Different types of Elasticity of Demand :
Price Elasticity of Demand
Price elasticity of demand is commonly known as elasticity of demand. This is because price is the most influential factor affecting demand. "Elasticity of demand measures the responsiveness of the quantity demanded to changes in the price".
(1) Price Elasticity of Demand: The price elasticity of demand; commonly known as the elasticity of demand refers to the responsiveness and sensitiveness of demand for a product to the changes in its price. In other words, the price elasticity of demand is equal to
\({ E }_{ p }=\frac { Proportionate \ change \ in \ quantity \ demanded }{ Proportionate \ change \ in \ price } \)
Numerically,
\({ E }_{ p }=\frac { \triangle Q }{ \triangle P } \times \frac { P }{ Q } \)
Where, \(\triangle Q={ Q }_{ 1 }-{ Q }_{ 0 },\triangle P={ P }_{ 1 }-{ P }_{ 0 },Q1\)=New quantity,
\({ Q }_{ 0 }\)=Original quantity, \({ P }_{ 1 }\)=New price, \({ P }_{ 0 }\)=Original price.
(2) Income 'Elasticity of Demand: The income is also a factor that influences the demand for a product. Hence, the degree of responsiveness of a change in demand for a product due to the change in the income is known as income elasticity of demand. , The formula to compute the income elasticity of demand is:
\({ E }_{ Y }=\frac { Proportionate\ change\ in\ quantity\ Demanded\ for\ a\ product }{ Proportionate\ change\ in\ Income } \)
For most of the goods, the income elasticity of demand is greater than one indicating that with the change in income the demand will also change and that too in the same direction, i.e. more income means more demand and vice-versa.
(3) Cross Elasticity of Demand The cross elasticity of demand refers to the percentage change in quantity demanded for one commodity as a result of a small change in the price of another commodity. This type of elasticity usually arises in the case of the interrelated goods such as substitutes and complementary goods. The cross elasticity of demand for goods X and Y can be expressed as:
\({ E }_{ C }=\frac { Proportionate\ change\ in\ Demanded\ of\ commodity\ X }{ Proportionate\ change\ in\ price\ of\ commodity\ Y } \)
(4) Advertising Elasticity of Demand: The responsiveness of the change in demand due to the change in advertising or other promotional expenses, is known as advertising 'elasticity-of demand. It can be expressed as:
\({ E }_{ a }=\frac { Proportionate\ change\ in\ Demand }{ Proportionate\ change\ in\ Advertising\ Expenditure } \)

Importance or Application of the Law of DMU:
(1) The Law of DMU is one of the fundamental laws of consumption. It has applications in several fields of study.
(2) This law is the basis for other consumption laws such as Law of Demand, Elasticity of Demand, Consumer's Surplus and the Law of Substitution etc.
(3) The Finance Minister taxes a more-moneyed person more and a less-moneyed person less. When a person's income rises, the tax-rate rises because the MU of money to him falls with every rise in his income. Thus, the Law of DMU is the basis for progressive taxation.
(4) This law emphasises an equitable distribution of wealth. The MU of money to the more-moneyed is low. Hence, redistribution of income from rich to poor is justified.
(5) Adam Smith explains the famous "diamond-water paradox". Diamond is scarce, hence, its MU is high and its price is high, even though it is not very much needed. Water is abundant, hence, its MU is low and its price is low, even though it is very much essential.

Importance of Elasticity of Demand
The concept of elasticity of demand is of much practical importance.
(1) Price fixation: Each seller Under monopoly and imperfect competition has to take into account elasticity of demand while fixing the price for his product. If the demand for the product is inelastic, he can fix a higher price.
(2) Production: Producers generally decide their production level on the basis of demand for the product.
(3) Distribution: Elasticity of demand also helps in the determination of rewards for factors of production.
(4) International trade: Elasticity of demand helps in finding out the terms of trade between two countries. Terms of trade depends upon the elasticity of demand for the goods of the two countries.
(5) Public finance: Elasticity of demand helps the government in formulating tax policies. For example, for imposing tax on a commodity.
(6) Nationalization: The concept of elasticity of demand enables the government to decide over nationalization of industries.

(i) Indifference curve must have a negative slope.
(ii) Indifference curves are convex to the origin.
(iii) Indifference curve cannot intersect
(iv) Indifference curve do not touch the horizontal or vertical axis

(i) A consumer wants to spend his limited income on apple and orange.
(ii) He will be in equilibrium when he gets maximum satisfaction.

\(\mathrm{K}=\frac{M \mathrm{U_A}}{\mathrm{P_A}}=\frac{M U_O}{\mathrm{P_O}}\)
If \(\frac{MU_A}{P_ A}\) is less than \(\frac{M U_O}{P_O}\) he would transfer money from apple to orange till both are equal.

Total utility	Marginal utility
Increases at a diminishing rate	Goes on diminishing
Reaches maximum	Becomes zero
Diminishes	Becomes negative

Characteristics
Wants are unlimited
(i) Wants are countless and various in kinds.
(ii) When one want is satisfied another want arises.
Wants become habits
(i) When a man starts reading newspaper in the morning it becomes a habit.
Wants are satiable
(i) We can satisfy particular wants at a given time.
(ii) When one feels hungry, he takes food and that want is satisfied.
Wants are alternative
(i) There are alternative ways to satisfy a particular want (eg) idly, dosa.
Wants are competitive
(i) There is competition among wants.
(ii) So we have to choose more urgent wants and satisfy them first.
Wants are complementary
(i) Satisfaction of a particular want requires the use of more than one commodity. (eg) car and petrol.
Wants are recurring
(i) Some wants occur again and again. For ex. if we feel hungry, we take food and satisfy our want.
(ii) But after some time we again feel hungry and want food.