Answer :
Certainly! Let's proceed with the detailed, step-by-step solution for each part of the question:
### Part (a): Price increases from 3.00 ETB per unit to 4.00 ETB per unit
Given Data:
- Initial price ([tex]\(P_{initial}\)[/tex]) = 3.00 ETB
- New price ([tex]\(P_{new}\)[/tex]) = 4.00 ETB
- Initial quantity demanded ([tex]\(Q_{initial}\)[/tex]) = 3250 units
- New quantity demanded ([tex]\(Q_{new}\)[/tex]) = 2000 units
1. Calculate the Percentage Change in Price:
[tex]\[ \text{Percentage Change in Price} = \frac{P_{new} - P_{initial}}{P_{initial}} \times 100 \][/tex]
Substitute the given values:
[tex]\[ \text{Percentage Change in Price} = \frac{4.00 - 3.00}{3.00} \times 100 = \frac{1.00}{3.00} \times 100 = 33.3333\% \approx 33.33\% \][/tex]
2. Calculate the Percentage Change in Quantity Demanded:
[tex]\[ \text{Percentage Change in Quantity} = \frac{Q_{new} - Q_{initial}}{Q_{initial}} \times 100 \][/tex]
Substitute the given values:
[tex]\[ \text{Percentage Change in Quantity} = \frac{2000 - 3250}{3250} \times 100 = \frac{-1250}{3250} \times 100 \approx -38.4615\% \approx -38.46\% \][/tex]
3. Calculate the Price Elasticity of Demand:
[tex]\[ \text{Price Elasticity of Demand} = \frac{\text{Percentage Change in Quantity}}{\text{Percentage Change in Price}} \][/tex]
Substitute the calculated values:
[tex]\[ \text{Price Elasticity of Demand} = \frac{-38.4615}{33.3333} \approx -1.1538 \approx -1.15 \][/tex]
So, the price elasticity of demand when the price increases from 3.00 ETB per unit to 4.00 ETB per unit is approximately [tex]\(-1.15\)[/tex].
### Part (b): The price falls from 4.00 ETB per unit to 3.00 ETB per unit
Given Data:
- Initial price ([tex]\(P_{initial}\)[/tex]) = 4.00 ETB
- New price ([tex]\(P_{new}\)[/tex]) = 3.00 ETB
- Initial quantity demanded ([tex]\(Q_{initial}\)[/tex]) = 2000 units
- New quantity demanded ([tex]\(Q_{new}\)[/tex]) = 3250 units
1. Calculate the Percentage Change in Price:
[tex]\[ \text{Percentage Change in Price} = \frac{P_{new} - P_{initial}}{P_{initial}} \times 100 \][/tex]
Substitute the given values:
[tex]\[ \text{Percentage Change in Price} = \frac{3.00 - 4.00}{4.00} \times 100 = \frac{-1.00}{4.00} \times 100 = -25\% \][/tex]
2. Calculate the Percentage Change in Quantity Demanded:
[tex]\[ \text{Percentage Change in Quantity} = \frac{Q_{new} - Q_{initial}}{Q_{initial}} \times 100 \][/tex]
Substitute the given values:
[tex]\[ \text{Percentage Change in Quantity} = \frac{3250 - 2000}{2000} \times 100 = \frac{1250}{2000} \times 100 = 62.5\% \][/tex]
3. Calculate the Price Elasticity of Demand:
[tex]\[ \text{Price Elasticity of Demand} = \frac{\text{Percentage Change in Quantity}}{\text{Percentage Change in Price}} \][/tex]
Substitute the calculated values:
[tex]\[ \text{Price Elasticity of Demand} = \frac{62.5}{-25} = -2.5 \][/tex]
So, the price elasticity of demand when the price falls from 4.00 ETB per unit to 3.00 ETB per unit is [tex]\(-2.5\)[/tex].
### Summary:
- Part (a): When the price increases from 3.00 ETB to 4.00 ETB, the price elasticity of demand is [tex]\(-1.15\)[/tex].
- Part (b): When the price falls from 4.00 ETB to 3.00 ETB, the price elasticity of demand is [tex]\(-2.5\)[/tex].
### Part (a): Price increases from 3.00 ETB per unit to 4.00 ETB per unit
Given Data:
- Initial price ([tex]\(P_{initial}\)[/tex]) = 3.00 ETB
- New price ([tex]\(P_{new}\)[/tex]) = 4.00 ETB
- Initial quantity demanded ([tex]\(Q_{initial}\)[/tex]) = 3250 units
- New quantity demanded ([tex]\(Q_{new}\)[/tex]) = 2000 units
1. Calculate the Percentage Change in Price:
[tex]\[ \text{Percentage Change in Price} = \frac{P_{new} - P_{initial}}{P_{initial}} \times 100 \][/tex]
Substitute the given values:
[tex]\[ \text{Percentage Change in Price} = \frac{4.00 - 3.00}{3.00} \times 100 = \frac{1.00}{3.00} \times 100 = 33.3333\% \approx 33.33\% \][/tex]
2. Calculate the Percentage Change in Quantity Demanded:
[tex]\[ \text{Percentage Change in Quantity} = \frac{Q_{new} - Q_{initial}}{Q_{initial}} \times 100 \][/tex]
Substitute the given values:
[tex]\[ \text{Percentage Change in Quantity} = \frac{2000 - 3250}{3250} \times 100 = \frac{-1250}{3250} \times 100 \approx -38.4615\% \approx -38.46\% \][/tex]
3. Calculate the Price Elasticity of Demand:
[tex]\[ \text{Price Elasticity of Demand} = \frac{\text{Percentage Change in Quantity}}{\text{Percentage Change in Price}} \][/tex]
Substitute the calculated values:
[tex]\[ \text{Price Elasticity of Demand} = \frac{-38.4615}{33.3333} \approx -1.1538 \approx -1.15 \][/tex]
So, the price elasticity of demand when the price increases from 3.00 ETB per unit to 4.00 ETB per unit is approximately [tex]\(-1.15\)[/tex].
### Part (b): The price falls from 4.00 ETB per unit to 3.00 ETB per unit
Given Data:
- Initial price ([tex]\(P_{initial}\)[/tex]) = 4.00 ETB
- New price ([tex]\(P_{new}\)[/tex]) = 3.00 ETB
- Initial quantity demanded ([tex]\(Q_{initial}\)[/tex]) = 2000 units
- New quantity demanded ([tex]\(Q_{new}\)[/tex]) = 3250 units
1. Calculate the Percentage Change in Price:
[tex]\[ \text{Percentage Change in Price} = \frac{P_{new} - P_{initial}}{P_{initial}} \times 100 \][/tex]
Substitute the given values:
[tex]\[ \text{Percentage Change in Price} = \frac{3.00 - 4.00}{4.00} \times 100 = \frac{-1.00}{4.00} \times 100 = -25\% \][/tex]
2. Calculate the Percentage Change in Quantity Demanded:
[tex]\[ \text{Percentage Change in Quantity} = \frac{Q_{new} - Q_{initial}}{Q_{initial}} \times 100 \][/tex]
Substitute the given values:
[tex]\[ \text{Percentage Change in Quantity} = \frac{3250 - 2000}{2000} \times 100 = \frac{1250}{2000} \times 100 = 62.5\% \][/tex]
3. Calculate the Price Elasticity of Demand:
[tex]\[ \text{Price Elasticity of Demand} = \frac{\text{Percentage Change in Quantity}}{\text{Percentage Change in Price}} \][/tex]
Substitute the calculated values:
[tex]\[ \text{Price Elasticity of Demand} = \frac{62.5}{-25} = -2.5 \][/tex]
So, the price elasticity of demand when the price falls from 4.00 ETB per unit to 3.00 ETB per unit is [tex]\(-2.5\)[/tex].
### Summary:
- Part (a): When the price increases from 3.00 ETB to 4.00 ETB, the price elasticity of demand is [tex]\(-1.15\)[/tex].
- Part (b): When the price falls from 4.00 ETB to 3.00 ETB, the price elasticity of demand is [tex]\(-2.5\)[/tex].
