Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Understanding Price Elasticity of Demand Using the Midpoint Method
#### Explanation of the Graph:
The graph above represents a demand curve analysis for two different demand lines: \(D_1\) (in blue) and \(D_2\) (in red). The vertical axis \(P\) represents the price, while the horizontal axis \(Q\) represents the quantity demanded.
Important points on the graph:
- Point \(A\) at coordinates (100, $5) on demand curve \(D_1\).
- Point \(B\) at coordinates (80, $10) on demand curve \(D_1\).
- Point \(C\) at coordinates (90, $10) on demand curve \(D_2\).
#### Calculating Price Elasticity of Demand Using the Midpoint Method:
Use the midpoint formula to calculate the price elasticity of demand between points \(A\) and \(B\) on \(D_1\). The midpoint formula is given by:
\[
\text{Price Elasticity of Demand} = \frac{(Q_2 - Q_1)}{(Q_2 + Q_1) / 2} \div \frac{(P_2 - P_1)}{(P_2 + P_1) / 2}
\]
Where:
- \((Q_1, P_1)\) = (100, $5) at point \(A\).
- \((Q_2, P_2)\) = (80, $10) at point \(B\).
Now, substitute the values into the formula:
\[
\text{Price Elasticity of Demand} = \frac{(80 - 100)}{(80 + 100)/2} \div \frac{(10 - 5)}{(10 + 5)/2}
\]
\[
\text{Price Elasticity of Demand} = \frac{-20}{90} \div \frac{5}{7.5}
\]
\[
\text{Price Elasticity of Demand} = -0.222 \div 0.666
\]
\[
\text{Price Elasticity of Demand} = -0.333
\]
Hence, the price elasticity of demand from point \(A\) to point \(B\) on \(D_1\) is \(-0.333\).
This formula helps in understanding how](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3b445b4-cac0-4f0d-9c18-1a4527eab73b%2Fcdfd27b2-a52d-4366-a25d-63b6421e5035%2F9v9gsmm_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Price Elasticity of Demand Using the Midpoint Method
#### Explanation of the Graph:
The graph above represents a demand curve analysis for two different demand lines: \(D_1\) (in blue) and \(D_2\) (in red). The vertical axis \(P\) represents the price, while the horizontal axis \(Q\) represents the quantity demanded.
Important points on the graph:
- Point \(A\) at coordinates (100, $5) on demand curve \(D_1\).
- Point \(B\) at coordinates (80, $10) on demand curve \(D_1\).
- Point \(C\) at coordinates (90, $10) on demand curve \(D_2\).
#### Calculating Price Elasticity of Demand Using the Midpoint Method:
Use the midpoint formula to calculate the price elasticity of demand between points \(A\) and \(B\) on \(D_1\). The midpoint formula is given by:
\[
\text{Price Elasticity of Demand} = \frac{(Q_2 - Q_1)}{(Q_2 + Q_1) / 2} \div \frac{(P_2 - P_1)}{(P_2 + P_1) / 2}
\]
Where:
- \((Q_1, P_1)\) = (100, $5) at point \(A\).
- \((Q_2, P_2)\) = (80, $10) at point \(B\).
Now, substitute the values into the formula:
\[
\text{Price Elasticity of Demand} = \frac{(80 - 100)}{(80 + 100)/2} \div \frac{(10 - 5)}{(10 + 5)/2}
\]
\[
\text{Price Elasticity of Demand} = \frac{-20}{90} \div \frac{5}{7.5}
\]
\[
\text{Price Elasticity of Demand} = -0.222 \div 0.666
\]
\[
\text{Price Elasticity of Demand} = -0.333
\]
Hence, the price elasticity of demand from point \(A\) to point \(B\) on \(D_1\) is \(-0.333\).
This formula helps in understanding how
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