Question

The diagram below depicts the demand curve for "miniburgers" in a nationwide fast-food market. Use the information in this diagram to answer the questions that follow.

Quantity (mini burgers per day)

a. What is the price elasticity of demand along with the range of the demand curve between a price of $\backslash (0.20$per miniburger and a price of role="math" localid="1651796932841" $\backslash )0.40$per miniburger? Is demand elastic or inelastic over this range?

b. What is the price elasticity of demand along with the range of the demand curve between a price of $\backslash (0.80$ per miniburger and a price of $\backslash )1.20$ per miniburger? Is demand elastic or inelastic over this range?

c. What is the price elasticity of demand along with the range of the demand curve between a price of $\backslash (1.60$ per miniburger and a price of $\backslash )1.80$ per $m$ ? Is demand elastic or inelastic over this range?

Short answer

a) The price elasticity of demand along the range is determined as$0.18$

b) The quality demand changes due to the reduction in price is determined as changes from $40to60$units

c) The quality demand changes due to the reduction of price changes from

$10to20$units

Step-by-step solution

Introduction 

In economics, a demand curve is a graphic representation of the connection between product price and quantity demanded.

The ratio of the percentage change in quantity demanded of a product to the percentage change in price is known as price elasticity of demand. Economists use it to figure out how things work.

Step 2

The percentage change in quantity demand and the price are used to compute the price elasticity of demand.

(a) The quantity required fluctuates from $80to90$proposing a price drop to units of mini burgers each day $\$0.20$ from $\$0.40$.

Step 3

The price elasticity of demand is calculated as follows.

${\mathrm{E}}_{\mathrm{p}}=\frac{\frac{\Delta \mathrm{Q}}{{\mathrm{Q}}_1+{\mathrm{Q}}_2/2}}{\frac{\Delta \mathrm{P}}{{\mathrm{P}}_1+{\mathrm{P}}_2/2}}$

role="math" $=\frac{\frac{90-80}{170/2}}{\frac{0.40-\theta .20}{0.60/2}}$

$=\frac{\frac{10}{85}}{\frac{\$0.20}{0.30}}$

$$\begin{gathered} =\frac{0.12}{0.67} \\ {E}_p=0.18 \end{gathered}$$

Thus, along with the specified range of demand curves, the price elasticity of demand is $0.18$. It is deemed inelastic if the measured elasticity is less than one. As a result, demand price elasticity is inelastic.

Step 4

(b) Because of the price reduction, the quantity requested increases from $40$to $60$units is $\$0.80$from $\$1.20$.

The price elasticity of demand is calculated as follows.

${\mathrm{E}}_{\mathrm{p}}=\frac{\frac{\Delta \mathrm{Q}}{{\mathrm{Q}}_1+{\mathrm{Q}}_2/2}}{\frac{\Delta \mathrm{P}}{{\mathrm{P}}_1+{\mathrm{P}}_2/2}}$

$=\frac{\frac{60-40}{100/2}}{\frac{\$1.20-0.80}{\$2.00/2}}$

$$\begin{gathered} =\frac{\frac{20}{50}}{\frac{0.40}{1}} \\ {E}_p=1 \end{gathered}$$

As a result, the price elasticity of demand along with the given demand curve range is $1$. When the price elasticity equals one, the elasticity is said to be unitary elastic. As a result, demand price elasticity is unit-elastic.

Step 5

(c) Due to a price decrease from $\$1.80$to $\$1.60$, the quantity demanded increases from $10$to $20$units.

The price elasticity of demand is calculated as follows.

${\mathrm{E}}_{\mathrm{p}}=\frac{\frac{\Delta \mathrm{Q}}{{\mathrm{Q}}_1+{\mathrm{Q}}_2/2}}{\frac{\Delta \mathrm{P}}{{\mathrm{P}}_1+{\mathrm{P}}_2/2}}$

$=\frac{\frac{20-10}{30/2}}{\frac{\$1.80-1.60}{3.40/2}}$

$$\begin{gathered} \Rightarrow \frac{\frac{10}{15}}{\frac{0.20}{1.7}} \\ {E}_p=5.6 \end{gathered}$$

Thus, along with the specified range of demand curves, the price elasticity of demand is $5.6$. As a result, demand price elasticity is elastic.