# 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__ 2__200__

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.

- Price Elasticity of Demand, Income Elasticity of Demand

- Ascertain what effect a rise in price would have on total revenue

- 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 = __Δ____Q__ __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.

- Q = 200 – 2P and the provided P = $10

- P = 2000 – 30P and the provided P = $50

- P = 100 – 0.2Q and the provided P = $10

__Solution__

- 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.**

- 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.**

- 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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**Other topics under Demand Analysis and Theory of Consumer Choice:**

- Constant Rate of Change
- Consumer's Behavior Cardinal Utility Analysis
- Consumer's Equilibrium - Doctrine of Equi-Marginal Utility
- Chief Property of Indifference Curves
- Demand Estimation
- Demand Forecasting
- Demand Indifference Curve Analysis
- Exposed Inclination Theory of Demand
- Income Effect and Income Consumption Curve
- Weak Axiom of Exposed Inclination