Measurement of Price Elasticity: Total Outlay Method

In general, elasticity of demand means price elasticity. The concept of price elasticity is widely used in demand analysis. There are three methods of measuring price elasticity – total outlay method, point method and arc method. Here we concentrate only on total outlay method.

Total Outlay Method or Expenditure Method

In total outlay method, we see the change in expenditure as a result of change in price. Then on the basis of change in expenditure, we say whether the elasticity is equal to unity or greater than unity or less than unity. This can be illustrated by the help of schedule and figures.

1. Elasticity of Demand Equal to Unity (Ed = 1)
If the change in price does not change the total expenditure, the elasticity of demand is said to be equal to unity. In the table, the price falls from $10 to $9 to $8, but the total expenditure (PQ) remains unaltered at $10,000. So, the elasticity of demand is equal to unity.

Demand Schedule with Different Elasticities
Elastic Demand
Unit Elastic Demand
Inelastic Demand
P
Q
PQ (TE)
P
Q
PQ (TE)
P
Q
PQ (TE)
$10
$9
$8
1,000
2,000
3,000
10,000
18,000
24,000
10
9
8
1,000
1,111
1,250
10,000
10,000
10,000
10
9
8
1,000
1,050
1,100
10,000
9,450
8,800
Adapted from Watson & Getz: Price Theory & Its Uses

The unitary elastic demand can be illustrated by the help of a figure below.
Unitary Elastic Demand
In the figure, at initial price OP, quantity demanded is OM and total outlay (PXQ) is equal to rectangle OMRP. When the price falls to OP1, quantity demanded increases to OM1, and total expenditure is equal to rectangle OM1R1P1. The total expenditure falls by the area marked (-) and rises by the area marked (+). The area (-) is equal to area (+). So, the spending remains unaltered. In other words, new total expenditure OM1R1P1 = initial total expenditure OMRP. So, elasticity of demand is equal to unity. When the demand curve is rectangular hyperbola, the elasticity of demand on all points of it is equal to unity.

2. Elasticity of Demand Greater than Unity (Ed > 1)
If the total expenditure increases with fall in price, elasticity of demand is said to be greater than unity. As shown in table, as the price falls from $10 to $9 to $8, the total expenditure increases from $10,000 to $18,000 to $24,000. So, the elasticity of demand is greater than unity. This can be illustrated by the help of following figure.
Greater Than Unity
In the figure, the total expenditure at price OP is equal to rectangle OMRP. When price falls to OP1, the total expenditure increases to the rectangle OM1R1P1. The total expenditure falls by area marked (-), but rises by the area marked (+). The area (+) exceeds the area (-). The total spending increases. Hence, the elasticity of demand is greater than unity.

3. Elasticity of Demand Less than Unity (Ed < 1)
If the total expenditure falls with fall in price, the elasticity of demand is said to be less than unity. As shown in table, as the price falls from $10 to $9 to $8, the total expenditure falls from $10,000 to 9,450 to $8,800. Hence, elasticity of demand is less than unity. This can be illustrated by the help of a figure below.
Less Than Unity
As shown in the figure, when price is OP, the total expenditure is equal to rectangle OMRP. When price falls to OP1, the total expenditure falls to the rectangle OM1R1P1. The total expenditure falls by the area marked (-) but rises by the area marked (+). The area (+) is smaller than the area (-). The total expenditure falls. Hence, elasticity of demand is less than unity.

Cross Elasticity of Demand

Cross Elasticity of Demand

Some goods are related to each other. So a fall in the price of a commodity causes change in the demand for other commodity. As for example, demand for tea is related to the price of substitute, coffee. When the price of coffee increases, the demand for tea increases. Hence, cross elasticity of demand means the responsiveness of quantity demanded of a commodity to the change in price of other commodity. The cross elasticity of demand is defined as the percentage in the quantity demand of good x resulting from a 2 percent change in the price of good y.
According to C. E. Ferguson, “Cross elasticity is the proportionate change in the quantity demanded of good x divided by the proportionate change in the price of y.”
The formula to calculate cross elasticity is,

Cross Elasticity = Proportionate change in quantity demanded of x/Proportionate change in price of y

Symbolically, Ec = Δqx/Δpy x Py/Qx

The concept of cross elasticity can be illustrated by the help of a numerical example. Suppose that x and y are two substitute goods. Suppose when the initial price of y is $4.50, the initial quantity of x is 60kg. Now when the price of y increases to $5, the quantity demanded of x increases to 70kg. The cross elasticity is calculated as,

Ec = Δqx/Δpy x Py/Qx 
= 10/5.0 x 4.5/60 = 3/2 = 1.5

1.5 coefficient shows that the cross elasticity is positive.

Types of Cross Elasticity

The goods may be either substitutes or complements. So the cross elasticity is of two types as follows:
1. Positive Cross Elasticity (Ec > 1)
When two goods are substitutes of each other, the cross elasticity is positive. As for example, tea and coffee. The increase in price of one commodity leads to an increase in quantity demanded of other commodity. Because, people substitute one commodity for other.
Positive Cross Elasticity
In the figure, demand curve DD shows positive cross elasticity. Because, with the increase in price X from OP to OP1, demand for Y has increased from OM to OM1.

2. Negative Cross Elasticity (Ec < 0)
When two goods are complements, cross elasticity is negative. As for example, shoe and shoelaces. The increase in price of one commodity causes fall in the quantity demanded of other commodity.
Negative Cross Elasticity
In the figure, demand curve DD shows negative cross elasticity. Because due to the increase in price of X from OP to OP1, demand for Y has declined from OM to OM1.

When the goods are not related to each other, the cross elasticity is zero. As for example, book and coat. The change in price of one does not affect the demand for other. Hence, the demand curve will be a vertical straight line. But this is not counted as cross elasticity.

Income Elasticity of Demand

Income Elasticity of Demand

The income elasticity measures the responsiveness in quantity demanded to the change in income. In other words, it measures by how much the quantity demanded changes with change in income. The income elasticity of demand is defined to be the percentage change in quantity demanded resulting from a 1 percent change in consumer’s income.

According to C. E. Ferguson, “Income elasticity of demand is the proportionate change in quantity demanded divided by proportionate change in income.”

The formula to measure income elasticity is,

Income elasticity = Proportionate change in quantity demanded/Proportionate change in income

Symbolically, 
Ey = Δq/Δy  x   y/q

Where, y denotes income

The concept of elasticity of income can be illustrated by the help of an example. Suppose that when the income is $100, demand is 25 units. Now suppose that the income increase to $150. As a result of its demand increases to 30 units. The elasticity of income is calculated as,

EyΔq/Δy  x   y/
= 5/50 x 100/25 = 2/5

The coefficient 2/5 shows that the demand is inelastic.

Types of Income Elasticity

There are three types of income elasticity in practice. They are:

1. Positive income elasticity (Ey > 0)
If the demand for the commodity increases with increase in income elasticity is said to be positive. For most commodities increase in income lead to increases in quantity demanded. Such goods are called normal goods. Normal goods have positive income elasticities.

2. Negative Income Elasticity (Ey < 0)
If the demand decreases in income, income elasticity is said to be negative. Inferior goods such as cheap foods have negative income elasticities.

3. Zero Income Elasticity (Ey = 0)
The boundary between positive and negative income elasticity is zero income elasticity. If the demand for the commodity does not change with the increase in income, income elasticity is said to be zero. This happens in case of neutral goods such as salt, matches etc.

These three types of income elasticity have been shown in a single diagram below:
Types of Income Elasticity
In the figure, demand curves show zero, positive and negative income elasticity. Good A has zero income elasticity. Good B is a normal good with a positive income elasticity. Good C is an inferior good with a negative income elasticity.

It should, however, be noticed that a good does not have to be in the same category at all levels of income. The same good may have zero income elasticity at very low level of income; positive elasticity at higher level of income and negative income elasticity at very high level of income.
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Elasticity of Demand

Elasticity of Demand

The term ‘elasticity’ denotes the quantity of a good to expand and contract. Hence, the change in quantity demanded due to change in price is called elasticity of demand. The economists like Courot, J. S. Mill, introduced the concept of elasticity of demand in economics. The credit is given to Dr. Alfred Marshall for the development of this concept.

The law of demand tells that the quantity demanded of a commodity varies inversely with price. But it does not tell how much quantity demanded changes with change in price. This task is accomplished by elasticity of demand. The elasticity of demand tells by how much the quantity demanded changes with change in price.
In the words of Alfred Marshall, “The elasticity (or responsiveness) of demand in a market is great or small according as the amount demanded increase much or little for a given fall in price and diminishes much or little for a given rise in price.”
According to Stonier and Hague, “Elasticity of demand is, therefore, a technical term used by the economists to describe the degree of responsiveness of the demand for the commodity to a fall in its price.”
In brief, elasticity of demand measures the rate of change in quantity demanded as a result of the change in price.

Kinds of Elasticity of Demand

Broadly speaking, there are three main types of elasticity of demand. They are price elasticity, income elasticity and cross elasticity.

Price Elasticity of Demand

In general, elasticity of demand means price elasticity of demand. This concept is most popular and most frequently used. Price elasticity means the responsiveness of quantity demanded to the change in price. The price elasticity of demand is defined to be the percentage change in quantity demanded resulting from 1 percent change in price. The price elasticity shows at what rate the demand changes with change in price. In the words of C. E. Ferguson, “Price elasticity is the proportionate change in quantity demanded divided by the proportionate change in price.”

The formula to find out price elasticity is,

Price elasticity = Proportionate change in quantity demanded/Proportionate change in price

Symbolically,

Ep = Δq/Δp x p/q

Where Ep = elasticity of price, P = price, Δ = small change and q = quantity. The concept of price elasticity can be illustrated by the help of a numerical example. Suppose that the original price (P1) of a commodity is $10 per unit and quantity demanded (Q1) is 2000 units. Now suppose that when price (P2) fall to $9, quantity demanded increases to 2500 units. The price elasticity is calculated as follows:

Ep = Δq/Δp x p/q

= 500/-1 x 10/2000 = -5/2 = -2.5

It shows that the quantity demanded increase by 2.5 percent with one percent fall in price. The minus sign shows the inverse relationship between price and quantity demanded. In general, this sign is not used, since the inverse relationship is an implied one. 2.5 is called co-efficient of elasticity of demand. The coefficient >1, =1, <1, =0 and = ∞ shows elastic, unitary elastic, inelastic, perfectly inelastic and perfectly elastic demand respectively.

Types of Price Elasticity

The price elasticity of demand is classified into following five parts:

1. Perfectly Elastic Demand (Ep = ∞ )
The demand is said to be perfectly elastic if the quantity demanded increases in unlimited quantity with small fall in price or quantity demanded falls to zero with a small rise in price. Such situation is rarely found in real life.
Perfectly Elastic Demand
In figure, demand curve DD is a horizontal straight line or parallel to the OX axis. It shows that the negligible change in price causes infinite rise or fall in quantity demanded.

2. Perfectly Inelastic Demand (Ep = 0)
If the demand remains constant whatever be the price, demand is said to be perfectly inelastic. The case of perfectly elastic demand is also rarely found in real life.
Perfectly Inelastic Demand
In the figure, the demand curve DD is a vertical straight line. It shows that the demand remains constant whatever be the change in price. As for example, even after the increase in price from OP to OP1 and fall in price from OP to OP2, the quantity demanded remains OM.

3. Relatively Elastic Demand (Ep > 1)
If there is a great change in demand with a small change in price, it is called relatively (more) elastic demand. The demand for luxury goods is considered to be more elastic.
Relatively Elastic Demand
In the figure, the demand curve DD is more flatter which shows that the demand is more elastic. The small fall in price from OP to OP1, has led to greater increase in demand from OM to OM1. Likewise, demand decrease more with small increase in price.

4. Relatively Inelastic Demand (Ep < 1)
If there is small change in demand with greater change in price, the demand is said to be relatively inelastic. The demand for basic goods such as salt, matches are said to be less elastic.
Relatively Inelastic Demand
In the figure, demand curve DD is steeper which shows that the demand is less elastic. The greater fall in price from OP to OP1 has caused small change in demand from OM to OM1. Likewise, great increase in price leads to small fall in demand.

5. Unitary elastic demand (Ep = 1)
If the ratio of change in demand is equal to the ratio of change in price, the demand is said to be unitary elastic. This kind of elasticity is also an imaginary one.
Unitary Elastic Demand
In the figure, demand curve DD is a rectangular hyperbola, which shows that the demand is unitary elastic. The fall in price from OP to OP1 has caused equal proportionate increase in demand from OM to OM1. Likewise, when price increase, the demand decreases in the same ratio.