasticity since there is less opportunity for substitutes. The narrower the definition of the good the higher the elasticity, since there are more substitutes.
Page 19 of 34

— Example:
A buyer who likes Japanese cars and has relative preference for Toyota products may have higher price elasticity of demand for Camry than the price elasticity of demand for Toyota cars. His price elasticity of demand for Toyota cars is higher than the price elasticity of demand for Japanese cars. And his price elasticity of demand for Japanese cars is higher than the price elasticity of demand for cars in general. Why?
— Example:
Consider the relative price elasticity of demand for a good such as apples compared to a good such as fruits. What is the difference between apples and fruits? Apples are, of course, a fruit but so are lots of other goods as well.
Hence, more substitutes exist for apples than exist for the broader category of fruits. We have already determined that as the number of substitutes increase then so does that goods relative price elasticity of demand.
2. Proportion of total expenditures to Income
— The higher the proportion of income spent on the good, the higher the elasticity of demand. Expensive good take a greater proportion of an individual’s income and expenditures than the inexpensive goods; so expensive good are more elastic.
— Example:
Consider the price elasticity of demand for a good such as a pen compared to that for a good such as a car. One of the big differences between these two types of goods is that the price of a pen is small as a proportion of the income while the price of a car is typically a large percentage of income. Doubling the price of pens will not, therefore, have a big impact on one’s income. However, doubling the price of cars will have a large impact on one’s income.
Thus, the demand for high-priced goods such as cars tends to be more price elastic than the demand for low-priced good such as bread or salt.
Page 20 of 34

3. The Time Elapsed Since Price Change (Length of Time)
— Over time, demand tends to be more elastic because time is available to search for substitutes for a good when a longer time period is considered.
— Example:
Consider what happens as the price of a good such as gasoline doubles. People respond to the higher price by decreasing their use of gas. However, in just a short time period it is more difficult to do this than in a longer period. Essentially, the longer the time period people have to adjust, the more alternatives they can find to reduce their consumption of gas. For example, they might be able to move closer to work, buy a more fuel-efficient car, use public transportation, arrange with friends to go in on car, etc.
— Thus, in short run, the response is very limited ⇒ demand is less elastic; over time, demand tends to be more elastic because time is available to search for substitutes and adjust to the new situation
4. Necessary vs. Luxury goods
— Demand for necessary goods, goods that are critical to our everyday life and have no close substitute, is relatively inelastic (food, medicine).
— Demand for luxury goods, goods with many substitutes and we would like to have but are not likely to buy unless our income jumps or the price declines sharply, is relatively elastic (cars, traveling to foreign countries for vacation).
— Nevertheless, what is one person's luxury is another person's necessity
5. Durability of the product:
— The demand for durable goods (such as cars) tends to be more price elastic than the demand for non-durable goods, such as foods.
— This is because durable goods have the possibility of postponing purchase, have the possibility of repairing the existing ones, and the possibility of buying used ones.
Page 21 of 34

— As a result a small percentage change in the prices of durable goods cause larger percentage change in the quantity demanded.
The Elasticity of Derived Demand:
— The demand for intermediate goods (goods used in producing the final good) is called a derived demand , since the demand for these goods is directly associated with the demand for the final good. The derived demand for a specific intermediate good will be more inelastic:
1. The more essential is that good to the production of the final good.
2. The more inelastic the demand for the final good.
3. The smaller the share of that good in the cost of producing the final good.
4. The shorter the time passes after the price changes.
Page 22 of 34

INCOME ELASTICITY OF DEMAND
— The income has an impact upon demand.
— Recall that the relationship between income and demand may be direct or inverse, depending on whether the good is a normal good or an inferior good.
— Income Elasticity of Demand (E
Y
) measures the responsiveness of Q d
of a good to a change in income. It is the percentage change in quantity demanded divided by percentage change in income.
— It may be calculated across and arc for big changes in income using the following formula:
E
Y
=
% ∆ Q
% ∆ Y d =
O
2
Q
2
−
+
Q
1
Q
1
2
÷ y
2
Y
2
−
+
Y
1
Y
1
2
=
O
2
Q
2
− Q
1
+ Q
1
÷
Y
2
Y
2
−
+
Y
1
Y
1
=
O
2
Q
2
− Q
1
+ Q
1
×
Y
2
Y
2
+ Y
1
− Y
1
— For small changes in income using the point elasticity:
E
Y
=
% ∆ Q
% ∆ Y d =
⎝
⎜⎜
⎛
⎝
⎜
⎛ dQ
Q d dY
Y d
⎠
⎟⎟
⎞
⎠
⎟
⎞
= dQ d dY
X
Y
Q d
— E
Y
> 1 ⇒ Demand is income elastic and the good is normal and luxury. % ∆ Q d
> % ∆
Y
(A small percentage change in income results in a large percentage change in Q d
)
— 0 < E
Y
< 1 ⇒ Demand is income inelastic and the good is normal and necessary. % ∆ Q d
< % ∆ Y (A large percentage change in income results in a small percentage change in Q d
)
— E
Y
< 0 (negative) ⇒ the good is an inferior good.
— Examples:
Given Q
A
= 3 – 2P
A
+1.5Y + 0.8P
B
– 3P
C
If P
A
= 2, Y=4, P
B
=2.5, P
C
=1
Calculate E
Y dQ
A
/dY = 1.5, Q
A
= 3 – 2(2) +1.5(4) + 0.8(2.5) – 3(1) = 4
E
Y
=
∆ Q
∆ Y
A X
Y
Q
A
= 1 .
5 X
4
4
= 1 .
5 > 1 ⇒ Normal (luxury) good
Page 23 of 34

— Example:
The manager of Global Food Inc heard the news that government plans to give a 15% raise to all its employees who represent 70% of the labor force of the country. If the estimated income elasticity of demand for global food products is
0.85, find the expected change in the demand for the firm products.
% U Y = 15% X 70% =10.5%
E
0 .
Y
=
85 =
%
%
∆ Q
∆ Y d
% ∆ Q
10 .
5 d
=
⇒ % U Q d
= 10.5 X 0.85 = 8.9%
— Examples:
1. If people’s average income increased from BD300 to BD350 per month and as a result their purchase of orange juice increased from 5000 liters to 5800 liters per month, Calculate E
Y
E
Y
= 0.96.
The increase in income by 10% results in an increase in the Q d
of orange juice by 9.6% .Orange juice is a normal, necessary good. People buy more of it when their income increases.
2. If people’s average income increased from BD300 to BD350 per month and as a result their purchase of used mobiles decreased from 400 units to 300 units per month, Calculate E
Y
E
Y
= - 1.86.
The increase in income by 10% results in a decrease in the Q d
of used mobiles by 18.6%. Since the sign is negative this means the mobile is an inferior good. People buy less of it when their income increases.
3. If income ↑ by 5% and Q d
↑ by 10% ⇒ E
Y
= +2 ⇒ normal, luxury good
4. If income ↑ by 5% and Q d
↓ by 10% ⇒ E
Y
= -2 ⇒ inferior good
Page 24 of 34

CROSS ELASTICITY OF DEMAND
— The decision to buy a good depends not only on its price but also on the price and availability of other goods (substitutes or complements).
— We know that as the price of related good changes, the demand for the good will also change.
— What we want to know here is how much will quantity demanded rise or fall as the price of the related good changes. That is, how elastic is the demand curve in response to changes in prices of related goods.
— Cross elasticity measures the responsiveness of Q d
of a particular good to changes in the prices of its substitutes and its complements.
— If X and Y are two goods, the cross elasticity of demand is the percentage change in Q d
of good X to the percentage change in price of good Y
— The arc elasticity formula:
E
R
=
% ∆ Q x
% ∆ P y
=
Q
2 x
Q
2 x
−
+
Q
1 x
Q
1 x
2
÷
P
2 y
P
2 y
− P
1 y
+ P
1 y
2
=
Q
2 x
Q
2 x
− Q
1 x
+ Q
1 x
×
P
2 y
P
2 y
+
−
P
1 y
P
1 y
— For small price changes, the cross elasticity may be calculated as a point elasticity using the following formula:
E
R
=
% ∆ Q x
% ∆ P y
=
⎝
⎜⎜
⎛
⎜
⎜
⎝
⎛ dQ x
Q dP
P y x y
⎠
⎟⎟
⎞
⎟
⎟
⎠
⎞
= dQ x dP y
X
P y
Q x
— When the cross elasticity of demand has a positive sign, the two goods are substitute goods.
— When the cross elasticity of demand has a negative sign, the two goods are complementary goods
— When E
R
=0 ⇒ no relation between P
X and D
Y
— The size of cross elasticity of demand coefficient is primarily used to indicate the strength of the relationship between the two goods in question.
Page 25 of 34

— Two products are considered good substitutes or complements when the coefficient is larger than 0.5 (in absolute terms)
— Example:
If P
1x
= 20, P
2x
= 30
Q
1y
= 200 Q
2y
= 250
Q
1z
= 150 Q
2z
= 140
Determine the relationship between X and Y, and the relationship between X and Z
E
R(xy)
= 0.556 ⇒ X and Y are strong substitutes
E
R(xz)
= - 0.172 ⇒ X and Z are mild complements
— Example:
Given Q
A
= 3 – 2P
A
+1.5Y + 0.8P
B
– 3P
C
If P
A
= 2, Y=4, P
B
=2.5, P
C
=1
Calculate a. E
R between A and B b. E
R between A and C
Solution, dQ
A
/dP
B
= 0.8, dQ
A
/dP
C
= -3,
Q
A
= 3 – 2(2) +1.5(4) + 0.8(2.5) – 3(1) = 4 a.
E
R
= dQ
A dP
B
X
P
B
Q
A
=
0 .
8 X
2 .
5
=
0 .
5
⇒ Strong Substitutes
4 b.
E
R
= dQ
A dP
C
P
C
X
Q
A
= −
3 X
1
4
= −
0 .
75
⇒ Strong Complements
— Example:
Nissan Maxima and Toyota Camry are competing substitutes in the market for small passenger cars. The Nissan Manager would like to predict the negative effect of Toyota’s 15% discount on Camry during Ramadhan. From previous years, Nissan manager has an estimate of the cross elasticity of 2.0 between these two brands.
Page 26 of 34

Given this information, calculate the expected effect on Nissan sales of Maxima cars.
Solution
E
R
2
=
=
%
∆
Q
Mamima
%
∆
P
Camry
%
∆
Q
Maxima
−
15 %
=
⇒ % U Q
Maxima
= 2 X (-15%) = -30%
⇒ Maxima sales are expected to drop by 30% as a result of Toyota discounts
— Exercise
Find the point price elasticity, the point income elasticity, and the point cross elasticity at P=10, Y=20, and P
R
=9, if the demand function were estimated to be:
Q d
= 90 - 8P + 2Y + 2P
R
Is the demand for this product elastic or inelastic? Is it a luxury or a necessity?
Does this product have a close substitute or complement? Find the point elasticities of demand.
Solution
First find the quantity at these prices and income:
Q d
= 90 - 8P + 2Y + 2P
R
= 90 -8(10) + 2(20) + 2(9) =90 -80 +40 +18 = 68
E d
= ( ∂ Q/ ∂ P)(P/Q) = (-8)(10/68)= -1.17 which is elastic
E
Y
= ( ∂ Q/ ∂ Y)(Y/Q) = (2)(20/68) = +.59 which is a normal good, but a necessity
E
R
= ( ∂ Q x
/ ∂ P
R
)(P
R
/Q x
) = (2)(9/68) = +.26 which is a mild substitute
Page 27 of 34

NET OR COMBINED EFFECT OF ELASTICITY
— To find the total effect of change in more than one variable on the quantity demanded, we may combine the effect of price elasticity of demand (E d
), income elasticity of demand (E
Y
), and cross elasticity of demand (E
R
), and or any other elasticity, thus calculating the net effect of theses changes.
— Most managers find that prices and income change every year.
— By definition we know that: o
E d
= % ∆ Q/ % ∆ P ⇒ % ∆ Q = E d
(% ∆ P) o
E
Y
= % ∆ Q/ % ∆ Y ⇒ % ∆ Q = E
Y
(% ∆ Y) o
E
R
= % ∆ Q/ % ∆ P
R
⇒ % ∆ Q = E
R
(% ∆ P
R
)
— If you knew the price, income, and cross price elasticities, then you can forecast the percentage changes in quantity.
— Combining these effects (assuming independent and additive functions) we have:
% ∆ Q = E d
(% ∆ P) + E
Y
(% ∆ Y) + E
R
(% ∆ P
R
)
Where, P is price, Y is income, and P
R
is the price of a related good.
— Example:
LTC has a price elasticity of -2, and an income elasticity of 1.5 for its laptops.
The cross elasticity with another brand is +.50 a. What will happen to the quantity sold if LTC raises price 3%, income rises
2%, and the other brand companies raises its price 1%? b. Will Total Revenue for this product rise or fall?
Solution a. % ∆ Q = E d
(% ∆ P) + E
Y
(% ∆ Y) + E
R
(% ∆ P
R
)
= -2 (3%) + 1.5 (2%) +0.50 (1%) = -6% + 3% + 0.5% = -2.5%.
We expect sales to decline. b. Total revenue will rise slightly (about + 0.5%), as the price went up 3% and the quantity of laptops sold falls 2.5%.
Page 28 of 34

— Example:
AMANA Company is planning to increase its price by 10% next year. At the same period; it is estimated that disposable income will increase by 6%. The company is currently selling two million units.
If the estimates of elasticities of next period is E d
= -1.3 and E
Y
= 2, what would be the quantity demanded next period?
Solution
% U Q
1
= E d
(% U P) + E
Y
(% U Y)
Q
2
= Q
1
+ % U Q
1
XQ
1
= Q
1
+ (1 + % U Q
1
)
= Q
1
+ [1 + E d
(% U P) + E
Y
(% U Y)]
= 2,000,000 [1 + (-1.3) (10%) + (2) (6%)]
= 2,000,000 (1 – 0.13 + 0.12)
= 2,000,000 (1 – 0.01)
= 2,000,000 (0.99) = 1,980,000
The effect of price increase is more than the effect of the increase in income.
— Example:
If E d
= -1.8, E
Y
= 2.2, E
R
= 1.5 a. By how much Q d changes if P increases by 8%, income increases by 5%, and a substitute price increases by 6%? b. What is the new Q, if the initial sale is 20,000?
Solution a. % U Q = -1.8 (8%) + 2.2 (5%) +1.50 (6%) = -0.144 + 0.11 + 0.09
= 0.056 = 5.6% b. Q
2
= Q1 (1+% U Q)
= 20,000 (1+0.056)
= 20,000(1.056)
= 21,120
Page 29 of 34

— When demand increases, the equilibrium
price rises and the equilibrium quantity increases. But does the price rise by a large or a little amount? And does the quantity increase by large or a little
P 1
P 2
P 0
D 0
S 1
D 1
S 2 amount? The answer depends on the responsiveness of quantity supplied to a
Q 0 Q 1 Q 2 change in price.
— Elasticity of supply measures the responsiveness of quantity supplied to a change in the price of a good when all other influences on selling plans remain the same.
— Arc elasticity of supply
E s
=
% ∆ Q s
% ∆ P
=
∆ Q s
Q avg
∆ P
P avg
=
(
(
Q
Q
2
P
2
2
+
−
Q
Q
1
− P
1
)
1
/
P
2
+ P
1
) / 2
2
=
Q
2
Q
2
P
2
P
2
− Q
1
+
−
Q
1
P
1
+ P
1
=
Q
2
Q
2
−
+
Q
1
Q
1
×
P
2
P
2
+ P
1
− P
1
= +
— Point elasticity of Supply
— ε s
=
% ∆ Q
% ∆ P s = dQ s
Q dP
P
= dQ s dP
×
P
Q s
— Elasticity coefficient is positive to show the direct relationship between P and Q s
— Example:
Suppose you have the following data
P
1
=20
P
2
=30
Q
Q
1
2
=10
=13
E s
=
13
13
−
+
10
10
2
÷
30
30
−
+
20
20
2
= 0 .
65
Page 30 of 34

Supply Elasticity Categories
1. If E s
> 1; % ∆ Q s
> % ∆ P (if P ↑ by 1%, Q s
↑ by more than 1%) ⇒ supply is elastic
2. If E s
< 1; % ∆ Q s
< % ∆ P (if P ↑ by 1%, Q s
↑ by less than 1%) ⇒ supply is inelastic
3. If E s
= 1; % ∆ Q s
= % ∆ P (if P ↑ by 1%, Q s
↑ by 1%) ⇒ supply is unit elastic
4. If E s
= ∞ , supply is perfectly elastic with horizontal supply curve. The same price is charged regardless of Q s
. Any price decrease would cause supply to fall to zero. Shifts in demand curve results in no change in P.
P
5. If E s
= 0, supply is perfectly inelastic with a vertical supply curve. Q s
remains the same regardless of any change in price. Shifts in demand curve results in no change in Q s
.
P
P
S
S
S
D 1
D 0
D
1
Q s Q s
D 0
Q s
Perfectly Elastic SC
E s
= ∞
Unit Elastic SC Perfectly inelastic SC
E s
= 1 E s
= 0
Page 31 of 34

Factors that influence elasticity of supply
Price elasticity of supply depends on:
1. Resource substitution possibilities
— In general, the supply of most goods and services has elasticity between zero and infinity.
— The easier it is to substitute among the resources used to produce a good or service, the greater is its elasticity of supply.
— If the resources of a good are common and available, the supply is more elastic and supply curve is almost horizontal (wheat and corn)
— When goods can be produced in different countries, the supply is more elastic and supply curve is almost horizontal (sugar, beef, computers)
— If the resources of a good are unique, the supply of that good is highly inelastic and the supply curve is vertical. (Paintings)
P
MS
SS
2. Time Frame for Supply Decision
LS
— The more time that passes after a price change, the greater is the elasticity of supply.
— We distinguish between three time frames of supply: Q s a. Momentary Supply (MS): Immediate response of producers to price change.
In general, when price changes, most goods usually have a perfectly inelastic momentary supply with a vertical supply curve. No matter what is the price, production decision is already made earlier and it is difficult to change factors of production and technology immediately. (for example the production of agricultural products such grains and fruits) b. The SR supply curve (SS) is more elastic than momentary supply but is less elastic than long term supply. It shows how the quantity supplied responds to price changes when only some factors and technology affecting production are possible to change. The short response is a sequence of adjustments: firms may increase or decrease the amount of labor force and number of
Page 32 of 34

work hours. Firms may plan additional training to the new workers or may buy new tools and equipments
Short run supply curve slopes upward because producers can change quantity supplied in response to price changes quickly. c. The long run supply curve (LS) is usually highly elastic. It shows the response of quantity supplied to price change after all necessary adjustments and changes in factors of production and technology (building new plants, expanding the existing plants, training new worker)
Page 33 of 34

THE ADVERTISING ELASTICITY OF DEMAND:
— Managers’ decision on how much to spend on advertisement is an investment decision that has to be justified on some economic base.
— The decision rule to be followed here is again the marginal one, expand expenditures on advertisement as long as the marginal revenue exceeds the marginal cost of advertisement and don’t spend more when advertisement MR equates its MC.
— For a manager to take this decision he should know in advance expected increase in sales due to the planned additional spending on advertisement.
— Based on actual data collected from previous years, the firm research center may calculate the sensitivity or responsiveness of sales to advertisement expenditures.
— The elasticity of sales (the quantity demanded) will accomplish this task easily, and may be calculated across an arc or at appoint in the same way used previously.
E
Ad
=
Q
2
Q
2
−
+
Q
1
Q
1
÷
AD
2
AD
2
−
+
AD
1
AD
1
E
Ad
=
% ∆ Q
% ∆ Ad
=
∆ Q
∆ AD
X
AD
Q d
— Example:
By how much the manager of Hope Company should increase the firm spending on advertisement in order to increase sales by 20% the coming year, if you know that the elasticity of sales with respect to advertisement is 1.75?
E
Ad
1 .
75
=
% ∆ Q
=
% ∆ Ad
20 %
% ∆ Ad
⇒ % ∆ Ad =
20 %
1 .
75
= 11 .
4 %
Page 34 of 34