Question

demand function P=4-5x². For what value of x the elasticity of demand will be unity​

Answer 1

Step-by-step explanation:

given

p= 4-((5x)^2)

dp/dx = -10x

elasticity of demand = (-p/x)(dx/dp)

given elasticity of demand if unity

therefore 1 = (-p/x)(dx/dp)

1 = (-(4-(5x^2))/x)(-1/10x)

1 = (-(4-(5x^2))/x)(-1/10x)

-10 = (-(4-(5x^2))/x)(1/x)

10 = (4-(5x)^2)/x(1/x)

10 = (4-(5x)^2)/x^2

10x^2 = (4 - (5x^2))

10x^2 + 5x^2 = 4

15x^2 = 4

x^2 = 4/15

square root on both side

x = √(4/15)

therefore x = 2/√15.