Elasticity of Demand

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Questions:

Generic 3

15 x 3 = 45

Calculate the price elasticity of demand for a commodity when its price increases by 25% and quantity demanded falls from 150 units to 120 units.

The quantity demanded of a commodity at a price of Rs 8 per unit is 600 units. Its price falls by 25 percent and the quantity demanded rises by 120 units. Calculate the price elasticity of demand. Is its demand elastic? Give reason for your answer

The demand for a good rises by 20 percent as a result· of fall in its price. Its price elasticity of demand is (-)0.8. Calculate the percentage fall in price.

When price of a commodity falls by 20%, the quantity demanded of it increases by 80%. Find out its price elasticity of demand.

As a result of increase in price from 4 to 5, the quantity demanded decreases by 20%. Comment on PED.

Price elasticity of demand for a product is 'unity'. A household buys 25 units of this product at the price of RS 5 per unit. If the price of product rises by Rs 1, how much quantity of the product will the household buy?

The demand for a good at Rs10 per unit is 40 units. Price falls by Rs 5. If price elasticity of demand is (-) 3, calculate the new quantity demanded.

A consumer buys 80 units of a good at a price of Rs 5 per unit. Suppose, the price elasticity of demand is (-) 2. At what price will he buy 64 units?

A decline in the price of good X by Rs 5 causes an increase in its demand by 20 units to 50 units. The new price is Rs 15. Calculate elasticity of demand.

10.

A consumer spends Rs 80 on a commodity when price is Rs 1 per unit. If the price increases by Rs 1, his expenditure becomes Rs 96. Comment on PED.

11.

The demand for a goods falls to 500 units in response to rise in price by Rs 10. If the original demand was 600 units at the price of Rs 30, calculate price elasticity of demand.

12.

Suppose the price elasticity of demand for a good is -0.2. If there is a 5% increase in the price of the good, by what percentage will the demand for the good go down?

13.

Consider the demand curve D(P) = 10 - 3p. What is the elasticity at price 5/3?

14.

Consider the demand for a good. At price Rs 4, the demand for the good is 25 units. Suppose price of the good increases to Rs 5, and as a result, the demand for the good falls to 20 units. Calculate the price elasticity?

15.

Explain price elasticity of demand.

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Answers Key:

Generic 3

15 x 3 = 45

Original Quantity (Q)=150 units	% Change in Price = 25%
New Quantity (Q₁) = 120 units	Elasticity of Demand (ED) =?
Change in Quantity(\(\triangle\)Q)= -30 units

Percentage change in demand=\({\triangle Q\over Q}\times 100={-30\over150}\times100=-20\%\)
Price Elasticity of Demand\ (ED)\(={\%Change\ in\ quantity\ demanded \over \%Change\ in\ price}={-20\% \over 25\%}\)
Price Elasticity of Demand (ED)= (-) 0.8
ED = (-)0.8; Demand is less elastic because ED < 1.

Original Quantity (Q)=600 units	% Change in Price = -25%
Change in Quantity (\(\triangle\)Q) = 120 units	Elasticity of Demand (ED) =?
NewQuantity (Q_l) = 720 units

Percentage change in demand=\({\triangle Q\over Q}\times 100={120\over600}\times100=20\%\)
Price Elasticity of Demand (ED) \(={\%Change\ in\ quantity\ demanded \over \%Change\ in\ price}={20\% \over -25\%}\)
Price Elasticity of Demand (ED)= (-) 0.8
ED = (-)0.8; Demand is less elastic because ED < 1.

%Change in Demand = 20%	% Change in Price =?
Elasticity of Demand (ED)= -0.8

\((-)0.8={20\%\over \% Change\ in\ Price}\)Percentage Fall in Price = 25%
Price for the goods will fall by 25%

% Change in Demand = 80%	% Change in Price = - 20%
Elasticity of Demand (ED)= ?

Price Elasticity of Demand (ED)\(={\%Change\ in\ Quantity\ demanded \over \% Change\ in\ Price}={80\% \over -20\%}=-4\)
ED = (-)4 (Demand is highly elastic as ED > 1).

Original Price(P)= 4	Percentage change in quantity demanded =(-)20%
New Price (P₁)=5	ED =?
\(\triangle\)P= 1

Percentage change in price \(={\triangle P\over P}\times 100={1\over4}\times 100=25\%\)
\(PED={Percentage\ change\ in\ Quantity\ demended \over Percentage\ change\ in\ price}\)
\(={[-]20\%\over 25\%}=[-]0.8\)
Negative Sign of ED indicates that inverse relationship between price and quantity demanded. PED = 0.8 [Less than unitary elastic demand or inelastic demand].

Original Quantity (Q)= 25 units	Original Price (P)=Rs 5
New Quantity (Q_I)=?units	Rise in Price(\(\triangle\) P) =Rs 1
Change in Quantity(\(\triangle\) Q)=?	New Price (P₁)=Rs 6
Elasticity of Demand (ED)=1

Price Elasticity of demand (ED)=\({\triangle Q\over \triangle P}\times {P\over Q}\)
\(1={ \triangle Q\over1}\times {5\over 25}i.e.\triangle Q=5 units\)
As price is increasing, the quantity demanded will decrease. It means that
New quantity = Original quantity (Q) - Change in quantity (\(\triangle\)Q) = 25 - 5 = 20 units
New Quantity = 20 units

Original Quantity (Q)= 40 units	Original Price (P)=Rs 10
New Quantity (Q_I)=?units	fall in Price(\(\triangle\) P) =-Rs 5
Change in Quantity(\(\triangle\) Q)=?	New Price (P₁)=Rs 5
Elasticity of Demand (ED)= -3

Price Elasticity of demand (ED)=\({\triangle Q\over \triangle P}\times {P\over Q}\)
\((-)3={ \triangle Q\over(-)5}\times {10\over 40}i.e.\triangle Q\)= 60 units
As price is decreasing, the quantity demanded will increase. It means that New Quantity = Original Quantity (Q) + Change in Quantity (\(\triangle\)Q) = 40 + 60 = 100 units New Quantity = 100 units.

Original Quantity (Q)= 80 units	Original Price (P)=Rs 5
New Quantity (Q_I)=64units	New Price (P_I) =?
Change in Quantity(\(\triangle\) Q)=-16 units	Change in Price(\(\triangle\) P) =?
Elasticity of Demand (ED)= -2

Price Elasticity of demand (ED)=\({\triangle Q\over \triangle P}\times {P\over Q}\)
\(-2={-16\over \triangle P}\times {5\over 80}=\triangle P=Rs\ 0.5\)
As the quantity demanded is decreasing, price will increase. It means that New Price = Original Price (P) + Change in Price (P) = 5 + 0.5 = Rs 5.5 New Price = Rs 5.5.

Let Initial Price [P] = x
New Price [P₁]= [Initial Price] x - 5 [As given that price falls by 5]
New Price [P₁] = 15 [Given]
Then, Initial Price [P] =New Price [P_I] + 5 = 15 + 5 = 20
Initial Quantity [Q]= 30[As given quantity increase by 20 units and which goes to 50]
New quantity [Q₁] = 50

Initial Price (P)= 20	Initial Quantity (Q)= 30
New Price (P₁)= 15	New Quantity (Q₁) = 50
\(\triangle P=[-]5\)	\(\triangle Q=20\)

\(PED={\triangle Q\over \triangle P}\times {P\over Q}={20\over (-)5}\times {20\over30}={400\over(-)150}=(-)2.66\)
Negative Sign of ED indicates that inverse relationship between price and quantity demanded.
PED = 2.66 [More than unitary elastic demand or Elastic demand]

10.

Initial Price (P) = 1	Initial Expenditure = 80	Initial DD (Q)\({80\over1}\)=80
New Price (P₁) = 2	New Expenditure = 96	NewDD (Q₁)=\({96\over2}\) =48
\(\triangle P=1\)		\(\triangle Q=-32\)

\(PED={\triangle Q\over \triangle P}\times{P\over Q}={[-]32\over1}\times {1\over 80}=[-]{4\over10}=[-]0.4\)
Negative Sign of ED indicates the inverse relationship between price and quantity demanded.
PED = 0.4 [Less than unitary elastic demand or inelastic demand]

11.

New Quantity (Q₁)= 500 units	Rise in Price (\(\triangle\)P)= Rs 10
Original Quantity (Q) =600 units	Original Price (P) = Rs 30
Change in Quantity(\(\triangle\)Q)=-100 units	New Price (P₁)= -Rs 40
Elasticity of Demand (ED) = ?

Price Elasticity of demand (ED)=\({\triangle Q \over \triangle P}\times {P\over Q}={-100\over10}\times {30\over600}=(-)0.5\)
ED = (-) 0.5 (Demand is inelastic as ED < 1)
Negative sign indicates the inverse relationship between price and quantity demanded.

12.

%Change in Demand =?	% Change in Price = 5%
Elasticity of Demand (ED) = (-) 0.2

Price Elasticity of Demand (ED) = \({\% \ change \ in \ quntity \ Demand \over \% \ Change \ in \ price}\)
\((-)0.2={\% \ change \ in \ quntity \ Demand \over \% 5}\)
Percentage fall in demand = 1%
Demand for the piece of goods will fall by 1%.

13.

Given Q = 10 - 3P.
When P = \({5\over3},Q=10-3\times{5\over3}=5\)
Differentiating Q with respect to P,
we get,
We know,\({\triangle Q\over \triangle P}=-3\)
\(ED={\triangle Q\over \triangle P}\times {P\over Q}=-3\times{5/3\over 5}\)
\(=-3\times{5\over3}\times{1\over5}=[-]1\)
Negative Sign of ED indicates that inverse relationship between price and quantity demanded.
PED = 1 [Unitary elastic demand].

14.

Original Quantity (Q) = 25 units	Original Price (P) = Rs 4
Fall in Quantity (\(\triangle\)Q) = - 5 units	Rise in Price (DP) = Rs 1
New Quantity (Q₁) = 20 units	New Price (P₁)=Rs 5
Elasticity of Demand (ED) =?

Price Elasticity of demand (ED) \(={\triangle Q\over \triangle P }\times {P\over Q}={-5\over 1}\times {4\over25}=(-)0.8\)
ED = (-) 0.8 (Demand is less elastic as ED < 1)
Negative sign indicates the inverse relationship between price and quantity demanded.

15.

The degree of responsiveness of quantity demanded to changes in price of commodity is known as price elasticity of demand.