Respuesta :
Answer:
The required elasticity is [tex]E_p=\frac{p}{357-p}[/tex].
The demand is inelastic.
The required value of p for which total revenue is maximum is 178.5
Step-by-step explanation:
Consider the provided function.
[tex]D_p= 357-p[/tex]
[tex]D_p=q= 357-p[/tex]
Part (A) The elasticity
The elasticity of demand is: [tex]E_p=\frac{p}{q} \cdot \frac{dq}{dp}[/tex]
[tex]\frac{dq}{dp}=-1[/tex]
But elasticity is always positive therefore,
[tex]E_p=\frac{p}{357-p}[/tex]
Hence, the required elasticity is [tex]E_p=\frac{p}{357-p}[/tex].
Part (b) The elasticity at p=89, stating whether the demand is elastic, inelastic or has unit elasticity.
Substitute p=89 in above elasticity formula.
[tex]E_{89}=\frac{89}{357-89}[/tex]
[tex]E_{89}=\frac{89}{268}[/tex]
The above value is less than 1, therefore the demand is inelastic.
Part (C) The value(s) of p for which total revenue is a maximum (assume that p is in dollars).
For maximum revenue substitute E=1.
[tex]1=\frac{p}{357-p}[/tex]
[tex]357-p=p[/tex]
[tex]2p=357[/tex]
[tex]p=178.5[/tex]
Hence, the required value of p for which total revenue is maximum is 178.5
