To determine the elasticity of supply for maize based on the provided supply schedule, we will follow a step-by-step approach. Elasticity of supply measures how responsive the quantity supplied of a good is to a change in its price. The formula for calculating the price elasticity of supply (PES) is:
[
\text{PES} = \frac{\%\text{ Change in Quantity Supplied}}{\%\text{ Change in Price}}
]
Step 1: Identify the Changes in Price and Quantity Supplied
From the table, we have two price points and their corresponding quantities supplied:
- At a price of 24 Naira, the quantity supplied is 480 kg.
- At a price of 16 Naira, the quantity supplied is 400 kg.
Step 2: Calculate the Change in Quantity Supplied and Change in Price
-
Change in Quantity Supplied (ΔQ):
[
\Delta Q = Q_2 - Q_1 = 400 \, \text{kg} - 480 \, \text{kg} = -80 \, \text{kg}
]
-
Change in Price (ΔP):
[
\Delta P = P_2 - P_1 = 16 \, \text{Naira} - 24 \, \text{Naira} = -8 \, \text{Naira}
]
Step 3: Calculate the Percentage Changes
-
Percentage Change in Quantity Supplied:
[
\%\Delta Q = \frac{\Delta Q}{Q_1} \times 100 = \frac{-80}{480} \times 100 \approx -16.67\%
]
-
Percentage Change in Price:
[
\%\Delta P = \frac{\Delta P}{P_1} \times 100 = \frac{-8}{24} \times 100 \approx -33.33\%
]
Step 4: Calculate the Price Elasticity of Supply
Now we can substitute these percentage changes into the PES formula:
[
\text{PES} = \frac{\%\Delta Q}{\%\Delta P} = \frac{-16.67\%}{-33.33\%} \approx 0.5
]
Conclusion
The calculated price elasticity of supply for maize is approximately
0.5. This indicates that the supply of maize is inelastic, meaning that the quantity supplied is not very responsive to price changes.
Explanation of Options
-
Option A (0.3): This value suggests a very inelastic supply, which is lower than our calculated value. It implies that a price change would result in an even smaller change in quantity supplied than what we found.
-
Option B (0.4): This is also lower than our calculated value of 0.5, indicating a less responsive supply than what we observed.
-
Option C (0.5): This is the correct answer, as it matches our calculated elasticity of supply.
-
Option D (0.6): This value suggests a more elastic supply than what we calculated, indicating that the quantity supplied would change more significantly in response to price changes than what we found.
Revision Summary
- The price elasticity of supply (PES) measures how much the quantity supplied changes in response to a price change.
- The formula for PES is (\text{PES} = \frac{\%\Delta Q}{\%\Delta P}).
- For maize, the PES was calculated to be approximately 0.5, indicating inelastic supply.
- The correct answer is C (0.5), as it matches our calculations.