The price of a good rises from $16 to $24, and the quantity supplied rises from 90 to 110 units. Calculate with the midpoint method, the price elasticity of supply is. If the price... The price of a good rises from $16 to $24, and the quantity supplied rises from 90 to 110 units. Calculate with the midpoint method, the price elasticity of supply is. If the price elasticity of supply is zero, the supply curve is.
Understand the Problem
The question is asking us to calculate the price elasticity of supply using the midpoint method based on given price and quantity changes. The second part assesses the nature of the supply curve based on elasticity. This involves applying economic principles related to supply elasticity.
Answer
The price elasticity of supply is $\frac{1}{2}$ and the supply curve is vertical when elasticity is zero.
Answer for screen readers
The price elasticity of supply calculated is $0.5$ (or $\frac{1}{2}$), so the correct choice is b. If the price elasticity of supply is zero, the supply curve is vertical.
Steps to Solve
- Calculate Change in Price and Quantity
Determine the change in price and quantity supplied.
- Change in Price: $P_{new} - P_{old} = 24 - 16 = 8$
- Change in Quantity Supplied: $Q_{new} - Q_{old} = 110 - 90 = 20$
- Calculate Average Price and Quantity
Use the midpoint method to find the average price and quantity supplied.
- Average Price: $\frac{P_{new} + P_{old}}{2} = \frac{24 + 16}{2} = 20$
- Average Quantity: $\frac{Q_{new} + Q_{old}}{2} = \frac{110 + 90}{2} = 100$
- Calculate Price Elasticity of Supply
Calculate the price elasticity of supply using the formula: $$ E_s = \frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}} $$ Where:
- Percentage Change in Quantity Supplied: $$ \frac{20}{100} = 0.2 $$
- Percentage Change in Price: $$ \frac{8}{20} = 0.4 $$ So: $$ E_s = \frac{0.2}{0.4} = 0.5 $$
- Determine the Nature of the Supply Curve
If the price elasticity of supply is zero, it means the supply curve is vertical. However, since we calculated an elasticity of 0.5, the answer to this part of the question is that the supply curve is upward sloping, reflecting that supply does respond to price, but not in a perfectly elastic manner.
The price elasticity of supply calculated is $0.5$ (or $\frac{1}{2}$), so the correct choice is b. If the price elasticity of supply is zero, the supply curve is vertical.
More Information
Price elasticity of supply measures how responsive the quantity supplied is to a change in price. An elasticity of 0.5 indicates that for a 1% increase in price, the quantity supplied increases by 0.5%. A perfectly elastic supply curve (elasticity of infinity) would be horizontal, while a perfectly inelastic supply curve (elasticity of 0) would be vertical.
Tips
- Confusing the changes in quantity and price; make sure to clearly calculate the differences.
- Not using the average values for price and quantity in the midpoint method; always use the average to calculate elasticity accurately.
- Misinterpreting the elasticity value directly or incorrectly associating the elasticity value with the nature of the supply curve.
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