Question

QUESTION :-when price rupees 10 per unit demand for a commodity is 100 units.
as the price falls to rupees 8 per unit demand expands to 150 units calculate elasticity of

question 2:-the market demand for a good is rupees 4 unit is 100 units.m due to increase in price the demand market falls to 75 minutes find out the new price a price elasticity of demand is -1 .​

Answer 1

ANSWER :

• ✎ If when price is Rs. 10 per unit, demand for a commodity is 100 units and as the price falls to Rs. 8 per unit, demand expands to 150 units; then the Price Elasticity of Demand will be (-)2.5.

• ✎ If the market demand for a good is Rs. 4 per unit is 100 units and Due to increase in price, the demand market falls to 75 units when Price elasticity of demand is -1; then the New Price of the good will be Rs. 1.

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SOLUTION :

[1]

❒ Given :-

• When price is Rs. 10 per unit, demand for a commodity is 100 units.

• As the price falls to Rs. 8 per unit, demand expands to 150 units.

❒ To Calculate :-

• Elasticity of Demand = ?

❒ Calculation :-

Here,

• Original Quantity, Q = 100 units

• Original Price, P = Rs. 10

• New Quantity, Q₁ = 150 units

• New Price, P₁ = Rs. 8

∴ Change in Quantity, △Q = Q₁ - Q = (150 - 100) units = 50 units

∴ Change in Price, △P = P₁ - P = Rs. (8 - 10) = - Rs. 2

We know that,

• $\dag \: \: \underline {\boxed{ \sf{ \: E_d = \dfrac{ \Delta \: Q}{ \Delta \: P} \times \dfrac{P}{Q}}}}$

Using this formula, we get,

• $\bigstar \: \: \tt{Price \: \: Elasticity \: \: of \: \: Demand, E_d = \dfrac{ \Delta \: Q}{ \Delta \: P} \times \dfrac{P}{Q}}$

$: \longrightarrow \tt{Price \: \: Elasticity \: \: of \: \: Demand, E_d = \dfrac{ 50}{ - 2} \times \dfrac{10}{100}}$

$\therefore \: \tt{Price \: \: Elasticity \: \: of \: \: Demand, E_d = \underline{- 2.5}}$

Hence,

• The Price Elasticity of Demand is (-) 2.5.

As E꒯ > 1; the Demand is highly elastic. The negative sign of E꒯ indicates the inverse relationship between price and quantity demanded.

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[2]

❒ Given :-

• The market demand for a good is Rs. 4 per unit is 100 units.

• Due to increase in price, the demand market falls to 75 units.

• Price elasticity of demand is -1.

❒ To Find :-

• The new price the good = ?

❒ Calculation :-

Here,

• Price Elasticity of Demand, E꒯ = - 1

• Original Quantity, Q = 100 units

• Original Price, P = Rs. 4

• New Quantity, Q₁ = 75 units

∴ Change in Quantity, △Q = Q₁ - Q = (75 - 100) units = - 25 units

Suppose,

• Change in Price = △P

We know that,

• $\dag \: \: \underline {\boxed{ \sf{ \: E_d = \dfrac{ \Delta \: Q}{ \Delta \: P} \times \dfrac{P}{Q}}}}$

Using this formula, we get,

• $\ \circledcirc \: \: \tt{Price \: \: Elasticity \: \: of \: \: Demand, E_d = \dfrac{ \Delta \: Q}{ \Delta \: P} \times \dfrac{P}{Q}}$

$: \longrightarrow \: \tt{- 1 = \dfrac{- 25}{\Delta \: P} \times \dfrac{4}{100}}$

$\therefore \: \tt{\Delta \: P = \underline{Rs. \: 1}}$

So, the change in price = Rs. 1

Now,

• ★ New Price = Original Price + Change in Price

➨ New Price = Rs. 4 + Rs. 1

∴ New Price = Rs. 5

Hence,

• The new price of the good is Rs. 5.