## Elasticity of Demand

### Given that if \(f\) is a differentiable demand function defined by
\(x=f(p)\), then the elasticity of demand at price \(p\) is given by
\(\displaystyle{ E(p)=-\frac{p\cdot f'(p)}{f(p)}}. \) (a) The demand is *elastic* if \(E(p)>1\). (b)
The demand is *unitary* if \(E(p)=1\). (c) The demand is *inelastic* if \(E(p)<1\).

### 1. Given the demand \(f(p)=x=15-\frac{5}{6}\, p \). (a) Compute \(E(p)\). (b) Is the demand elastic, unitary or inelastic when \($6\)? (c) For what \(p\) is the demand unitary? solution

### 2. The demand equation for a type of mp3 players is given by
\(x=f(p)=-\frac{7}{2}p+56\) where \(x\) (measured in units of hundred) is the
quantity demanded per week, and \(p\) is the unit price in dollars.

(a) Find the elasticity of demand \(E(p)\).

(b) Is the demand elastic, inelastic or unitary when \(p=4\).

(c) Is the demand elastic, inelastic or unitary when \(p=12\).

(d) For what \(p\) is the demand unitary?

(e) If the unit price is increased slightly from $4, will the revenue increase
or decrease?

(f) If the unit price is increased slightly from $12, will the revenue increase
or decrease?