Question

Suppose a rise in the price of peaches from Rs.5.50 to Rs.6.50 per bushel decreases the quantity demanded from 12,500 to 11,500 bushels. Calculate the price elasticity of demand .​

Answer 1

Given:

Suppose a rise in the price of peaches from Rs.5.50 to Rs.6.50 per bushel decreases the quantity demanded from 12,500 to 11,500 bushels.

To find:

Calculate the price elasticity of demand

Solution:

The initial price, P₁ = Rs. 5.50

The final price, P₂ = Rs. 6.50

The initial quantity demanded, Q₁ = 12500

The final quantity demanded, Q₂ = 11500

The required formula of price elasticity of demand is as follows:

$\boxed{\bold{E_d = \frac{\%\triangle Quantity \:Demanded}{\% \triangle Price} }}$

$\boxed{\bold{\%\triangle \:Q_d = \frac{Q_2-Q_1}{\frac{Q_2+Q_1}{2} }\times 100 }}\\\boxed{\bold{\%\triangle \:P = \frac{P_2-P_1}{\frac{P_2+P_1}{2} }\times 100 }}$

Now, on substituting the given values in the formulas above, we get

The percentage change in quantity,

= $\frac{11500-12500}{\frac{11500+12500}{2} }\times 100$

= $\frac{-1000}{12000 }\times 100$

= $\bold{-8.34\%}$

The percentage change in price,

= $\frac{6.50-5.50}{\frac{6.50+5.50}{2} }\times 100$

= $\frac{1}{6 }\times 100$

= $\bold{16.67\%}$

∴ The price elasticity of demand is,

=  $\frac{Percentage \:change \:in \:quantity}{Percentage \:change \:in \:price}$

= $\frac{-8.34\%}{16.67\%}$

= $\bold{-0.5}$

Thus, the price elasticity of demand is → - 0.5.

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