Math Problem Statement

Compute the Price Elasticity of Supply (PES) for the given combinations (A to B, C to D, E to D, C to B) using the midpoint formula.

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:

PES=%ΔQs%ΔPPES = \frac{\% \Delta Q_s}{\% \Delta P}

Where:

  • ΔQs\Delta Q_s is the percentage change in quantity supplied.
  • ΔP\Delta P is the percentage change in price.

To calculate the percentage change using the midpoint formula, use:

%Δ=New ValueOld ValueNew Value+Old Value2×100\% \Delta = \frac{\text{New Value} - \text{Old Value}}{\frac{\text{New Value} + \text{Old Value}}{2}} \times 100

Now, you need to compute the PES for the following combinations using the values provided in the table:

  1. A to B
  2. C to D
  3. E to D
  4. 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
  1. Calculate the percentage change in quantity supplied: %ΔQs=200175200+1752×100\% \Delta Q_s = \frac{200 - 175}{\frac{200 + 175}{2}} \times 100
  2. Calculate the percentage change in price: %ΔP=120100120+1002×100\% \Delta P = \frac{120 - 100}{\frac{120 + 100}{2}} \times 100
  3. Compute the PES using these values.

I'll calculate these step by step.For the combination A to B:

  • Percentage change in quantity supplied: 13.33%13.33\%
  • Percentage change in price: 18.18%18.18\%
  • Price Elasticity of Supply (PES): 0.730.73

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: 46.15%46.15\%
  • Percentage change in price: 6.06%-6.06\%
  • Price Elasticity of Supply (PES): 7.62-7.62 (a negative value indicates that supply and price move in opposite directions)

E to D:

  • Percentage change in quantity supplied: 66.67%-66.67\%
  • Percentage change in price: 34.48%-34.48\%
  • Price Elasticity of Supply (PES): 1.931.93

C to B:

  • Percentage change in quantity supplied: 8.96%-8.96\%
  • Percentage change in price: 22.22%-22.22\%
  • Price Elasticity of Supply (PES): 0.400.40

Would you like further details or clarifications on these calculations?

Here are 5 related questions to expand your understanding:

  1. What does a negative PES value indicate in terms of supply responsiveness?
  2. How does PES differ from Price Elasticity of Demand (PED)?
  3. How can firms use PES to optimize production decisions?
  4. What factors typically affect the elasticity of supply?
  5. 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)