Question

Consider the demand for a good at price rs4 the demand for the good is 25 unit suppose price of the good increase to rs5 and as a result the demand for good falls to 20 unit calculate the price elasticity

Answer 1

Given : At price Rs. 4, the demand of the good is 25 units. Price of the good increases to Rs.5 and as a result it's quantity demanded falls to 20 units.

To find : Price elasticity of demand

Solution :

Elasticity of demand refers to the change in quantity demanded with the change in its price.

With the given information provided in the question, we have :

• $\sf Initial\:price \:(P) = Rs. 4$
• $\sf Initial \: quantity\: demanded\:(Q) = 25\, units$
• $\sf \Delta P = Rs. 1$
• $\sf \Delta Q = 5\,units$

To find elasticity of demand $\sf E_{(d)}$, we have a formula :

$\sf\implies E_{(d)} = \dfrac{\% \,change\,in\, quantity\, demanded}{\%\, change\,in\,price}$

$\sf\implies E_{(d)} = \dfrac{\dfrac{\Delta Q\times 100}{Q}}{\dfrac{\Delta P\times 100}{P}}$

$\sf\implies E_{(d)} = \dfrac{\dfrac{5\times 100}{25}}{\dfrac{1\times 100}{4}}$

$\sf\implies E_{(d)} = \dfrac{\dfrac{5\times4}{1}}{\dfrac{25}{1}}$

$\sf\implies E_{(d)} = \dfrac{20}{25}$

$\underline{\boxed{\sf \pink{\implies E_{(d)} = 0.8}}}$

Therefore the elasticity of demand is (-) 0.8.

Here the elasticity of demand smaller than 1 implies that demand is less elastic and the negative sign denotes the inverse relationship between quantity demanded and price of the commodity.

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Answer 2

Given:

Original Quantity (Q) =25 units

Fall in Quantity (ΔQ)=−5 units

New Quantity (Q₁) =20 units

Original price (P)= ₹4

Rise in price (ΔP)= ₹ 1

New price (P₁)=₹5

Elasticity of Demand (Ed)=ΔQ/ΔP × P/Q =$\frac{-5}{1}$ × $\frac{4}{25}$=(−)0.8

Demand is less elastic as Ed<1. Negative sign indicates the inverse relationship between price and the quantity demanded.