Question

When price of a good gets halved its demand rises from 120 units to 150 units. Calculate its price elasticity of demand

Answer 1

Given -

• Price of good get halved .

• Quantity demanded changed from 120 to 150 units .

To Find :-

Price elasticity of demand .

Solution :-

Formula of price elasticity.

$\boxed{\sf{\red{E_d = (-) \frac{Percentage \; change \; in \; demand }{Percentage \; change \; in Price } }}}$

Let's Find out the percentage change in Quantity demanded firstly -

$\sf{\implies \; \frac{change \; in \; quantity }{Initial \; quantity} \times 100 }$

$\sf{\implies \frac{150 - 120 }{120} \times 100 }$

$\sf{\implies \frac{ 30}{120} \times 100 \rightarrow \frac{3000}{120} }$

$\sf{\implies 25 }$ percent

Now , finding the percentage change in price -

Let's assume initial price was 2x . Now it became x .

$\sf{\implies \frac{x - 2x }{2x } \times 100 }$

$\sf{\implies \frac{-x}{2x} \times 100 \rightarrow \frac{-100}{2} }$

$\sf{ \implies -50 \; percent }$

Now using the formula

$\sf{\implies E_d = (-) \frac{25}{-50}}$

Price elasticity of demand is 0.5