Chapter 5, Problem 1SCQ

From the data in Table 5.5 about demand for smart phones, calculate the price elasticity of demand from: point B to point C, point D to point E, and point G to point H. Classify the elasticity at each point as elastic, inelastic, or unit elastic.

To determine

Calculate the elasticity of demand at various points on the demand curve and classify them as inelastic, unit elastic and elastic.

Answer to Problem 1SCQ

Price elasticity of demand from point B to C is 0.5

The price elasticity of demand at point D to E is 0.75

The price elasticity of demand at point G to H is 1.32.

Explanation of Solution

Let’s calculate the price elasticity of demand from point B to C:

$\begin{array}{l}\text{e = }\frac{\text{ΔQ}}{\text{ΔP}}\text{×}\frac{\text{P}}{\text{Q}}\\ \text{e = }\frac{2,600-2,800}{80-70}\text{×}\frac{70}{2,800}\\ \text{e = }\frac{-200}{10}\text{×0}\text{.025}\\ \text{e = (-) -20 }\times \text{0}\text{.025}\\ \text{e = 0}\text{.5}\end{array}$

Therefore, the price elasticity of demand from point B to C is 0.5. Since the elasticity of demand is less than 1, the demand is inelastic, which means there is less change in quantity demanded as compared to the change in price level.

Now, we find out the price elasticity of demand at point D to E:

$\begin{array}{l}\text{e = }\frac{\text{ΔQ}}{\text{ΔP}}\text{×}\frac{\text{P}}{\text{Q}}\\ \text{e = }\frac{2,200-2,400}{100-90}\text{×}\frac{90}{2,400}\\ \text{e = }\frac{-200}{10}\text{×0}\text{.0375}\\ \text{e = (-) -20 }\times \text{0}\text{.0375}\\ \text{e = 0}\text{.75}\end{array}$

Therefore, the price elasticity of demand from point D to E is 0.75. Since the elasticity of demand is less than 1, the demand is inelastic, which means there is less change in quantity demanded as compared to the change in price level.

Now, we find out the price elasticity of demand at point G to H:

$\begin{array}{l}\text{e = }\frac{\text{ΔQ}}{\text{ΔP}}\text{×}\frac{\text{P}}{\text{Q}}\\ \text{e = }\frac{1,600-1,800}{130-120}\text{×}\frac{120}{1,800}\\ \text{e = }\frac{-200}{10}\text{×0}\text{.066}\\ \text{e = (-) -20 }\times \text{0}\text{.066}\\ \text{e = 1}\text{.32}\end{array}$

Therefore, the price elasticity of demand from point G to H is 1.32, since the elasticity of demand is greater than 1; the demand is elastic, which means there is large change in quantity demanded as compared to the change in price level.

Economics Concept Introduction

Price elasticity of demand: The degree of responsiveness to change in quantity demanded due to change in its price. The formula for calculating elasticity of demand is as follows:

$\text{e = }\frac{\text{ΔQ}}{\text{ΔP}}\text{×}\frac{\text{P}}{\text{Q}}$