Chapter 9R, Problem 3FRQ

a)

To determine

Price elasticity of demand for peanut butter

Explanation of Solution

  $\begin{array}{c}\text{Price elasticity of demand = }\frac{\text{ Percentage change in quantity demanded}}{\text{Percentage change in price}}\\ \text{Percentage change in quantity demanded = }\frac{\left(Qn-Qn-1\right) }{ \left(Qn+Qn-1\right)/2}\times 100\\ \text{= }\frac{\left(50-30\right) }{\left(50+30\right)/2}\times 100 \\ =50\\ \text{Percentage change in price = }\frac{\left(Pn-Pn-1\right) }{\left(Pn+Pn-1\right)/2}\times 100\\ \text{= }\frac{\left(4-5\right) }{\left(4+5\right)/2}\times 100 \\ =22.2\\ \text{Price elasticity of demand}=\frac{50 }{22.2 } \\ =2.25\end{array}$

The price elasticity of demand is more than 1, therefore it is elastic.

Economics Concept Introduction

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

b)

To determine

Cross price elasticity for peanut butter and chocolate and whether chocolate and peanut butter are substitute, complement or related goods.

Explanation of Solution

1. Cross price elasticity of peanut and chocolate

$\begin{array}{c}\text{Cross price elasticity = }\frac{\text{Percentage change in quantity demanded of product chocolate}}{\text{Percentage change in price of product peanut butter}}\\ \text{ = }\frac{0.14 }{ 0.11}\\ =1.27\end{array}$

Here, the cross-price elasticity is elastic.

2. Here, the cross-price elasticity is greater than 1 and it is positive, therefore the products are good substitute because when the price of chocolate increases the demand of peanut butter goes up.

Economics Concept Introduction

Introduction: Cross price elasticity refers to the measure how change in price of one commodity has impact on the demand of another good.

c)

To determine

Whether peanut butter is inferior, normal, or necessity goods.

Explanation of Solution

Economics Concept Introduction

Introduction: When income rise and demand decrease then it means goods are inferior and when there is no impact of income on demand then goods are necessary. And, if income increase then demand also increases then goods are normal.