Chapter 5, Problem 6PA

Subpart (a):

To determine

Calculating the price elasticity of demand.

Explanation of Solution

1. (i) If the income is $10,000, then the price of pizza rises from $8 to $10, and the quantity demanded decreases from 40 to 32. By midpoint method, the price elasticity of demand is calculated as follows:

$\begin{array}{c}{\text{Price elasticity of demand}}_{\text{Income \$20,000}}=\frac{\frac{{\text{Quantity}}_{\text{Present}}-{\text{Quantity}}_{\text{Previous}}}{\frac{{\text{Quantity}}_{\text{Present}}+{\text{Quantity}}_{\text{Previous}}}{2}}}{\frac{{\text{Price}}_{\text{Present}}-{\text{Price}}_{\text{Previous}}}{\frac{{\text{Price}}_{\text{Present}}+{\text{Price}}_{\text{Previous}}}{2}}}\\ =\frac{\frac{32-40}{\left(\frac{32+40}{2}\right)}}{\frac{10-8}{\left(\frac{10+8}{2}\right)}}\\ =\frac{\frac{-8}{\left(36\right)}}{\frac{2}{\left(9\right)}}\\ =\frac{-0.2222}{0.2222}\\ =-1\end{array}$

The price elasticity of demand for pizza is -1.

1. (ii) If the income is $12,000, then the price of pizza rises from $8 to $10, and the quantity demanded decreases from 50 to 45. By midpoint method, the price elasticity of demand is calculated as follows:

$\begin{array}{c}{\text{Price elasticity of demand}}_{\text{Income \$24,000}}=\frac{\frac{{\text{Quantity}}_{\text{Present}}-{\text{Quantity}}_{\text{Previous}}}{\frac{{\text{Quantity}}_{\text{Present}}+{\text{Quantity}}_{\text{Previous}}}{2}}}{\frac{{\text{Price}}_{\text{Present}}-{\text{Price}}_{\text{Previous}}}{\frac{{\text{Price}}_{\text{Present}}+{\text{Price}}_{\text{Previous}}}{2}}}\\ =\frac{\frac{45-50}{\left(\frac{45+50}{2}\right)}}{\frac{(10-8)}{\left(\frac{(10+8)}{2}\right)}}\\ =\frac{\frac{-5}{47.5}}{\frac{2}{9}}\\ =\frac{-0.11}{0.22}\\ =-0.5\end{array}$

The price elasticity of demand for pizza is -0.5.

Economics Concept Introduction

Concept Introduction:

Price elasticity of demand: Price elasticity of demand refers to the percentage change in the demand for goods and services due to change occurred in the price level.

Subpart (b):

To determine

Calculating the income elasticity of demand.

Explanation of Solution

1. (i) If the price is $12 and an income increases from $10,000 to $24,000, then the quantity demanded increases from 24 to 30. By midpoint method, the income elasticity of demand is calculated as follows:

$\begin{array}{c}{\text{Income elasticity of demand}}_{\text{Price \$12}}=\frac{\frac{{\text{Quantity}}_{\text{Present}}-{\text{Quantity}}_{\text{Previous}}}{\frac{{\text{Quantity}}_{\text{Present}}+{\text{Quantity}}_{\text{Previous}}}{2}}}{\frac{{\text{Income}}_{\text{Present}}-{\text{Income}}_{\text{Previous}}}{\frac{{\text{Income}}_{\text{Present}}+{\text{Income}}_{\text{Previous}}}{2}}}\\ =\frac{\frac{30-24}{\left(\frac{30+24}{2}\right)}}{\frac{12,000-10,000}{\left(\frac{12,000+10,000}{2}\right)}}\\ =\frac{\frac{6}{27}}{\frac{2,000}{11,000}}\\ =\frac{0.2222}{0.1818}\\ =1.22\end{array}$

The income elasticity of demand for pizza is 1.22.

1. (ii) If the price is $12 and an income increases from $20,000 to $24,000, then the quantity demanded increases from 24 to 30. By midpoint method, the income elasticity of demand is calculated as follows:

$\begin{array}{c}{\text{Income elasticity of demand}}_{\text{Price \$16}}=\frac{\frac{{\text{Quantity}}_{\text{Present}}-{\text{Quantity}}_{\text{Previous}}}{\frac{{\text{Quantity}}_{\text{Present}}+{\text{Quantity}}_{\text{Previous}}}{2}}}{\frac{{\text{Income}}_{\text{Present}}-{\text{Income}}_{\text{Previous}}}{\frac{{\text{Income}}_{\text{Present}}+{\text{Income}}_{\text{Previous}}}{2}}}\\ =\frac{\frac{12-8}{\left(\frac{12+8}{2}\right)}}{\frac{12,000-10,000}{\left(\frac{12,000+10,000}{2}\right)}}\\ =\frac{\frac{4}{10}}{\frac{2,000}{11,000}}\\ =0.4\times \frac{11}{2}\\ =2.2\end{array}$

The income elasticity of demand for pizza is 2.22.

Economics Concept Introduction

Concept Introduction:

Income elasticity of demand: It measures how much quantity demanded of a good responds to the change in consumers’ income.