Chapter 48, Problem 1CYU

To determine

The income elasticity of demand when the income of C changed from 12,000 to 18,000 and quantity increased from 10 to 40 a year.

Explanation of Solution

  $\begin{array}{c}\text{Income elasticity of demand = }\frac{\frac{\left(Q_2-Q_1\right)}{(\frac{Q_2{\text{+Q}}_1}{\text{2}})}}{\frac{\left(R_2-R_1\right)}{(\frac{R_2{\text{+R}}_1}{\begin{array}{l}\text{2}\\ \end{array}})}}\\ \text{= }\frac{\frac{\left(\text{40}-\text{10}\right)}{(\frac{\text{40+10}}{\text{2}})}}{\frac{\left(\text{18,000}-\text{12,000}\right)}{(\frac{\text{18,000+12,000}}{\begin{array}{l}\text{2}\\ \end{array}})}}\\ \text{= }\frac{1.2}{\begin{array}{l}\left(\text{0}\text{.4}\right)\\ \end{array}}\\ \text{= 3}\end{array}$

Here,

Q₂ is the new demand, Q₁ is the old demand, R₁ is the old income and R₂ is the new income.

The income elasticity of demand is 3.

Economics Concept Introduction

Introduction: Income elasticity of demand represents the measure of sensitivity of demand to income that shows how change in income affects the quantity demanded.

Midpoint method is used to calculate elasticity by using the average percentage change in quantity and average percentage change in price.