Percentage or Proportionate method For calculating Price Elasticity

Price elasticity of demand is measured by the ratio of percentage change in quantity demanded to percentage change in price of the commodity.

As explained below :

price elasticity

Mathematically speaking, price elasticity of demand is a negative number because of the negative slope of the demand curve, the price and the quantity change in the opposite directions from each other.

Factors affecting Price Elasticity of Demand

It is important to know that demand for some goods is more elastic (e_p>1, percentage change in quantity demanded is more than percentage change in price) while for others it is less elastic (e_p<1, percentage change in quantity demanded is less than percentage change in price), depending on many factors.

Some of the important determinants of price elasticity of demand are:

1) Nature of commodity :

Nature of commodity refers to whether the commodity is ‘necessary’, ‘luxury’ or ‘comfort’ in nature.

‘Necessary’ commodities, such as food items are essential for existence, these goods have to be purchased in fixed quantities, whether the price is high or low.

A change in the price of the necessities may have a small impact on the demand i.e. have inelastic demand (e_p<1).

‘luxury’ or ‘comfort’ commodities, such as television, a.c, furniture etc are not necessary for existence and their consumption can be postponed. Thus their demand changes by larger amount due to a small change in price i.e. have elastic demand (e_p>1).

The demand for necessities is inelastic and the demand for luxuries and comforts is elastic.

Price Elasticity of Demand

By studying Law of demand, we know that demand of a commodity is greatly influenced by the its price.
We learnt that increase in the price of the commodity causes contraction in demand, while decrease in price causes extension in demand.

Thus, law of demand makes a qualitative statement only. It does not tell us about the magnitute/degree of change in quantity demanded in response to change in the price.
It only tells about the direction of change.

Degree of change in quantity demanded in response to change in the price is the subject matter of Elasticity of Demand. 
It makes a Quantitative statement.It tells us about the extent to which the demand responds to change in price.

While measuring the degree of change in demand we always consider percentage values, not the absolute values.

Price elasticity of demand is defined as a measurement of percentage in quantity demanded in response to a given change in own price of the commodity.

e_p = Percentage change in quantity demanded

        Percentage change in price

(Where e_p refers to price elasticity of demand)

Kinds of Price Elasticity of Demand :

There are five different kinds of price elasticity of Demand:

1) Perfectly Elastic Demand : 

A Perfectly Elastic Demand refers to a situation when demand is infinite at the prevailing price.
It is a situation where the slightest rise in the price causes the quantity demanded  of the commodity to fall to zero.

As shown in the figure below. DD is the perfectly elastic demand curve, parallel to X axis.

elastic demand

It shows that at Price Rs.4, quantity demanded may be 10,20, 30 or more units i.e. demand for the commodity is infinite. But if the price increased from Rs.4, the demand falls to zero.And at price lower than Rs.4 an infinitely large quantity is demanded.Cases of perfectly elastic demand curve is very rare.

  e_p = ∞

2) Perfectly Inelastic Demand : 

A Perfectly Inelastic Demand refers to a situation when change in price causes no change in the quantity demanded.The elasticity of demand is zero.

As shown in the figure below. DD is the perfectly inelastic demand curve, parallel to Y axis.

inelastic demand

When price is Rs.2, demand is for 4 units. When the price rises to Rs. 4 or Rs.6 quantity demanded remains constant at 4 units.Hence, elasticity of demand is zero. Cases of perfectly elastic demand curve are also rare.

e_p = 0

Consumers Equilibrium Indifference Curve Approach

A consumer attains his equilibrium when he maximizes his total utility, given his income and the prices of the two commodities. We combine the indifference curve and the budget line to get consumer’s equilibrium.

Two condition is needed for the consumer to be in equilibrium.

1) MRS_xy = P_x/P_y

MRS_xy refers marginal rate of Substitution- It is the rate at which consumer is willing to substitute one good for another without changing the level of satisfaction.

For example: There are two commodities food(X) and clothing (Y).The marginal rate of Substitution X for Y is defined as the amount of X(food) the consumer is willing to give up to get one additional unit of Y(clothing) while maintaining the same level of satisfaction.

Given the amount of money which the consumer wants to spend on two commodities and given the prices of the two commodities, we can draw a budget line.

A budget line is a negatively sloping line as if a consumer wants to purchase more of one commodity, he has to sacrifice some amount of the other commodity. Its slope depends on the prices of the two commodities i.e. P_x/Py

Thus, the budget line shows the various combination which the consumer can afford to buy with his given budget and given prices of the two goods, the indifference map shows the consumer scale of preferences between various combinations of two goods.

Superiority of Indifference Curve Analysis Over Marginal Utility Analysis

1) Measurement of Utility :
The indifference approach is superior to the cardinal utility analysis (Marginal Utility) because it measures utility ordinally.
A consumer can compare the satisfaction (utility) derived from different goods or from different units of the same good.The ordinal method make this technique more realistic.

2) Study combination of two goods:
The cardinal utility approaches a single commodity analysis in which the utility of one commodity is regarded independent of the other.It does not speak of substitute or complementary goods, but group them as one commodity.

This assumption is less realistic as consumer buys not one but combination of goods at time.

The indifference curve technique is a two commodity model which discusses consumer behavior in case of substitutes, complementaries and related goods.

3) Marginal Utility of Money is not constant :

The utility analysis assumes constant marginal utility of money because it takes consumer income to be constant, but this is not realistic condition as with rise or fall in income the Marginal utility of money changes.

Properties of Indifference Curve

Indifference Curve analysis has rejected the concept of cardinal utility approach (Marginal Utility Analysis) and adopted the concept of ordinal utility.
This implies that consumer compare the utility (which goods or which combination of goods give him the same, more or less utility) derived from different goods. In this utility is not measured in quantitative terms but on the scale of preference.
Below shown is the Indifference Curve.

Properties of Indifference Curve :

indifference curve

1) Has a Negative Slope :

An indifference curve slopes downwards from left to right. This is due to the assumption of Marginal Rate of Substitution.

This means that as the consumer consumes more of one commodity say X, he must consume less quantity of the other say Y, then only  he will have the same level of satisfaction from different combinations of the two commodities.

As shown in the below graph, going to combination B from A, to get 1 additional unit of food,he has to give up 3 units of clothing. If unit of food is increased, without changing the unit of clothing than the consumer will prefer new combination to the previous one as the new combination gives him more utility.

Law of EquiMarginal Utility

A rational consumer will maximize his utility subject to their budget constraint or income.
A consumer will be at equilibrium when he allocates his given income in the purchase of different goods in such a way that he maximizes his utility.
Law of Equi-Marginal Utility solves the above problem of consumers.

 The law says that-
“The Consumer maximizing his total utility will allocate his income among various commodities in such a way that the marginal utility of the last unit of money (rupee) spent on each commodity is equal.”

Now, to understand what is - marginal utility of the last unit of money is (rupee) spent on each commodity

Marginal utility of a rupee we spend on a good say ‘X’ is calculated by
( MUx / Px )

Where,  MUx is marginal utility of the good ‘X’ and Px is the price

Similarly, Marginal utility of a rupee we spend on a good say ‘Y’ is
calculated by ( MUy / Py )

Now we will understand why a consumer maximizes his total utility when the marginal utility of the last rupee spent on each good is equal.

If a consumer is getting more utility form a rupee spend on commodity X than with Y, he will switch one rupee from Y to get commodity X. Thus total utility of his will rise.

The utility maximizing consumer will continue to switch his expenditure from Y to X as long as one rupee spent on X brings him more utility than Y.

This will leads to more quantity of X and less of  Y. But remember the law of diminishing marginal utility (with increase in each successive units, the utility derived from the additional unit goes on decreasing), marginal utility derived from X will start falling.

This process of reallocation of expenditure will ultimately lead to equalization of marginal utility of last rupee spent on each of the two commodities.
This is the satiation point for the consumer, he will not gain by further reallocation of expenditure from commodity Y to commodity X.

The consumer will spend his money income on different goods in such a way that marginal utility of each good is proportional to its price.

(MUx / Px)  = (MUx / Py)  = MU per unit of money

Let us illustrate the law of equi-marginal utility by taking a numerical example:

Calculate which combination of goods A and B provide maximum utility to the consumer?

Units	MUx	MUy	MUx/Px	MUy/Py
1	10	30	5	7.5
2	8	24	4	6
3	6	20	3	5
4	4	16	2	4
5	2	14	1	3.5
6	1	8	0.5	2

Total Utility and Marginal Utility

Relationship between Total Utility and Marginal Utility

There is a definite and well defined relationship between total utility and marginal utility.

Total Utility

It refers to the total satisfaction derived by the consumer from the consumption of a specific quantity of a commodity.

For example, the total utility of consuming two apples is the total satisfaction that these two apples provide.

Marginal Utility

It refers to the additional utility derived from the consumption of an additional unit of a commodity.

The relation between total utility and marginal utility is shown in below graph.

Graph ‘A’ shows that the total utility increases first,  reaches the maximum and then starts decreasing

Graph ‘B’ shows continuously decreasing marginal utility curve

marginal utility

Let us analyze the graph deeply

Movement Along demand curve and shift of demand curve

1) Change in Quantity demanded

When the amount demanded of a commodity changes (rises/falls) as a result of change in its own price, while other determinants of demand (like income, tastes and preferences etc.) remain constant, it is known as change in quantity demanded.
They are of two types:

a) Extension of demand :
When the quantity demanded of a commodity rises due to fall in its price, other things remaining the same (i.e. factors that affects demand like income,tastes and preferences etc), it is called ‘rise in quantity demanded’ or ‘extension of demand’.

b) Contraction of demand :
When the quantity demanded of a commodity falls due to rise in its price, other things remaining the same (i.e. factors that affects demand like income,tastes and preferences etc), it is called ‘fall in quantity demanded’ or ‘contraction of demand’.

demand curve

As explained in the above graph,when the price is OP, quantity demanded is OQ.

When the price rises to OP₁, quantity demanded falls to OQ₁.
This movement from A to B in upward direction on the demand curve DD is the contraction of demand,since quantity demand falls (contracts) due to rise in price.

Exception to law of Demand

Exception to the law of Demand / when demand curve slopes upward / a positive slope demand curve

Law of demand may not operate in many situations.

These are known as the exception to the law of demand, where demand curve may not have negative slope.

A positively sloped demand curve shows with rise in price, quantity demanded rises and with fall quantity demanded falls.

Discussed below are the various exceptions.

1) Giffen Goods:

Named after economist Sir Robert Giffen, he said giffen goods are those inferior goods on which the consumer spends a large part of his income and the demand for which falls with a fall in their price.
for example - maize and jowar are considered to be inferior food grains for average consumers.

As the price of maize falls, real income rises, know the consumer may afford to purchase superior foods like wheat or rice.

Since there is a limit to intake of food, quantity demanded for maize would be lower.

Similarly, if the price of maize rises, poor consumers will be forced to spend more on the purchase of maize because it is essential for their survival.

They cannot afford to purchase the same quantity of superior food items that they purchased earlier because they would be left with lesser money to spend on other commodities.

Thus, they will increase the demand for maize at the cost of wheat or rice.

Law of Demand

The law of demand states that other thing remaining equal, the quantity demanded of a commodity increases when its price falls and decreases when its price rises.

The law indicates an inverse relationship between the price and quantity demanded of a commodity.

The law of demand is based on the following main assumptions:

1) There should be no change in income of the consumer.

2) There should be no change in tastes and preferences of the consumers.

3) Prices of the related commodities should remain unchanged.

4) Size of the population should not change.

5) The distribution of income should not change.

6) The commodity should be a normal commodity.

Explanation of law of demand/Why demand curve slope downwards to the right/why demand curve has a negative slope

1) Law of diminishing marginal utility : 

This law states that as consumption of a commodity increases, the utility from each successive unit goes on diminishing. So for every additional unit to be purchase the consumer is willing to pay less and less price.
Thus more is purchase only when own price of the commodity falls.

Explanation through example:

Units of shirt	Marginal utility
1 2 3 4 5	700 650 600 500 350

Demand Schedule

Demand Schedule:
It is a tabular statement that shows different quantities of a commodity that would be demanded at different prices.  It is of two types: 

1) Individual Demand schedule :
It shows various quantities of a commodity that would be purchased at different prices during a given period.

Individual Demand schedule for apples

Price(Rs. Per kg)	Quantity demanded (kg/week)
40 30 20 10	1 2 4 6

2) Market Demand schedule :

It shows various quantities of a commodity that would be purchased at different prices by all the buyers during a given period.

Market Demand Schedule for For Apples

Price(Rs./kg)	Quantity demanded by ‘A’(Kg per week)	Quantity demanded by ‘B’(Kg per week)	Total market Demand (Kg per week) (A+B)
40 30 20 10	1 2 4 6	2 3 5 7	1+2=3 2+3=5 4+5=9 6+7=13

Demand Curve

The picturization of demand schedule is ‘Demand curve’. It   is a graphic presentation of the law of demand. It is of two types:

1) Individual Demand Curve : 
A curve that shows different quantities of the goods which a consumer is willing to buy at different prices during a given period of time. Below shown is individiual demand curve.

demand curve

In the above figure DD is the Demand Curve. The demand curve slopes downwards from 
left to right, indicating an inverse relationship between price and the quantity demanded.