Math Problem Statement

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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).

Solution

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

  • P1=10,000P_1 = 10,000
  • P2=12,000P_2 = 12,000
  • Q1=1,000Q_1 = 1,000
  • Q2=2,000Q_2 = 2,000

The formula below these values:

(QQ1)(PP1)=(Q2Q1)(P2P1)\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:

Elasticity=ΔQ/QaverageΔP/Paverage\text{Elasticity} = \frac{\Delta Q / Q_{\text{average}}}{\Delta P / P_{\text{average}}}

Using the values given, let's solve for the slope between P1,Q1P_1, Q_1 and P2,Q2P_2, Q_2 using:

Q2Q1P2P1=200010001200010000\frac{Q_2 - Q_1}{P_2 - P_1} = \frac{2000 - 1000}{12000 - 10000}

  1. Step 1: Calculate the change in quantity (Q2Q1Q_2 - Q_1): Q2Q1=20001000=1000Q_2 - Q_1 = 2000 - 1000 = 1000

  2. Step 2: Calculate the change in price (P2P1P_2 - P_1): P2P1=1200010000=2000P_2 - P_1 = 12000 - 10000 = 2000

  3. Step 3: Substitute these values: Q2Q1P2P1=10002000=0.5\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 0.50.5.

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 Q2Q_2 were smaller than Q1Q_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.

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Math Problem Analysis

Mathematical Concepts

Elasticity of Demand
Slope Calculation

Formulas

(Q - Q1) / (P - P1) = (Q2 - Q1) / (P2 - P1)
Elasticity = (ΔQ / Q_average) / (ΔP / P_average)

Theorems

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Suitable Grade Level

High School Economics or Algebra