Solved Questions- Price Elasticity of Demand using Total Expenditure Approach

 

1.      From the following table, calculate the price elasticity of demand by the percentage method.

Price of X ( ₹per unit)

Total Expenditure (₹)

4

600

5

525


Solution:

      The values of Quantity demanded can be calculated with the help of the given formula:

      Total Expenditure = Price × Quantity Demanded

       Quantity Demanded = Total Expenditure/ Price

Price of X

( ₹per unit)

Total Expenditure (₹)

Q.D

P=4

600

Q=600/4= 150

P1=5

525

Q1=525/5=105

      ΔP = P1-P

            =5-4

            = 1

Ed =?

          ΔQ= Q1-Q

     =105-150

= -45

 









Price Elasticity of Demand = 1.2

2. When the price of a good change to ₹ 3 per unit, the consumer’s demand rises from 18 units to 30 units. The price elasticity of demand is 1. What was the price before change? Use the expenditure approach of price elasticity of demand to get the solution.

Solution: The following information is given:

 

Q = 18 units

 

Q1= 30 units

 

P =?

 

P1= ₹3

 

Ed = 1

 

 

 

 

 


Using the given formula,

Total expenditure = Price × Q.D

Total expenditure = ₹ 3 × 30 = ₹ 90. It will remain constant as the price elasticity of demand is 1.

The value of initial price can also be calculated by putting the values of the initial quantity and total expenditure in the formula given above:

Initial Price = Total expenditure / Q.D

                    = 90/18=₹ 5

The Price before change is ₹ 5


3. 8 units of goods are demanded at a price of ₹7. Price Elasticity of demand is (-1). How many units will be demanded if the price rises to ₹8 per unit? Use expenditure approach of Price Elasticity of Demand to answer this question.

Solution:  Given the values above in the question, the total expenditure can be calculated using the formula:

      Total Expenditure = Price × Q.D

Since the elasticity of demand is (-1) or unitary. Therefore, total expenditure will be ₹56 and the value of quantity demand can be calculated as follows:

T.E =P1 × Q1

56 = 8 ×Q1

Q1= 56/8 =7 units

Quantity demanded will be 7 units when price rises to ₹8.


4.  When the price of a good falls from ₹ 10 per unit to ₹ 9 per unit, its demand rises from 9 units to 10 units. Compare expenditure on the good to determine whether demand is elastic or inelastic.

Solution: Given the values above in the question, the total expenditure can be calculated using the formula:

Price of X

( ₹per unit)

Q.D

(units)

Total Expenditure (₹)

P=₹10

Q=9

90

P1=₹9

Q1=10

90


The demand will be unitary elastic or 1 since the total expenditure has come out to be same or constant i.e. ₹90 in both cases.

5.  Price Elasticity of Demand of a good is (-) 1. The consumer spends ₹ 50 on the good at the prevailing price. When the price changes, he buys 25 units. What is the new price? Use the Total Expenditure Method of calculating Price Elasticity of Demand to answer this question.

Solution:

When the elasticity of demand is -1, it means total expenditure i.e. ₹ 50 will remain same.

 The value of new price will be calculated using the given formula:

  T.E = P×Q.D

  50 = P×25

  P= 50÷25=₹2

The value of new price is ₹2 per unit.

 














% Change in Q.D = -0.2  60 = (-12) %

Let initial Price (P) = ₹ 100

New Price (P1) = (Initial Price) 100+ 100 ×60% (As the price increased by 60%)

New Price (P1) = ₹160.

 Let Initial Quantity (Q) = 100 units

New Quantity (Q1) = (Initial quantity) 100 –100 ×12% (As quantity demanded decreased by 12%)

New Quantity (Q1) =100-12 = 88 units.

So, Initial Expenditure will be P  i.e. 100  =₹10000 and final expenditure will be P1  Q1 i.e. 160×88 =₹14080


If Initial Expenditure is ₹10000, then the final expenditure is ₹14080

If Initial Expenditure is ₹1000 (given), then final expenditure will be 14080/10000 × 1000 = ₹1408

New Expenditure=₹1408




Solution:

 The following information is given: Ed = -0.4 and  = 0.2

 Percentage change in Q.D =  =0.2  =20%

The percentage change in price can be calculated with the help of the given formula:




 

% Change in Q.D = 20/-0.4= (-50) %

Let initial Price (P) = ₹ 100

New Price (P1) = (Initial Price) 100- 100×50% (As price decreased by 50%)

New Price (P1) = ₹50.

 Let Initial Quantity (Q) = 100 units

New Quantity (Q1) = (Initial quantity) 100 +100 ×20% (As quantity demanded increased by 20%)

New Quantity (Q1) =100+20 = 120 units.

So, Initial Expenditure will be P  i.e. 100  =₹10000 and final expenditure will be P1  Q1 i.e. 50×120 =₹6,000

 

If Initial Expenditure is ₹10,000, then the final expenditure is ₹6,000

If Initial Expenditure is ₹2,000 (given), then final expenditure will be  6000/10000 ×2000 = ₹1200

New Expenditure=₹1200

 

8. Given Ed= - 0.2 and percentage increase in quantity demanded = 20%, find the percentage change in expenditure.

Solution: The  following information is given:

Ed is -0.2

Percentage increase in quantity demanded =20%

Putting the values in the formula given below: 








Let initial Price (P) = ₹ 200

New Price (P1) = (Initial Price) 200- 100×100% (As price decreased by 100%)

New Price (P1) = ₹100.

 Let Initial Quantity (Q) = 100 units

New Quantity (Q1) = (Initial quantity) 100 +100 ×20% (As quantity demanded increased by 20%)

New Quantity (Q1) =100+20 = 120 units.

So, Initial Expenditure (TE) will be P  i.e. 200  =₹20,000 and final expenditure (TE1) will be P1  Q1 i.e. 100×120 =₹12,000



(ΔTE= TE1-TE = 12000-20000= -8000)



Therefore, Total expenditure reduces by 40%

If Initial Expenditure is ₹10,000, then the final expenditure is ₹6,000

If Initial Expenditure is ₹2,000 (given), then the final expenditure will be 6000/1000  × 2000 = ₹1200

New Expenditure=₹1200

Note: In this question, we cannot assume initial price be ₹100 as the price further decreases by 100%

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