Chapter 46, Problem 1FRQ

a.

To determine

To define: The price elasticity of demand along with its formula that can be used for its calculation.

Explanation of Solution

Calculation:

Price elasticity of demand refers to the measure that is used to determine the effect of change in quantity demand with respect the change in price. It can be computed by using midpoint method formula as shown below:

  $\text{Price elasticity}=\frac{\left(\frac{\text{Change in quantity demanded}}{\text{Average quantity}}\right)}{\left(\frac{\text{Change in price}}{\text{Average price}}\right)}$

Economics Concept Introduction

Demand and Supply: Demand refers to the curve that depicts the relationship between the quantity demand at given price whereas supply refers to the curve that depicts the relationship between the quantity that supplier is ready to sell at given price.

Price elasticity of demand: The relationship between the change in demand due to change in price is referred as price elasticity of demand.

b.

To determine

The price elasticity of demand for good X.

Explanation of Solution

Given Information:

Price	Quantity demand
$2	800
$4	500

Calculation:

  $\begin{array}{c}\text{Price elasticity}=\frac{\left(\frac{\text{Change in quantity demanded}}{\text{Average quantity}}\right)}{\left(\frac{\text{Change in price}}{\text{Average price}}\right)}\\ =\frac{\frac{800-500}{\frac{800+500}{2}}}{\frac{2-4}{\frac{2+4}{2}}}\\ =\frac{\frac{300}{650}}{\frac{2}{3}}\\ =\frac{0.461538}{0.66667}\\ =0.6923\end{array}$

Economics Concept Introduction

Demand and Supply: Demand refers to the curve that depicts the relationship between the quantity demand at given price whereas supply refers to the curve that depicts the relationship between the quantity that supplier is ready to sell at given price.

c.

To determine

The change in quantity demanded if price is increased by 10%.

Explanation of Solution

Calculation:

  $\begin{array}{c}\text{Price elasticity}=\frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}\\ 0.6923=\frac{\text{Percentage change in quantity}}{10\%}\\ \text{Percentage change in quantity}=6.923\%\end{array}$

Economics Concept Introduction

Price elasticity of demand: The relationship between the change in demand due to change in price is referred as price elasticity of demand.