ELASTICITY
LEC 4
ELASTICITY
A
general concept used to quantify the
response in one variable when another
variable changes
 elasticity of A with respect to B =
% A/ %B
Calculating Elasticities
Price per P
Pound
P
Price per
Pound
P1 = 3
P1 = 3
P2 = 2
P2 = 2
D
0
Q1 = 5
Q2= 10
Pounds of X per week
Pounds of X per month
Slope: Y = P2 – P1
X = Q2 – Q1
= 2 – 3 = -1
10 – 5 = 5
Q
D
0
Q1 = 80
Q2= 160
Ounces of X per week
Ounces of X per month
Slope: Y = P2 – P1
X = Q2 – Q1
= 2 – 3 = -1
160 –80 = 80
Q
Point Price Elasticity of Demand
Ratio of the percentage of change in quantity
demanded to the percentage change in price.
% Q
Ep =
Point Definition
% P
Q / Q
Q P
EP 


P / P
P Q
Point Price Elasticity of Demand
For P approaching 0
Q/P = dQ/dP
Linear equation = dQ/dP = constant
dQ/dP = ap
Qd = B + apP = B + dQ/dP P
Point Price Elasticity of demand
7
-5
A
6
B
5
-2
C
-1
Px
4
F
3
-0.5
G
2
Dx
-0.2
H
1
J
0
0
100
200
300
400
Qx
500
600
700
Arc Price Elasticity of Demand
Ep = Q2 - Q1
(Q2 + Q1)/2
EP 
Q 2  Q1
P2  P1

P2 - P1
(P2 + P1)/2
P2  P1
Q 2  Q1
Example
 Calculate
the arc price elasticity from point C to
point F.
= (300 – 200)/ (3-4) * ((3+4)/ (300+200))
= -1.4
Problem
Present Loss
:
$ 7.5 million
Present fee per student
:
$3,000
Suggested increase
:
25%
Total number of students
:
10000
Elasticity for enrollment at state universities is -1.3 with respect to tuition changes
1% increase in tuition = 1.3% decrease in enrollment
Increase of 25%
decline in enrollment by 32.5%
3000 * 10000 = $30,000,000
3750 * 6750 = $25,312,500
Perfectly Inelastic Demand
Price P
Perfectly Elastic Demand
Price P
D
D
0
Qty Demanded
Q
0
Qty Demanded
Q
Perfectly inelastic demand
Qd does not change at all when price changes
Inelastic demand
-1 < E  0
Unitary elastic demand
E = -1
Elastic demand
E < -1
Perfectly elastic demand
Qd drops to zero at the slightest increase in price
Exercise

For each of the following equations, determine whether
the demand is elastic, inelastic or unitary elastic at the
given price.
a) Q =100 – 4P and P = $20
b) Q =1500 – 20 P and P = $5
c) P = 50 – 0.1Q and P = $20
a) -4, elastic
b) -0.07, Inelastic
c) -0.67, Inelastic
TOTAL AND MARGINAL REVENUE &
ELASTICITY
P=Price, Q=Quantity
TR (Total Revenue)=P X Q
MR (Marginal Revenue)= d(TR)/dQ= d(PQ)/dQ
Price
Quantity
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
Total
Marginal
Revenue Revenue
10
18
8
24
6
28
4
30
2
30
0
28
-2
24
-4
18
-6
10
-8
Total and Marginal Revenue
Price
Quantity
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
Total
Marginal
Revenue Revenue
10
18
8
24
6
28
4
30
2
30
0
28
-2
24
-4
18
-6
10
-8
Total Revenue
35
30
Total Revenue
25
20
15
10
5
0
0
2
4
6
8
10
12
Quantity per period
MR/Price
15
10
5
Average Revenue
0
0
2
4
6
8
12
Quantity Demanded
-5
Marginal Revenue
-10
10
Marginal Revenue Equation
Demand Equation Q = B + ap P
P = -B/ap + Q/ap
TR = PQ = -B/ap*Q + Q2/ap
MR = d(PQ)/dQ = -B/ap+ 2Q/ap
MR = 0
For Q < B/2 , MR = +ve
, Q = B/2
Q > B/2 , MR = -ve
Relation of Demand & Marginal Revenue
Curve

The curves intercept y-axis at same point

Intercept of MR & Demand (DD) curve = -B/ap

Slope of (DD) curve = 1/ ap

Slope of MR curve = 2/ ap = 2 DD curve
Calculate Elasticity
Price
Quantity
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
Total
Marginal
Revenue Revenue
10
18
8
24
6
28
4
30
2
30
0
28
-2
24
-4
18
-6
10
-8
Total Marginal Elasticity
Price Quantity
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
Total
Marginal Price
Revenue Revenue Elasticity
10
-10.00
18
8
-4.50
24
6
-2.67
28
4
-1.75
30
2
-1.20
30
0
-0.83
28
-2
-0.57
24
-4
-0.38
18
-6
-0.22
10
-8
-0.10
Total Revenue
35
30
Total Revenue
25
20
15
10
5
0
0
2
4
6
8
10
12
Quantity per period
15
MR/Price
Elastic
Ep < - 1
10
Unitary elastic
Ep = - 1
Inelastic
5
-1 < Ep < 0
0
0
2
4
6
8
12
Quantity Demanded
-5
Marginal Revenue
-10
10
Marginal Revenue and Price Elasticity of
Demand
MR = d(PQ) = dQ*P + dP*Q
dQ
dQ
dQ
= P + QdP = P 1 + dP.Q
dQ
dQ P

1 
M R  P 1 

EP 

P
* Qd = TR
Elastic Demand
P
* Qd = TR
Elastic Demand
P
* Qd = TR
Inelastic Demand
P
* Qd = TR
Inelastic Demand
Exercise1

A consultant estimates the price-quantity relationship
for New World Pizza to be at
P = 50 – 5Q.
 At what output rate is demand unitary elastic?


Over what range of output is demand elastic?
At the current price, eight units are demanded
each period. If the objective is to increase total
revenue, should the price be increased or
decreased? Explain.
P =50 -5Q
MR = 50-10Q
 For unitary elastic MR = 0 so Q =5
 MR will be +ve when Q<5, so demand will be elastic
when 0<=Q<5.
 P for Q=8 is P=50-5*8 = 50-40 = 10

Ep= -1/5*10/8 = -0.25. As demand is inelastic,
when we increase price, TR increases.
Q / P  1 / 5
Exercise2

The coefficient of price elasticity of a commodity is
given by –1.5. Find the percentage change in Total
Revenue when its price falls by 10%

If Price decreases by 10% corresponding increase in
quantity demanded will be 15% and therefore change
in TR = (1.15*.9 PQ – PQ)/PQ *100
= 3.5%
Determinants of Price Elasticity of
Demand
Demand for a commodity will be less elastic if:

It has few substitutes

Requires small proportion of total expenditure

Less time is available to adjust to a price change
Determinants of Price Elasticity of Demand
Demand for a commodity will be more elastic if:

It has many close substitutes

Requires substantial proportion of total expenditure

More time is available to adjust to a price change
Income Elasticity of Demand
The responsiveness of demand to changes in income.
Other factors held constant, income elasticity of a
good is the percentage change in demand associated
with a 1% change in income
Point Definition
EI 
Q / Q
I / I

Q
I

I
Q
Income Elasticity of Demand
Arc Definition
EI 
Q 2  Q1
I 2  I1

I 2  I1
Q 2  Q1
 Normal


Goods ΔQ/ΔI = +ve, EI = +ve
Necessities 0 < EI  1
Luxuries EI > 1
 Inferior
Goods ΔQ/ΔI = -ve, EI = -ve
Exercise1
Demand of automobiles as a function of income is
Q = 50,000 + 5(I)
Present Income = $10,000
Changed Income = $11,000
I1 = $10,000,
I2 = $11,000,
Q = 100,000
Q = 105,000
EI = 0.512
Exercise2



The coefficient of income for the quantity
demanded for a commodity on price, income and
other variables is 10.
Calculate the income elasticity of demand for this
commodity at income of $ 10,000 and sales of
80000 units.
What would be the income elasticity of demand if
sales increased from 80000 to 90000 units and
income rose from $10000 to $11000? What type of
good is this commodity?




aN = 10
EI = 10*10000/80000= 1.25
EI = {(90000-80000)/(11000-10000)}*
{(11000+10000)/(90000+80000)}
= 1.235
Luxury
Cross-Price Elasticity of Demand
Responsiveness in the demand for commodity X
to a change in the price of commodity Y. Other
factors held constant, cross price elasticity of a
good is the % change in demand for commodity
X divided by the % change in the price of
commodity Y
Point Definition
E XY 
Q X / Q X
 PY / PY

Q X
 PY

PY
QX
Cross-Price Elasticity of Demand
Arc Definition
Substitutes
E XY  0
E XY 
QX 2  QX1
PY 2  PY 1

PY 2  PY 1
QX 2  QX1
Complements
E XY  0
Exercise



Acme Tobacco is currently selling 5000 pounds of pipe
tobacco per year. Due to competitive pressures, the
average price of a pipe declines from $15 to $12. As a
result, the demand for Acme pipe tobacco increase to
6,000 pounds per year.
What is the cross elasticity of demand for pipes and pipe
tobacco?
Assuming that the cross elasticity does not change, at what
price of pipes would the demand for the pipe tobacco be
3,000 pounds per year? Use $15 as the initial price of a
pipe.

EXY = {(6000-5000)/(12-15)}*{(12+15)/(6000+5000)
= -0.818
P1 = $15, Q2 = 3000 and Q1 = 5000
Therefore, P2 = 28.23
Importance of Elasticity in Decision
making

To determine the optimal operational policies

To determine the most effective way to respond to
policies of competing firms

To plan growth strategy
Importance of Income Elasticity

Forecasting demand under different economic
conditions

To identify market for the product

To identify most suitable promotional campaign
Importance of Cross price Elasticity

Measures the effect of changing the price of a
product on demand of other related products
that the firm sells

High positive cross price elasticity of demand is
used to define an industry
Problem
Qx = 1.5 – 3.0Px + 0.8I + 2.0Py – 0.6Ps + 1.2A
Px=$2
I=$2.5
Ps=$0.50
Py=$1.8
A=$1
Qx =1.5 – 3*2 + 0.8*2.5 + 2*1.8 – 0.6*0.50 + 1.2*1
=2
Ep = -3(2/2) = -3
Exy = 2(1.8/2) = 1.8
EI = 0.8(2.5/2) = 1
Exs = -0.6(0.50/2) = -0.15
EA = 1.2(1/2) = 0.6
Next Year:
P=5% A=12% I=4%
Py=7% Ps=8%
Q’x =
Qx + Qx(Px /Px) Ep + Qx (I/ I) EI + Qx (Py/Py)Exy
+Qx (Ps/Ps)Exs + Qx (A/A)EA
=2+2(0.05)(-3)+2(0.04)(1)+2(0.07)(1.8)+2(-0.08)(-0.15)+2(0.12)(0.6)
=2(1.1)
=2.2