Question

Q. 1. The demand function is q(p) = (p+1)-2  

a. What is the price elasticity of demand?

b. At what price is the price elasticity of demand equal to (-1)?

c. Write an expression for total revenue as a function of the price

Answer 1

$a)$

Given that $g(p)=(p+1)^{-2}$, the price elasticity of demand is given as,

$e_p={p\over g(p)}\times{g'(p)}$

$g'(p)=-2(p+1)^{-3}$

$e_p={p\over (p+1)^{-2}}\times -2(p+1)^{-3}=-{2p\over p+1}$

Therefore, the price elasticity of demand at price $p$ is $-2p\over p+1$

$b)$

We set the price elasticity of demand found above equal to $-1$ and solve for the price $p$

So,

${-2p\over p+1}=-1\implies -2p=-p-1\implies p=1$

Therefore, when price=1, the price elasticity of demand is -1.

$c)$

The  total revenue is given as, $R(p)=g(p)\times p={1\over (p+1)^2}\times p={p\over (p+1)^2}$. Therefore, the total revenue is given as,

$R(p)={p\over(p+1)^2}$.