Question

If the demand function is p = (4 - 5x) square, for what value of x the elasticity of demand will be unity.

Answer 1

Answer:

so the demand is elastic when p=60. or 5p=800-10p. That is, the demand is unitary when p=160/3. So if the demand is elastic at p (E(p) > 1), then an increase in unit price will cause the revenue to decrease, whereas a decrease in the unit price will cause the revenue to increase.

Answer 2

We recall the formula for the elasticity of demand

$e=-\frac{p}{x}.\frac{dx}{dp}$

where $p$  is the demand function

Given:

$p=(4-5x)^{2}$

We differentiate,

$\frac{dp}{dx}=-10(4-5x)$

We have, elasticity as unity,

$e=-\frac{p}{x}.\frac{dx}{dp}$

$1=-\frac{(4-5x)^{2} }{x} .\frac{1}{-10(4-5x)}$

$1=\frac{4-5x}{10x}$

$10x=4-5x$

$x=\frac{4}{15}$