Elasticity Of Demand

Definition:

Elasticity means responsiveness. Thus, elasticity of demand means the responsiveness of demand due to some changes to the factors which influence demand.

There three types of elasticity of demand:

1. Price Elasticity of Demand (PED) - (Ed)2. Income Elasticity of Demand (IED) - (EI)3. Cross Elasticity of Demand (CED) - (Ec)

1. Price Elasticity of Demand (PED) a. Definition of PED:

It measures the responsiveness of quantity demanded due to a change in its price.

b. Formula :

i. Ed = % ∆ in Qty demanded for product A (Percentage Method)% ∆ in price for product A

Ed = % ∆Q% ∆P

Note: The following are the steps to convert from percentage method to proportionate method:

∆Q × 100%q0

= _________ ∆P × 100%p0

Ed = ∆Q × p0 ∆P q0

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ii. Ed = ∆Q × p0 (Proportionate Method) ∆P q0

Ed = (q1 − q0)× p0 absolute value (p1 − p0) q0

Note: All answers must be for PED must be converted by the absolute

value to turn it to positive.

Example 1:

If the price of product Y has increased by 10% then the quantity demanded has decreased by 20%. Calculate the price elasticity of demanded when price increases.

% ∆P = 10%% ∆Q = −20%

Ed = % ∆Q

% ∆P

Ed = −20% 10%

Ed = −2 absolute value

Ed = 2 (Since 1<Ed < ∞ , the demand is elastic)

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Example 2:

Given the price of product X is RM 4 and the quantity demanded is 12 units. When the price of product X increases to RM 5 the quantity demanded is 6 units. Calculate the price elasticity of demanded when price increases.

p0 = RM4 q0 = 12p1 = RM5 q1 = 6

Ed = ∆Q × p0 (Proportionate Method)∆P q0

Ed = (q1 − q0) × p0

(p1 − p0) q0

= (6 − 12) × 4 (5 − 4) 12

= − 6 × 1 1 3

= − 2

Ed = 2 (Since 1<Ed < ∞ , the demand is elastic)

c. Objective for PED or Degrees of PED:

Once we have calculated the PED then we need to interpret the coefficient value. For PED coefficient there are degrees of PED :

Elastic Demand , (1<Ed < ∞) Inelastic Demand , (0< Ed < 1) Unitary Elastic Demand , ( Ed = 1) Perfectly Inelastic Demand , ( Ed = 0) Perfectly Elastic Demand , ( Ed = ∞)

2. Income Elasticity of Demand (IED)

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a. Definition of IED:It measures the responsiveness of quantity demanded due to a change in consumer’s income.

b. Formula :

i. EI = % ∆ in Qty demanded (Percentage Method)% ∆ in Income

EI = % ∆Q Note : I’m using notation I for Income but the % ∆I manual is using Y.

Note: The following are the steps to convert from percentage method to proportionate method:

∆Q × 100% q0

= _________ ∆I × 100% I0

= ∆Q × I0 ∆I q0

ii. EI = ∆Q × I0 (Proportionate Method)∆I q0

EI = (q1 − q0)× I0

(I1 − I0) q0

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b. Objective for IED:Is to identify the types of good.

Luxury Goods, if (EI > 1) i.e antique furniture, antique cars

i. Normal Goods Necessity Goods, if (0< EI =< 1) i.e clothings, shoes.

(Note : As income increased , the quantity demanded will also increased.)

ii. Inferior Goods (EI < 0)(Giffen Goods)

i.e low-grade rice, black&white TV, secondhand clothings

(Note : As income increased , the quantity demanded will also decreased.)

iii. Essential Goods (EI = 0) i.e Insulin for diabetic patient

(Note : As income increased , the quantity demanded no changed.)

c. Example 1 :

Given the consumer’s income increased by 10% , the quantity demanded for houses have increased by 5% . Calculate the income elasticity of demanded for houses when income increases.

Given : %∆I = 10% % ∆Q = 5%

EI = % ∆Q = 5% % ∆I 10%

EI = 0.5 ( Since 0<Ed =<1 , the good is Necessity good)

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Example 2:Given the following table:

Income ($)

Qty for Good A

Qty for Good B

Qty for Good C

300 20 20 20400 25 18 20500 30 15 20600 35 10 20700 40 5 20800 45 0 20

Questions:Find the EI when consumer’s income changes from RM500 to RM600 for good A,B and C respectively. Then determine the type of goods from the above calculation.

Suggested Solutions:

Since we have three (A,B & C) goods, so there should be three calculation to find the EI for good A, B & C respectively.

For Good A : I0 = RM500 q0 = 30I1 = RM600 q1 = 35

EI = ∆Q × I0 (Proportionate Method) ∆I q0

(35 − 30) 500 = ×

(600− 500) 30

EI = 0.833 (Since EI is 0 < EI =< 1, thus the good is a necessity good)

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For Good B : I0 = RM500 q0 = 15I1 = RM600 q1 = 10

EI = ∆Q × I0 (Proportionate Method) ∆I q0

(10 − 15) 500 = ×

(600 − 500) 15 EI = − 1.67 (Since EI is EI < 0, thus the good is an inferior good)

For Good C : I0 = RM500 q0 = 20I1 = RM600 q1 = 20

EI = ∆Q × I0 (Proportionate Method) ∆I q0

(20 − 20) 500 = ×

(600 − 500) 20

EI = 0 (Since EI is EI = 0, thus the good C is an essential good)

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3. Cross Elasticity of Demand (CED)

a. Definition of CED:It measures the responsiveness of quantity demanded (i.e ∆ in Qx) due to a change in price of related product (∆ in Py).

b. Formula :

i. Ec = % ∆ in Qty of X (Percentage Method)% ∆ in Price of Y

Ec = % ∆Qx % ∆Py

Note: The following are the steps to convert from percentage method to proportionate method:

∆Q x × 100% qx0

= _________ ∆Py × 100% py0

ii. Ec = ∆Q x × py0 (Proportionate Method) ∆Py q x0

c. Objective :

It is to establish the relationship between good X and good Y. There are three possibilities of goods:

i) X and Y are substitute goods => Ec = + (positive value)Note : As price Py increase, the quantity Qx will also increase.

ii) X and Y are complementary goods => Ec = − (negative value) Note : As price Py increase, the quantity Qx will also decrease.

iii) X and Y has no relationship => Ec = 0 (zero value)Note : As price Py increase, there is no effect on Qx.

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Examples :

The following table shows the demand for two goods Y and Z, when there is a change in price for good X :

Price of Good X Qty of Good Y Qty of Good Z5 10 56 8 87 7 108 6 14

Questions: 1. Calculate the CED of good Y when price of good X increased from

RM6 to RM7 per unit. 2. Calculate the CED of good Z when price of good X increased from

RM6 to RM7 per unit.

Suggested Solutions:

1. px0 = 6 q y0 = 8px1 = 7 q y1 = 7

Ec = ∆Q y × px0 (Proportionate Method) ∆Px q y0

(7 − 8) 6 = ×

(7 − 6) 8

Ec = − 0.75 (Since Ec is Ec < 0 , thus as Px increased the Q y will decreased which mean Good X & Y are complementary goods)

2. px0 = 6 q z0 = 8 px1 = 7 q z1 = 10

Ec = ∆Q y × px0 (Proportionate Method) ∆Px q y0

(10 − 8) 6 = ×

(7 − 6) 8 Ec = 1.5 (Since Ec is Ec > 0 , thus as Px increased the Q y will

increased which mean Good X & Z are substitute goods)

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