https://file.aiquickdraw.com/mathbot/file/17306949096609brcizky.jpg

The image shows values and an equation that appears to set up the calculation of the price elasticity of demand. The values are:

- \( P_1 = 10,000 \)
- \( P_2 = 12,000 \)
- \( Q_1 = 1,000 \)
- \( Q_2 = 2,000 \)

The formula below these values:

\[
\frac{(Q - Q_1)}{(P - P_1)} = \frac{(Q_2 - Q_1)}{(P_2 - P_1)}
\]

This formula resembles a setup for calculating the slope of a line between two points, or, in economics, the midpoint formula for elasticity. The elasticity of demand is often calculated using the formula:

\[
\text{Elasticity} = \frac{\Delta Q / Q_{\text{average}}}{\Delta P / P_{\text{average}}}
\]

Using the values given, let's solve for the slope between \( P_1, Q_1 \) and \( P_2, Q_2 \) using:

\[
\frac{Q_2 - Q_1}{P_2 - P_1} = \frac{2000 - 1000}{12000 - 10000}
\]

1. **Step 1:** Calculate the change in quantity (\( Q_2 - Q_1 \)):
   \[
   Q_2 - Q_1 = 2000 - 1000 = 1000
   \]

2. **Step 2:** Calculate the change in price (\( P_2 - P_1 \)):
   \[
   P_2 - P_1 = 12000 - 10000 = 2000
   \]

3. **Step 3:** Substitute these values:
   \[
   \frac{Q_2 - Q_1}{P_2 - P_1} = \frac{1000}{2000} = 0.5
   \]

So, the slope (or rate of change in quantity with respect to price) is \( 0.5 \).

Would you like further explanation on elasticity or related concepts?

Here are some related questions:
1. What does a slope of 0.5 imply about the relationship between price and quantity?
2. How is elasticity different from slope in economics?
3. How can we use this slope to calculate the price elasticity of demand?
4. What would happen if \( Q_2 \) were smaller than \( Q_1 \)?
5. What is the midpoint formula, and how does it differ from this approach?

**Tip:** In economics, elasticity calculations often use percentage changes rather than absolute changes to capture responsiveness.

Given P1 = 10,000, Q1 = 1,000, P2 = 12,000, and Q2 = 2,000, calculate the slope or elasticity using the formula (Q - Q1) / (P - P1) = (Q2 - Q1) / (P2 - P1).

Learn how to calculate the slope and elasticity of demand using given price and quantity values. This example includes P1 = 10,000, Q1 = 1,000, P2 = 12,000, and Q2 = 2,000, demonstrating step-by-step calculations for economics students.

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