Question

Given the demand function Q = 75 - 5P find the price elasticity of demand at P = 3 and P = 5

Answer 1

Solution:

Given :

Q =75 - 5P

Value of P = 3, 5

To find: Price Elasticity of demand

Formula to find Price Elasticity of demand:

Marginal function / Average function

Differentiating Q with respect to P,

Marginal function= dq/dp => -5

Average function =Q/P => (75 - 5P)/P

Substituting the value of Marginal function and Average function in the formula we get,

Elastic demand = -5/ (75 -5P)/P

=> -5p/75 -5P [equation 1]

When P=3,

Substituting P=3 in equation 1,

= 5(3) /(75 - 5(3))

= 15 (75 - 15)

= 15 / 60 =>0.25

When P=5,

Substituting P=5 in equation 1,

= 5(5) (75 - 5(5))

= 25 (75 - 25)

= 25/ (50) => 0.5

Therefore, Elastic demand at P=3=> 0.25 and when P=5=> 0.5