Chapter 4, Problem 1SPA

Rain spoils the strawberry crop, the price rises from $4 to $6 a box, and the quantity demanded decreases from 1,000 to 600 boxes a week.

a.    Calculate the price elasticity of demand over this price range.

b.    Describe the demand for strawberries.

To determine

Price elasticity of demand.

Explanation of Solution

The general formula for calculating price elasticity of demand is shown below.

$\text{Price elasticity of demand}=\left[\frac{\frac{\left({\text{Quantity }}_{\text{Present}}-{\text{Quantity }}_{\text{Previous}}\right)}{\frac{\left({\text{Quantity }}_{\text{Present}}+{\text{Quantity }}_{\text{Previous}}\right)}{2}}}{\frac{{\text{Price }}_{\text{Present}}-{\text{Price }}_{\text{Previous}}}{\frac{{\text{Price }}_{\text{Present}}+{\text{Price }}_{\text{Previous}}}{2}}}\right]$ (1)

By substitute the respective values in Equation (1) to calculate the price elasticity of demand.

$\begin{array}{c}\text{Price elasticity of demand}=\left[\frac{\frac{\left(600-1000\right)}{\frac{\left(600+1000\right)}{2}}}{\frac{6-4}{\frac{6+4}{2}}}\right]\\ =\left[\frac{\frac{-400}{800}}{\frac{2}{5}}\right]\\ =\frac{-0.5}{0.4}\\ =-1.25\end{array}$

Price elasticity of demand is -1.25.

Economics Concept Introduction

Price elasticity of demand: Price elasticity of demand refers to the responsiveness of changes or the change in quantity demanded due to the change in price.

To determine

Demand for strawberries.

Explanation of Solution

The price elasticity of demand for strawberries is exceeds 1, which means, the demand for strawberry is elastic.

Economics Concept Introduction

Price elasticity of demand: Price elasticity of demand refers to the responsiveness of changes or the change in quantity demanded due to the change in price.