Measuring Elasticity : Arc Elasticity of Demand

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Learning Contents:                                                            

·         Introduction to Arc Elasticity of Demand

·         Arc Elasticity of Demand is an improvement over the Proportionate method

·         Practical Problems Based on Arc Elasticity of Demand

·         Difference between Proportionate method and Arc Elasticity Method

Introduction to Arc Elasticity of Demand (Midpoint method)

Arc elasticity of demand measures the elasticity between two price (or two points on the demand curve) using the midpoint between the two curves. This method uses the average of both price and both quantity in the denominator (base) for finding the elasticity unlike the proportionate method that uses the initial price and initial quantity in the denominator (base). Therefore, when using arc elasticity, we need not be worried about which point is the starting point and which point is the ending point since it gives the same results whether price rises or falls. The formula used to calculate the arc elasticity of demand is given below:


Here,

P1= Original Price

P2= New Price

Q1= Original Quantity

Q2= New Quantity

Note: When calculating the elasticity using the arc method, we must ignore the negative sign.


Arc Elasticity of Demand is an improvement over the Proportionate method

In the case of proportionate method, the elasticity of demand may vary either we move up and down the demand curve as initial price or initial quantity will be different in both cases while calculating the percentage change. In other words, it is not clear that which price and quantity to be taken or used as base?

In the case of Arc Elasticity, the value of elasticity of demand comes out to be the same as we consider the average of both price and both quantities in the base instead of initial price and quantity.  

The calculation shows how the value of elasticity of demand is different in both methods. Let’s understand with the help of a given example.

 

Using Proportionate Method

Case 1:  Calculating Price Elasticity when the price of a newspaper increased from ₹ 2 to ₹ 4 and its daily sales decreased from 10 million units to 8 million units. Assuming the initial price is ₹2 and the initial quantity is 10 million units and movement on the demand curve is from point B to A. The value of elasticity of demand will be calculated as follows:

The following information is given

 P= ₹2    Q= 10 million

 P1= ₹4   Q1= 8 million          

ΔQ =Q1-Q = 8-10 = -2

ΔP =P1-P = 4-2 = 2

Plugging these numbers into the formula,






Case 2: Calculating price elasticity if the price had fallen from₹ 4 to ₹ 2 and sales increased from 8 million to 10 million units. Assuming now the initial price is ₹4 and initial quantity is 8 million units and movement on the demand curve is from point A to B. The value of elasticity of demand is calculated as follows:

Figure 2: Proportionate Elasticity of Demand













When the price movement is opposite,

 P= ₹4    Q= 8 million

 P1= ₹2   Q1= 10 million          

ΔQ =Q1-Q = 10-8 = 2

ΔP =P1-P = 2-4 = -2

Plugging these numbers into the formula,








Using Arc Elasticity Method

If the price of a newspaper rose from ₹ 2 to ₹ 4 and its daily sales fell from 10 million units to 8 million units. What is the price elasticity of demand?

The following information is given

P1= ₹2   Q1= 10 million

 P2= ₹4   Q2= 8 million         

Plugging these numbers into the formula,







Interpretation:

When using proportionate method, the value of elasticity comes out to be different in both cases due to change in initial price and initial quantity in base (denominator). Therefore, this method is less reliable.

When using Arc Elasticity method, the value of elasticity comes out to be the same as we have taken the average of both prices and quantities in base (denominator). Therefore, this method is more reliable.


Practical Problems Based on Arc Elasticity of Demand

1.If the price of good decreases from ₹500 to ₹400, leading to an increase in quantity demanded from 100 to 150 units, then the price elasticity of demand can be calculated as: (Use Arc Elasticity method)

Solution:

The following information is given

P1= ₹500   Q1= ₹100

 P2= ₹400 Q2= ₹150           

Plugging these numbers into the formula,


 




2. If the price of good decreases from ₹10 to ₹8, leading to an increase in quantity demanded from 40 to 60 units, then the price elasticity of demand can be calculated as: (Use Arc Elasticity method)

Solution:

The following information is given

P1= ₹10   Q1= ₹40

P2= ₹8     Q2= ₹60

Plugging these numbers into the formula,



 



3. If a coffee shop raises the price of its large cup of coffee from ₹60 to ₹100 and quantity demanded falls from 700 cups to 100 cups a day, the price elasticity of demand for coffee will be (Use Arc Elasticity method)

Solution:

The following information is given

P1= ₹60   Q1= ₹700

P2= ₹100     Q2= ₹100

Plugging these numbers into the formula,



 

 

 


4. Suppose the price of movies seen at a theatre rises from ₹120 to ₹200 per person. The theatre manager observes that the rise in price causes attendance at a given movie to fall from 300 persons to 200 persons. What is the price elasticity of demand for movies? (Use Arc Elasticity method)

Solution:

The following information is given

P1= ₹120   Q1= ₹300

P2= ₹200     Q2= ₹200

Plugging these numbers into the formula,



 



5. Suppose a department store has a sale on its glass crockery. If the price of a dinner set is reduced from ₹300 to ₹200 and the quantity demanded increases from 3000 units to 5000 units. What is the price elasticity of demand for dinner set? (Use Arc Elasticity method)

 

Solution:

The following information is given

P1= ₹300   Q1= ₹3000

P2= ₹200     Q2= ₹5000

Plugging these numbers into the formula,



 

 



6. Suppose the price of toy decreases from ₹7 to ₹6. As a result, the quantity demanded increases from 18 to 20 units. What will be its price elasticity of demand? (Use Arc Elasticity method)

Solution:

The following information is given

P1= ₹7   Q1= ₹18

P2= ₹6    Q2= ₹20

Plugging these numbers into the formula,



    



Difference between Proportionate Elasticity and Arc Elasticity

S.No.

Proportionate Elasticity

Arc Elasticity

1.

It measures elasticity at a particular point on the demand curve.

It measures elasticity between two points (or using midpoints) on the demand curve.

2

It uses initial price and initial quantity in the denominator for measuring the percent changes.

It uses the average price and average quantity in the denominator for measuring the percent changes

3.

It gives different values of elasticity whether price rises or falls.

It gives the same value of elasticity whether the price rises or falls.

4.

Proportionate method is used when the price change is very small.

Arc elasticity method is used when the price change is very significant or somewhat large.

 

 

Let’s try some questions

Choose the Correct Answer

1. Which of the following describes best about Arc Elasticity of demand?

a. A measure of elasticity of demand which involves an infinitely small change from some initial price.

b. A measure of elasticity of demand that consider total expenditure

c. A measure of average elasticity over a range of the demand curve,

d. None of above.

2. Which among the following is not correct about Arc Elasticity of Demand?

a. It is used when the price change is somewhat large.

b. It considers average price and average quantity as a base while calculating the elasticity

c. It gives the different value of elasticity whether price rises or falls

d. None of above.

3. If the price of a product changes from ₹7 to ₹9 and the quantity demanded changes from 50 to 40 units then the price elasticity of demand using the midpoint approach is ________.

a. 0.89

b. 1.57

c. 0.80

d. 0.70

 

4. The price of a pen is ₹10, and the quantity demanded is 5,000 units. When the price falls to ₹8, the quantity demanded increases to 7,000 units. Based on this information and using the midpoint method, the demand for Pen must be ________

a. Elastic

b. Inelastic

c. Unit-Elastic

d. None of the above. 


Answer Key

 

1.c

2.c

3.a

4.a

 

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