Question

If the demand function is : 𝑄𝑑 = 1300 − 10𝑃 − 𝑃2 Where P = 20, find the price elasticity of demand (show all working used)  

Answer 1

Price Elasticity of Demand

$Q_d=1300-10P-P^2$

$P=20$

$Q_d=1300-10(20)-20^2$

$Q_d=700$

$Price\ Elasticity = \frac{\%change\ in\ Quantity}{\%change\ in\ Price}$

To get percentage changes, we assume assume the price changes by an increase and decrease of 20%.

Increase;

new price $=1.2\times 20=24$

$Q=1300-10(24)-24^2$

$Q=484$

$Price\ Elasticity=\frac{(484-700)/700}{(24-20)-20}$

$=\bold{-1.5}$

Decrease;

new price $=0.8\times20=16$

$Q=1300-10(16)-16^2$

$Q=884$

$Price\ Elasticity=\frac{(884-700)/700}{(16-20)/20}$

$=Price\ Elasticity=\frac{(484-700)/700}{(24-20)-20}$

$=\bold{-1.3}$

Price Elasticity of Demand at both instances result to a negative number. The product therefore has an inelastic demand function.