Question

The consumer demand equation for tissues is given by q = (108 − p)2, where p is the price per case of tissues and q is the demand in weekly sales.
(a) Determine the price elasticity of demand E when the price is set at $32. (Round your answer to three decimal places.) E = Interpret your answer. The demand is going by % per 1% increase in price at that price level.
(b) At what price should tissues be sold to maximize the revenue? (Round your answer to the nearest cent.) $
(c) Approximately how many cases of tissues would be demanded at that price? (Round your answer to the nearest whole number.) cases per week

Answer 1

Answer:

a) -0.842

b) $0

c) 11,664 cases

Step-by-step explanation:

a)

The price elasticity of demand E at a given point $\large (p_1,q_1)$ is defined as

$\large E=\frac{p_1}{q_1}.\frac{\text{d}q}{\text{d}p}(p_1)$

and in this case, it would measure the possible response of tissues demand due to small changes in its price when the price is at $\large p_1$

When the price is set at $32 the demand is

$\large q=(108-32)^2=5,776$

cases of tissues, so

$\large (p_1,q_1)=(32,5776)\Rightarrow \frac{p_1}{q_1}=\frac{32}{5776}=0.00554$

Also, we have

$\large \frac{\text{d}q}{\text{d}p}=-2(108-p)\Rightarrow \frac{\text{d}q}{\text{d}p}(32)=-2(108-32)=-152$

hence

$\large E=\frac{p_1}{q_1}.\frac{\text{d}q}{\text{d}p}(p_1)=0.00554(-152)=-0.842$

That would mean the demand is going down about 0.842% per 1% increase in price at that price level.

b)

When the price is $108 the demand is 0, so the price should always be less than $108.

On the other hand, the parabola

$\large q=(108-32)^2=5,776$ is strictly decreasing between 0 and 108, that means the maximum demand would be when the price is 0.

c)

When the price is 0 the demand is  

$\large (108)^2=11,664$ cases