question\nthe price of cups increased from $3.75 to $4.05 and the quantity demanded of plates decreased from…

Explanation:

Step1: Calculate the percentage change in the price of cups

The formula for percentage - change is $\frac{\Delta P}{P_{avg}}$, where $\Delta P=P_2 - P_1$ and $P_{avg}=\frac{P_1 + P_2}{2}$. $P_1 = 3.75$, $P_2=4.05$. $\Delta P=4.05 - 3.75=0.3$. $P_{avg}=\frac{3.75 + 4.05}{2}=\frac{7.8}{2}=3.9$. The percentage change in price $%\Delta P=\frac{0.3}{3.9}\times100\approx7.69%$.

Step2: Calculate the percentage change in the quantity demanded of plates

The formula for percentage - change is $\frac{\Delta Q}{Q_{avg}}$, where $\Delta Q=Q_2 - Q_1$ and $Q_{avg}=\frac{Q_1 + Q_2}{2}$. $Q_1 = 4950$, $Q_2 = 4450$. $\Delta Q=4450 - 4950=- 500$. $Q_{avg}=\frac{4950 + 4450}{2}=\frac{9400}{2}=4700$. The percentage change in quantity $%\Delta Q=\frac{-500}{4700}\times100\approx - 10.64%$.

Step3: Calculate the cross - price elasticity of demand

The formula for cross - price elasticity of demand ($E_{xy}$) is $E_{xy}=\frac{%\Delta Q_y}{%\Delta P_x}$. $E_{xy}=\frac{-10.64%}{7.69%}\approx - 1.38$.

Answer:

$-1.38$