To determine whether the supply of this good is elastic or inelastic in each region using the midpoint method, we must calculate the price elasticity of supply (PES) for the two regions (V to W and X to Y).

Midpoint Method for Price Elasticity of Supply

The formula for price elasticity of supply using the midpoint method is:

$\text{PES} = \frac{\left(\frac{Q_2 - Q_1}{\left(\frac{Q_1 + Q_2}{2}\right)}\right)}{\left(\frac{P_2 - P_1}{\left(\frac{P_1 + P_2}{2}\right)}\right)}$

Where:

• $Q_1$ and $Q_2$ are the quantities at the two points.
• $P_1$ and $P_2$ are the prices at the two points.

The interpretation of the price elasticity of supply:

• If $PES > 1$, supply is elastic.
• If $PES < 1$, supply is inelastic.

1. Between Points V (7, 37.5) and W (17.5, 50)

• $Q_1 = 37.5$, $Q_2 = 50$
• $P_1 = 7$, $P_2 = 17.5$

Using the midpoint method formula:

$\text{PES} = \frac{\left(\frac{50 - 37.5}{\frac{50 + 37.5}{2}}\right)}{\left(\frac{17.5 - 7}{\frac{17.5 + 7}{2}}\right)}$

Let's calculate the PES for this region.

2. Between Points X (56, 225) and Y (63, 450)

• $Q_1 = 225$, $Q_2 = 450$
• $P_1 = 56$, $P_2 = 63$

Using the midpoint method formula:

$\text{PES} = \frac{\left(\frac{450 - 225}{\frac{450 + 225}{2}}\right)}{\left(\frac{63 - 56}{\frac{63 + 56}{2}}\right)}$

Let's calculate the PES for this region as well.

True or False: Elasticity at High Levels of Supply

The statement:

"As firms reach near maximum capacity at high levels of quantity supplied, supply becomes more elastic because firms may need to invest in additional capital in order to further increase production."

This statement is False. As firms approach maximum capacity, it becomes more difficult to increase production without significant investments in new capacity. In this situation, supply tends to become inelastic, not more elastic, because firms cannot easily respond to price increases by significantly increasing quantity supplied without incurring additional costs.

Let me calculate the exact values of PES for both regions next.### Elasticity Results:

1. Between Points V (7, 37.5) and W (17.5, 50):

   • The PES is approximately 0.33, which is inelastic since the value is less than 1.

2. Between Points X (56, 225) and Y (63, 450):

   • The PES is approximately 5.67, which is elastic since the value is greater than 1.

Conclusion:

• Between V and W, supply is inelastic.
• Between X and Y, supply is elastic.

The Statement:

"As firms reach near maximum capacity at high levels of quantity supplied, supply becomes more elastic..."

This is False. As firms approach capacity, supply typically becomes inelastic.

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Would you like more details on these calculations or have any further questions? Here are some related questions you might explore:

1. What are the key factors influencing price elasticity of supply?
2. How does elasticity change in the short run versus the long run for firms?
3. Can PES ever be negative, and if so, under what conditions?
4. How do technological advancements affect the elasticity of supply?
5. What role does supply chain management play in improving supply elasticity?

Tip: The closer a firm is to its production capacity, the less responsive it is to price changes, leading to more inelastic supply behavior.