suppose the demand for eggs sold by a convenience store is given by the graph above. suppose that the store…

Explanation:

Step1: Identify initial and new points

Let's assume from the graph, before the price - cut, when the price $P_1 = 6$ (approx), the quantity $Q_1 = 10$. After the price - cut to $P_2=3$, from the graph, the quantity $Q_2 = 60$.

Step2: Calculate the percentage change in quantity

The formula for the percentage change in quantity using the mid - point method is $%\Delta Q=\frac{Q_2 - Q_1}{\frac{Q_2+Q_1}{2}}\times100$. Substitute $Q_1 = 10$ and $Q_2 = 60$ into the formula: [ \begin{align*} %\Delta Q&=\frac{60 - 10}{\frac{60 + 10}{2}}\times100\ &=\frac{50}{\frac{70}{2}}\times100\ &=\frac{50}{35}\times100\ &\approx142.857% \end{align*} ]

Step3: Calculate the percentage change in price

The formula for the percentage change in price using the mid - point method is $%\Delta P=\frac{P_2 - P_1}{\frac{P_2+P_1}{2}}\times100$. Substitute $P_1 = 6$ and $P_2 = 3$ into the formula: [ \begin{align*} %\Delta P&=\frac{3 - 6}{\frac{3+6}{2}}\times100\ &=\frac{- 3}{\frac{9}{2}}\times100\ &=\frac{-3}{4.5}\times100\ &\approx - 66.667% \end{align*} ]

Step4: Calculate the price elasticity of demand

The formula for price elasticity of demand $E_d=\frac{%\Delta Q}{%\Delta P}$. [ \begin{align*} E_d&=\frac{142.857%}{-66.667%}\ &\approx - 2.143 \end{align*} ]

1. The percentage change in quantity is $142.857%$
2. The percentage change in price is $-66.667%$

Answer:

1. $142.857$
2. $-66.667$