To determine which scenario represents the most elastic supply in response to a price increase from $100 to $110, we need to consider the concept of price elasticity of supply, which measures how much the quantity supplied responds to a change in price.
The formula for price elasticity of supply (PES) is:
[
PES = \frac{%\text{ change in quantity supplied}}{%\text{ change in price}}
]
- Price change: The price increases from $100 to $110, which is a change of $10. The percentage change in price is:
[
%\text{ change in price} = \frac{10}{100} \times 100 = 10%
]
Now, let's analyze each option for the percentage change in quantity supplied:
-
Does not change: Quantity supplied remains at 20.
- Percentage change in quantity supplied = 0%
- PES = 0% / 10% = 0 (perfectly inelastic)
-
Increases from 20 to 30:
- Change in quantity supplied = 30 - 20 = 10
- Percentage change in quantity supplied = (\frac{10}{20} \times 100 = 50%)
- PES = 50% / 10% = 5 (elastic)
-
Increases from 20 to 22:
- Change in quantity supplied = 22 - 20 = 2
- Percentage change in quantity supplied = (\frac{2}{20} \times 100 = 10%)
- PES = 10% / 10% = 1 (unit elastic)
-
Increases from 20 to 40:
- Change in quantity supplied = 40 - 20 = 20
- Percentage change in quantity supplied = (\frac{20}{20} \times 100 = 100%)
- PES = 100% / 10% = 10 (very elastic)
Based on these calculations, the most elastic supply occurs when the quantity supplied increases from 20 to 40, resulting in a PES of 10.
Therefore, the answer is:
Increases from 20 to 40.