Math Problem Statement
Solution
The image you uploaded is related to Price Elasticity of Supply (PES), and it provides a table of price and supply values. The midpoint formula for PES is given by:
Where:
- is the percentage change in quantity supplied.
- is the percentage change in price.
To calculate the percentage change using the midpoint formula, use:
Now, you need to compute the PES for the following combinations using the values provided in the table:
- A to B
- C to D
- E to D
- C to B
I'll compute each of these using the midpoint formula. Let's start with the first one: "A to B".
A to B:
- Price A = 120, Supply A = 200
- Price B = 100, Supply B = 175
- Calculate the percentage change in quantity supplied:
- Calculate the percentage change in price:
- Compute the PES using these values.
I'll calculate these step by step.For the combination A to B:
- Percentage change in quantity supplied:
- Percentage change in price:
- Price Elasticity of Supply (PES):
Now, I will proceed with the next combinations: C to D, E to D, and C to B.Here are the results for the other combinations:
C to D:
- Percentage change in quantity supplied:
- Percentage change in price:
- Price Elasticity of Supply (PES): (a negative value indicates that supply and price move in opposite directions)
E to D:
- Percentage change in quantity supplied:
- Percentage change in price:
- Price Elasticity of Supply (PES):
C to B:
- Percentage change in quantity supplied:
- Percentage change in price:
- Price Elasticity of Supply (PES):
Would you like further details or clarifications on these calculations?
Here are 5 related questions to expand your understanding:
- What does a negative PES value indicate in terms of supply responsiveness?
- How does PES differ from Price Elasticity of Demand (PED)?
- How can firms use PES to optimize production decisions?
- What factors typically affect the elasticity of supply?
- Why might PES vary significantly between different products or industries?
Tip: Remember that the magnitude of PES helps to understand whether supply is elastic (>1), inelastic (<1), or unit elastic (=1).
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Math Problem Analysis
Mathematical Concepts
Price Elasticity of Supply
Midpoint Formula
Percentage Change
Formulas
PES = (% Change in Quantity Supplied) / (% Change in Price)
% Change = (New Value - Old Value) / ((New Value + Old Value) / 2) * 100
Theorems
Elasticity of Supply
Suitable Grade Level
Grades 10-12 (High School Economics)
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