Chapter 6, Problem 1DQ

Explain why the choice between 1, 2, 3, 4, 5, 6, 7, and 8 “units,” or 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, and 8,000 movie tickets, makes no difference in determining elasticity in Table 6.1. LO6.1

To determine

Price elasticity of demand.

Explanation of Solution

Price elasticity of demand can be calculated by using the below formula:

$\text{Elasticity}=\frac{\frac{\text{New quantity}-\text{Old quantity}}{\frac{\text{New quantity}+\text{Old quantity}}{2}}}{\frac{\text{New price}-\text{Old price}}{\frac{\text{New price}+\text{Old price}}{2}}}$ (1)

Price elasticity of demand for changing 1 unit to 2 units can be calculated by substituting the respective values in equation (1).

$\begin{array}{c}\text{Price elasticity of demand}=\frac{\frac{2-1}{\frac{2+1}{2}}}{\frac{7-8}{\frac{7+8}{2}}}\\ =\frac{\frac{1}{\frac{3}{2}}}{\frac{-1}{\frac{15}{2}}}\end{array}$

$\begin{array}{c}=\frac{\frac{1}{1.5}}{\frac{-1}{7.5}}\\ =\frac{0.6667}{-0.3333}\\ =-5\end{array}$

Price elasticity of demand for changing the quantity from 1 to 2 is 5 (ignore the sign).

Table -1 shows the price elasticity for the demand for changing quantity from one unit to other units that was obtained by using equation (1).

Table -1

Quantity in units	Price	Elasticity
1	8
2	7	5
3	6	2.6
4	5	1.57
5	4	1
6	3	0.64
7	2	0.38
8	1	0.26

Table-2 shows the price elasticity for the demand for changing quantity from one unit to other units that was obtained by using equation (1).

Table -2

Quantity (Actual)	Price	Elasticity
1,000	8
2,000	7	5
3,000	6	2.6
4,000	5	1.57
5,000	4	1
6,000	3	0.64
7,000	2	0.38
8,000	1	0.26

Table-1 and Table-2 clearly show that the elasticity of demand is the same regardless of the demand quantity in units or quantity demand in actual numbers. Thus, it makes no difference in determining price elasticity of demand for both the cases.

Economics Concept Introduction

Concept introduction:

Price elasticity of demand: Price elasticity of demand is defined as the percentage change in the quantity demanded due to percentage change in price. In other words, price elasticity of demand represents the relationship between change in quantity of a specific good and the price change.