Chapter 5, Problem 14SQP

(a)

To determine

Price elasticity of supply.

Explanation of Solution

The general formula for calculating price elasticity of supply is given below:

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

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

$\begin{array}{c}\text{Price elasticity of supply}=\frac{\left(\frac{40-50}{\left(\frac{40+50}{2}\right)}\right)}{\left(\frac{8-10}{\left(\frac{8+10}{2}\right)}\right)}\\ =\frac{\left(\frac{-10}{45}\right)}{\left(\frac{-2}{9}\right)}\\ =\frac{-0.222222}{-0.222222}\\ =1\end{array}$

Price elasticity of supply is 1.

Economics Concept Introduction

Price elasticity of supply: Price elasticity of demand is the responsiveness of the quantity supplied to the change in price, which is measured by dividing the percentage change in the quantity supplied of a product by the percentage change in the price of a product.

(b)

To determine

Price elasticity of supply.

Explanation of Solution

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

$\begin{array}{c}\text{Price elasticity of supply}=\frac{\left(\frac{30-40}{\left(\frac{30+40}{2}\right)}\right)}{\left(\frac{6-8}{\left(\frac{6+8}{2}\right)}\right)}\\ =\frac{\left(\frac{-10}{35}\right)}{\left(\frac{-2}{7}\right)}\\ =\frac{-0.285714}{-0.285714}\\ =1\end{array}$

Price elasticity of supply is 1.

Economics Concept Introduction

Price elasticity of supply: Price elasticity of demand is the responsiveness of the quantity supplied to the change in price, which is measured by dividing the percentage change in the quantity supplied of a product by the percentage change in the price of a product.

(c)

To determine

Price elasticity of supply.

Explanation of Solution

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

$\begin{array}{c}\text{Price elasticity of supply}=\frac{\left(\frac{20-30}{\left(\frac{20+30}{2}\right)}\right)}{\left(\frac{4-6}{\left(\frac{4+6}{2}\right)}\right)}\\ =\frac{\left(\frac{-10}{25}\right)}{\left(\frac{-2}{5}\right)}\\ =\frac{-0.04}{-0.04}\\ =1\end{array}$

Price elasticity of supply is 1.

Economics Concept Introduction

Price elasticity of supply: Price elasticity of demand is the responsiveness of the quantity supplied to the change in price, which is measured by dividing the percentage change in the quantity supplied of a product by the percentage change in the price of a product.

(d)

To determine

Price elasticity of supply.

Explanation of Solution

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

$\begin{array}{c}\text{Price elasticity of supply}=\frac{\left(\frac{10-20}{\left(\frac{10+20}{2}\right)}\right)}{\left(\frac{2-4}{\left(\frac{2+4}{2}\right)}\right)}\\ =\frac{\left(\frac{-10}{15}\right)}{\left(\frac{-2}{3}\right)}\\ =\frac{-0.666666}{-0.666666}\\ =1\end{array}$

Price elasticity of supply is 1.

Economics Concept Introduction

Price elasticity of supply: Price elasticity of demand is the responsiveness of the quantity supplied to the change in price, which is measured by dividing the percentage change in the quantity supplied of a product by the percentage change in the price of a product.

(e)

To determine

Price elasticity of supply.

Explanation of Solution

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

$\begin{array}{c}\text{Price elasticity of supply}=\frac{\left(\frac{0-10}{\left(\frac{0+10}{2}\right)}\right)}{\left(\frac{0-2}{\left(\frac{0+2}{2}\right)}\right)}\\ =\frac{\left(\frac{-10}{5}\right)}{\left(\frac{-2}{0}\right)}\\ =\frac{-2}{-2}\\ =1\end{array}$

Price elasticity of supply is 1.

Economics Concept Introduction

Price elasticity of supply: Price elasticity of demand is the responsiveness of the quantity supplied to the change in price, which is measured by dividing the percentage change in the quantity supplied of a product by the percentage change in the price of a product.