Questions: For the demand function q=D(p)=100/(p+3)^5, find the following.
a) The elasticity
b) The elasticity at p=8, stating whether the demand is elastic, inelastic or has unit elasticity
c) The value(s) of p for which total revenue is a maximum (assume that p is in dollars)
a) Find the equation for elasticity.
Transcript text: For the demand function $\mathrm{q}=\mathrm{D}(\mathrm{p})=\frac{100}{(\mathrm{p}+3)^{5}}$, find the following.
a) The elasticity
b) The elasticity at $p=8$, stating whether the demand is elastic, inelastic or has unit elasticity
c) The value(s) of $p$ for which total revenue is a maximum (assume that $p$ is in dollars)
a) Find the equation for elasticity.
\[
E(p)=\square
\]
Solution
Solution Steps
Step 1: Finding the Elasticity of Demand, E(p)
The elasticity of demand is given by E(p)=qp×dpdq=−p+35p.
Step 2: Elasticity at a Specific Price, p0
At p0=8, the elasticity of demand is E(p0)=−3.64, which classifies the demand as inelastic.
Step 3: Maximizing Total Revenue
The price that maximizes total revenue is found by solving dpd(TR)=0. The critical point is p=0.75.
Final Answer:
The elasticity of demand at p0=8 is -3.64, classified as inelastic. The price that maximizes total revenue is p=0.75.