Exercise 1 XYZ Beverages Ltd. produces coffee. The initial price of coffee was \( \$ 20 \) per kg , and the quantity demanded per month was \( 1,200 \mathrm{~kg} \). The price rose to \( \$ 25 \) per kg , but the quantity demanded decreased to \( 1,150 \mathrm{~kg} \). A. Calculate the elasticity of demand (PED)

The formula for calculating the price elasticity of demand (PED) is: \[ PED = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}} \] To calculate the percentage change in quantity demanded, we use the formula: \[ \text{Percentage change in quantity demanded} = \frac{\text{New quantity demanded} - \text{Initial quantity demanded}}{\text{Initial quantity demanded}} \times 100\% \] To calculate the percentage change in price, we use the formula: \[ \text{Percentage change in price} = \frac{\text{New price} - \text{Initial price}}{\text{Initial price}} \times 100\% \] Let's calculate the percentage change in quantity demanded and the percentage change in price first. Calculate the value by following steps: - step0: Calculate: \(\left(\frac{\left(1150-1200\right)}{1200}\right)\times 100\) - step1: Remove the parentheses: \(\left(\frac{1150-1200}{1200}\right)\times 100\) - step2: Subtract the numbers: \(\left(\frac{-50}{1200}\right)\times 100\) - step3: Divide the terms: \(\left(-\frac{1}{24}\right)\times 100\) - step4: Remove the parentheses: \(-\frac{1}{24}\times 100\) - step5: Reduce the numbers: \(-\frac{1}{6}\times 25\) - step6: Multiply: \(-\frac{25}{6}\) The percentage change in quantity demanded is approximately -4.17%. Next, let's calculate the percentage change in price. Calculate the value by following steps: - step0: Calculate: \(\left(\frac{\left(25-20\right)}{20}\right)\times 100\) - step1: Remove the parentheses: \(\left(\frac{25-20}{20}\right)\times 100\) - step2: Subtract the numbers: \(\left(\frac{5}{20}\right)\times 100\) - step3: Reduce the fraction: \(\frac{1}{4}\times 100\) - step4: Reduce the numbers: \(25\) The percentage change in price is 25%. Now, we can calculate the price elasticity of demand (PED) using the formula: \[ PED = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}} \] Let's substitute the values we calculated into the formula to find the elasticity of demand. Calculate the value by following steps: - step0: Calculate: \(\frac{-4.17}{25}\) - step1: Convert the expressions: \(\frac{-\frac{417}{100}}{25}\) - step2: Multiply by the reciprocal: \(-\frac{417}{100}\times \frac{1}{25}\) - step3: Multiply the fractions: \(-\frac{417}{100\times 25}\) - step4: Multiply: \(-\frac{417}{2500}\) The elasticity of demand (PED) is approximately -0.167.