Question

Given the demand function P = 20 – 5Q, find the price elasticity of demand when price of the commodity is 5 Birr per unit. Mention if the demand is price elastic or inelastic at this point

Answer 1

Solution:

Derive inverse demand function:

P = 20 – 5Q

Q = 4 – 0.2P

Q = 4 – 0.2(5) = 4 – 1 = 3

Q = 3

Price elasticity of demand (PED) = $\frac{\triangle Q}{\triangle P} \times \frac{P}{Q}$

$\frac{\triangle Q}{\triangle P}$ = -0.2

PED = $-0.2\times \frac{5}{3} = -0.33$

Price elasticity of demand (PED) = 0.33

 

The demand is price inelastic since it less than one. This means that a price change causes a smaller percentage change quantity demanded.