Question

When the price of shirts emblazoned with a college logo is $\backslash (20$, consumers buy $150$ per week. When the price declines to $\backslash )19$, consumers purchase $200$ per week. Based on this information, calculate the price elasticity of demand for logo-emblazoned shirts.

Short answer

The price elasticity of demand for logo-emblazoned shirts are calculated as $10$percent increase in price can bring down the demand by$55.7$percent

Step-by-step solution

Introduction 

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.

The objective is to calculate the price elasticity of demand for the logo emblazoned shirts

Price elasticity of demand 

The Law of Demand predicts how the quantity of a good demanded will change in relation to its price. When prices rise, demand declines, and when prices fall, demand rises, all other factors remaining constant.

The idea of price elasticity of demand, on the other hand, provides information on how much demand for a goodwill change as a result of a change in its price.

Step 3 

The following formula can be used to calculate price elasticity of demand.

$$\begin{gathered} Priceelasticityofdemand\left(E_p\right)=\frac{proportionatechangeinquantitydemanded}{proportionatechangeinprice} \\ Proportionatechangeinquantitydemanded=\frac{changeinquantitydemanded}{averageofthesumoforiginalandnewquantities} \\ =\frac{∆Q}{Q_1+Q_2/2} \end{gathered}$$

Where,

$\Delta Q=$New quantity - Original quantity

${\mathrm{Q}}_1=$Original quantity

${\mathrm{Q}}_2=$New Quantity

Proportionate change in price $=\frac{\text{change in price}}{\text{average of the sum of original and new prices}}$

$=\frac{\Delta P}{\left(P_1+P_2\right)/2}$

Where,

$∆P=NewPrice-originalprice$

$P_1=OriginalPrice$

$P_2=NewPrice$

Thus,

$E_p=\frac{\Delta Q}{\left(Q_1+Q_2\right)/2}÷\frac{\Delta P}{\left(P_1+P_2\right)/2}$

Step 4

In the case of logo-emblazoned shirts:

$$\begin{gathered} Q_1=150 \\ {Q}_2=200 \\ ∆Q=200-150=50 \\ {P}_1=\$20 \\ {P}_2=\$19 \\ ∆P=\$19-\$20 \\ =\$1 \end{gathered}$$

Step 5

In the equation, substitute the values.

$$\begin{gathered} E_p=\frac{∆Q}{(Q_1+Q_2/2)}÷\frac{∆P}{(P_1+P_2/2)}\} \\ {E}_p=\frac{50}{(150+200)/2}÷\frac{1}{(20+19)/2} \\ =\frac{50}{175}÷\frac{1}{19.5} \\ =0.285÷.051 \\ =5.57 \end{gathered}$$

As a result, demand for logo-emblazoned shirts has a significant price elasticity. A ten percent price rise will reduce demand by $55.7$ percent.