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Four Methods of Measuring Price Elasticity of Demand
Introduction
The concept of elasticity of demand has tremendous advantages. At the same time, it is not just enough to conclude whether the demand for a commodity is more elastic or less elastic. In order to apply the concept in the real life situations, it is crucial to find out the precise way of measuring elasticity. There are four methods of measuring price elasticity: the percentage method, total outlay method, point or geometrical elasticity method, and arc method. Let us look at each method one by one.
The Percentage Method
Price elasticity of demand (e_{p}) = (ΔQ/ΔP) × (P/Q)
This method is further known as ratio method, because we measure the ratio as: e_{p} = %ΔQ/%ΔP
Where,
%ΔQ = percentage change in demand
%ΔP = percentage change in price
Total Outlay Method
Marshall recommended the simplest technique to determine whether demand is elastic or inelastic. According to his technique, in order to determine the demand elasticity, you have to examine the change in total outlay of the consumer or total revenue of the firm.
Total Revenue (TR) = (Price (P) × Quantity Sold (Q))
TR = (P × Q)
Marshall has further attributed the following propositions:
(a) e_{p} > 1
 Elastic demand
 The percentage increase in quantity demanded is greater than the percentage fall in price of a commodity
 Revenue increases because the increase in quantity demanded brings more revenue irrespective of the decrease in price
 In this case, price and revenue move in opposite directions
(b) e_{p }< 1
 Inelastic demand
 The percentage increase in quantity demanded is less than the percentage decrease in price
 Revenue decreases because of the fall in price and very small increase in quantity demanded
 In this case, price and revenue move in the same direction
(c) e_{p} = 1
 Unitary elastic demand
 The percentage increase in quantity demanded equals the percentage decline in price
 Revenue remains the same because the fall in price is offset by the increase in quantity demanded of the commodity.
Table 1: Total Outlay Method
Price
 Quantity (in units)
 Total Outlay (or revenue)
 Elasticity of demand


Original 3
 10
 30
 Unitary elasticity (price elasticity = 1)

Change 2
 15
 30
 
Original 3
 10
 30
 Elastic demand (price elasticity > 1)

Change 2
 17
 34
 
Original 3
 10
 30
 Inelastic demand (price elasticity < 1)

Change 2
 11
 22

Table 2: Changes in price, outlay and elasticities of demand
Demand
 If price increases, Expenditures
 If prices decreases, Expenditures


Inelastic demand
 Increase
 Decrease

Elastic demand
 Decrease
 Increase

Unitary demand
 Remain unchanged
 Remain unchanged

The following diagram (figure 1) is helpful to understand the relationship between the total outlay and price elasticity of demand:
When the price decreases from OP_{3} to OP_{2}, the total outlay rises from OQ_{2} to OQ_{1}. The portion UT of the total outlay curve refers to e_{p }> 1.
Suppose the price increases from OP_{2}to OP_{3}. In this case, the total outlay decreases. Note that between OP_{2} and OP_{1} prices, the total outlay does not change or remains constant. The portion ST of the total outlay curve refers to e_{p} = 1.
Consider a price rise from OP_{1} to OP_{2}. In this case, the total outlay is constant. Note that between P_{1} and any price less than P_{1}, the total outlay decreases. For instance, if the price decreases from OP_{1} to OP, the total outlay also decreases from OQ_{1} to OQ. If price rises from OP to OP_{1}, total expenditure also rises. The portion RS of the total outlay curve refer to e_{p} < 1.
Point or Geometrical Elasticity Method
If you study the total outlay method carefully, you can understand that the method ignores the analysis of price range. The total outlay method applies the terms ‘elastic’ and ‘inelastic’ to the entire demand for a commodity. However, this is not the case in real life economic situations because in one price range, the demand for a commodity may be elastic and in another price range, the demand for the same commodity can be inelastic.
The demand curve is said to be linear, when the it is a straight line. Graphically, the point elasticity of a linear demand curve is shown by the ratio of the right segment to the left segment of the particular point.
If you take a point on the demand curve (for example, midpoint P in figure 2), it divides the curve into two parts.
Point Elasticity = Lower segment of the demand curve (below the given point) / Upper segment of the demand curve (above the given point)
Or e_{p} = L/U
Where,
‘e_{p}’ denotes point elasticity
‘L’ denotes the lower segment
‘U’ denotes the upper segment.
Therefore,
1. The point elasticity is unity (e_{p} = 1) at the midpoint (P) of the linear demand curve.
2. e_{p} < 1 at any point to the right of P
3. The point elasticity is greater than unity (e_{p} > 1) at any point to the left of P; at point R, e_{p} = α; at point M, the e_{p} = 0.
Nonlinear demand curve
We have just seen how to measure point elasticity when you have linear demand curve. What will you do if you have a nonlinear demand curve? To measure point elasticity from a nonlinear demand curve, just draw a tangent at the given point and let it touch both the axes.
Now elasticity at P = PM/PR
Rectangular Hyperbola
If your demand curve is a rectangular hyperbola, elasticity of demand is unity throughout the demand curve. It means that at all points on the demand curve e_{p} = 1. Let us look at a numerical example to understand this scenario better.
Table 3
Price of X
 Quantity of X
 (Price of X) x (Quantity of X)


9
 1
 9

6
 1.5
 9

3
 3
 9

2
 4.5
 9

1
 9
 9

Hence, we could note that all rectangles have the same area. It implies that the total expenditure represented by rectangles is constant.
Arc Method
The drawback of the point elasticity method is that it becomes irrelevant when there is a substantial change in the price and quantity demanded of a commodity. The concept of point elasticity holds good when a change in price and quantity is immeasurably small. If the change in price and the consequent change in quantity demanded are substantial, we will have to use more relevant concept of arc elasticity method for a precise and concrete conclusion.
An arc represents a portion or a segment of a demand curve.
The issue now before us is to derive an appropriate formula for arc elasticity.
The formula under the percentage method is (ΔQ/ΔP) × (P/Q).
Let us calculate elasticity of demand (percentage method) using market demand schedule (table 4) and the market demand curve (figure 5).
Table 4
Point
 Price of X
 Quantity of X


A
 4
 10

B
 3
 20

C
 2
 30

From A to C: e_{p} = (ΔQ/ΔP) × (P/Q) = (20/2) × (4/10) = 4
From C to A: e_{p} = (ΔQ/ΔP) × (P/Q) = (20/2) × (4/30) = 0.66
We get one e_{p }when the price falls and another e_{p }when the price rises. Thus, the formula under the percentage method gives different results depending on whether the price is increased or decreased.
How do you resolve this problem? One way to get rid of this problems is to take an average of prices and quantities and then to measure elasticity at the midpoint of the arc.
Now, the formula becomes:
(ΔQ/ (1/2) (Q_{1} + Q_{2})) / (ΔP/ (1/2) (P_{1} + P_{2}))
When we apply this new version of formula to calculate e_{p} for a movement from A to C or for a movement from C to A,
We get, e_{p} = (20/ (1/2) (10 + 30)) / (2/ (1/2) (4 + 2)) = (20/20) × (3/2) = 1.5
This is the elasticity of demand at the midpoint, i.e., at point B.
© 2013 Sundaram Ponnusamy