    # Elasticity Of Demand Illustration 19

If a customer’s daily income hikes from \$1000 to \$1200, his purchase of a commodity X enhances from 50 units per day to 70 units, determine the income elasticity of demand for X.

Solution

Change in demanded quantity ΔM = M2 – M1

=          1200 – 1000    =          200

e1        =          Percentage change in demanded quantity
Percentage change in price

e1        =          ΔQ                   M2 + M1
ΔM      *          Q2 + Q1

ΔQ       =          70 – 50            =          20

=          20                    1200 + 1000
70        *             50 + 70

=          20                    2200
70        *          120

Income Elasticity of Demand             =          5.23

Illustration 20

Presume demand for cars in Seattle as a function of income is given by the following equation: Q = 30000 + 15M, where Q is the quantity demanded, M is per capita level of income in dollars.

Determine the income elasticity of demand when per capita annual income in Seattle is \$20000.

Solution

Income elasticity e1    =       ΔQ                   M
ΔM      *          Q

With respect to procure income elasticity, we have to first ascertain quantity demanded Q at level of income of \$20000. Therefore

Q         =          30000 + 15 * 20000 = 330000

It will be observed from the provided income demand function that co-efficient of income M is equal to 15. This entails that ΔQ = 15.
ΔM

With this price of information we can calculate income elasticity.

e1        =         ΔQ                   M
ΔM      *          Q

=          15 * 20000
330000

=          0.90

Illustration 21

The following demand function for apparels has been approximated, Q = 4000 + 40Y – 8.8 P. where Y is income in thousands of dollars, Q is the quantity demanded in units and P is the price per unit. When P = \$400 and Y = 40 thousand dollars ascertain the following.

1. Price Elasticity of Demand, Income Elasticity of Demand
1. Ascertain what effect a rise in price would have on total revenue
1. Asses how sales of trousers would change during a period of growing income

Solution

(1) Coefficient of P                 =          ΔQ       =          8.8
ΔP

Price elasticity of demand      =          ΔQ                   P
ΔP       *          Q

=          8.8       *          400
Q

Now, let us first ascertain the demanded quantity which is Q at the provided income Y = 40 thousand dollars and given price P = 400 per unit. Substituting the values of income and price in the provided demand function, we procure,

Q         =          4000 + 40Y – 8.8P

=          4000 + (40 * 40) – (8.8 * 400)

=          4000 + 1600 – 3520

=          2080

Therefore,        ep        =        ΔQ                   P
ΔP       *          Q

=          8.8       *          400
2080

=          1.70

Income elasticity         =          ΔQ                   Y
ΔY       *          Q

ΔQ = 40,         Q = 2080,        Y = 40 thousand dollars.
ΔY

=          40        *          40      =          0.77
2080

(2) Since price elasticity of demand for apparels is less than 1, hike in price would consequent enhancement in total revenue.

(3) As the income elasticity of demand for apparels is less than one, apparels are a requisite and hence the enhancement in income of the people will tend to less than a proportionate enhancement in their sales.

Illustration 22

From the following demand functions, ascertain whether demand is inelastic, elastic or unitary elastic at the provided price.

1. Q = 200 – 2P and the provided P = \$10
1. P = 2000 – 30P and the provided P = \$50
1. P = 100 – 0.2Q and the provided P = \$10

Solution

1. Q = 200 – 2P where P = \$10

In this demand function the derivative dQ    =          2
dP

Substituting the value of P in this demand function (1), we obtain

Q         =          200 – (2 * 10)  =          180

ep        =          dQ                   P
dP        *          Q

=          2          *          20 / 180

=          0.22

Since ep is less than 1, demand is inelastic.

1. Q = 2000 – 30P, where P = 50

In this demand function equation, the derivative dQ / dP     =          30

Substituting the value of P in this demand function

Q         =          2000 - 30 * 50

=          500

ep        =          30        *          1500 / 500

=          3

Since ep is >1, demand is elastic.

1. P = – 0.2Q and the provided P = \$10

Let us first express this demand function in terms of demanded quantity as a function of price.

P          =          100 – 0.2Q

0.2Q    =          100 – P

Q         =          100 – P
0.2

=          500 – 5P

Now price is given to be \$10. substituting in the Q equation, we obtain the following.

Q         =          500 – 5*10

=          500 – 50          =          450

The derivative of dQ which is 500 – 5P is 5.
dP

ep        =          dQ                   P
dP        *          Q

=          5          *          10        =          0.11
450

Since ep = 0.11 and is less than 1, demand is inelastic.

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