Chapter 48, Problem 1FRQ

a)

To determine

Price elasticity of demand for good A.

Explanation of Solution

  $\begin{array}{c}\text{Price elasticity of demand for good A = }\frac{\left(\text{Q2 - Q1}\right)\text{ / }\left[\left(\text{Q2 + Q1}\right)\text{ / 2}\right]}{\left(\text{P2 - P1}\right)\text{ / }\left[\left(\text{P2 + P1}\right)\text{ / 2}\right]}\\ \text{= }\frac{\left(\text{110 - 100}\right)\text{ / }\left[\left(\text{110 + 100}\right)\text{ / 2}\right]}{\left(\text{8 - 10}\right)\text{ / }\left[\left(\text{8+ 10}\right)\text{ / 2}\right]}\\ \text{= }\frac{\text{10 /105}}{\left(\text{2/9}\right)}\\ \text{= }\frac{\text{0}\text{.09}}{\left(\text{0}\text{.22}\right)}\\ \text{= 0}\text{.40}\end{array}$

The price elasticity of demand for good A is elastic.

Economics Concept Introduction

Introduction: Price elasticity of demand refers to the measure how the demand is sensitive to price or how the change in price affects the demand of the good.

b)

To determine

Cross price elasticity of demand between good A and B

Explanation of Solution

  $\begin{array}{c}\text{Cross price elasticity of demand between good A and good B}\\ \text{= }\frac{\left(\text{Qb2 - Qb1}\right)\text{ / }\left[\left(\text{Qb2 + Qb1}\right)\text{ / 2}\right]}{\left(\text{Pa2 - Pa1}\right)\text{ / }\left[\left(\text{Pa2 + Pa1}\right)\text{ / 2}\right]}\\ \text{= }\frac{\left(\text{10 - 5}\right)\text{ / }\left[\left(\text{10 + 5}\right)\text{ / 2}\right]}{\left(\text{8 - 10}\right)\text{ / }\left[\left(\text{8+ 10}\right)\text{ / 2}\right]}\\ \text{= }\frac{\text{5 /7}\text{.5}}{\left(\text{-2/9}\right)}\\ \frac{\text{= 0}\text{.66}}{\left(\text{-0}\text{.22}\right)}\\ \text{= -3}\end{array}$

The cross-price elasticity of demand between good A and B is inelastic.

Economics Concept Introduction

Introduction: Cross price elasticity of demand provides a measure how the price of one good affect the demand of another good.

c)

To determine

Relationship between two goods.

Explanation of Solution

The goods are somewhat complementary with each other because the cross-price elasticity is negative or inelastic which indicates good A provides value to good B.

Economics Concept Introduction

Introduction: Cross price elasticity of demand provides a measure how the price of one good affect the demand of another good.