Chapter 5, Problem 4SQP

(a)

To determine

Price elasticity of demand.

Explanation of Solution

The general formula for calculating price elasticity of demand is given below.

$\text{Price elasticity of demand curve}=\frac{\frac{{\text{Quantity}}_{\text{New}}-{\text{Quantity}}_{\text{Old}}}{\left(\frac{{\text{Quantity}}_{\text{New}}+{\text{Quantity}}_{\text{Old}}}{2}\right)}}{\frac{{\text{Price}}_{\text{New}}-{\text{Price}}_{\text{Old}}}{\left(\frac{{\text{Price}}_{\text{New}}+{\text{Price}}_{\text{Old}}}{2}\right)}}$ (1)

Substitute the respective values in Equation (1) to calculate the price elasticity of demand in the first case.

$\begin{array}{c}\text{Price elasticity of demand}=\frac{\left(\frac{40-20}{\left(\frac{40+20}{2}\right)}\right)}{\left(\frac{\text{20}-2\text{5}}{\left(\frac{\text{20}+2\text{5}}{2}\right)}\right)}\\ =\frac{\left(\frac{20}{30}\right)}{\left(\frac{-5}{22.5}\right)}\\ =\frac{0.666666}{-0.222222}\\ =-3\end{array}$

Price elasticity of demand is 3 (ignore the sign).

Economics Concept Introduction

Price elasticity of demand: Price elasticity refers to the responsiveness of changes or the change in quantity demanded due to the change in price.

(b)

To determine

Price elasticity of demand.

Explanation of Solution

By using Equation (1), the calculation of price elasticity of demand in second case is shown below:

$\begin{array}{c}\text{Price elasticity of demand}=\frac{\left(\frac{60-40}{\left(\frac{60+40}{2}\right)}\right)}{\left(\frac{15-20}{\left(\frac{\text{15}+20}{2}\right)}\right)}\\ =\frac{\left(\frac{20}{50}\right)}{\left(\frac{-5}{17.5}\right)}\\ =\frac{0.4}{0.285714}\\ =1.4\end{array}$

Price elasticity of demand is 1.4.

Economics Concept Introduction

Price elasticity of demand: Price elasticity refers to the responsiveness of changes or the change in quantity demanded due to the change in price.

(c)

To determine

Price elasticity of demand.

Explanation of Solution

By using Equation (1), the calculation of price elasticity of demand in third case is shown below:

$\begin{array}{c}\text{Price elasticity of demand}=\frac{\left(\frac{80-60}{\left(\frac{80+60}{2}\right)}\right)}{\left(\frac{10-15}{\left(\frac{\text{10}+15}{2}\right)}\right)}\\ =\frac{\left(\frac{20}{70}\right)}{\left(\frac{-5}{12.5}\right)}\\ =\frac{0.285714}{-0.4}\\ =-0.71\end{array}$

Price elasticity of demand is .71.

Economics Concept Introduction

Price elasticity of demand: Price elasticity refers to the responsiveness of changes or the change in quantity demanded due to the change in price.

(d)

To determine

Change in demand and supply.

Explanation of Solution

By using Equation (1), the calculation of price elasticity of demand in fourth case is shown below:

$\begin{array}{c}\text{Price elasticity of demand}=\frac{\left(\frac{100-80}{\left(\frac{100+80}{2}\right)}\right)}{\left(\frac{5-10}{\left(\frac{5+10}{2}\right)}\right)}\\ =\frac{\left(\frac{20}{90}\right)}{\left(\frac{-5}{7.5}\right)}\\ =\frac{0.222222}{-0.666666}\\ =-0.33\end{array}$

Price elasticity of demand is .33.

Economics Concept Introduction

Price elasticity of demand: Price elasticity refers to the responsiveness of changes or the change in quantity demanded due to the change in price.