### Understanding Price Elasticity of Demand with the Midpoint Method#### Graph ExplanationThe graph presented shows two demand curves, D₁ (blue) and D₂ (red), and illustrates a method to compute the price elasticity of demand using the midpoint (arc) method. Let's break down the components:- **Axes:** - The vertical axis (P) represents the price level. - The horizontal axis (Q) represents the quantity demanded.- **Points and Lines:** - Point A and Point C are the points of interest on demand curve D₁. - Point A is where price $ P $ is $5 and quantity demanded $ Q $ is 100 units. - Point B (located on the curve at intersection of $10 and quantity) corresponds to a point where price $ P $ is $10 and quantity demanded $ Q $ is 80 units. - Point C is a projection of Point B on demand curve D₁. Points A and C are used to apply the midpoint method:#### Calculation SetupTo apply the midpoint method:1. **Determine the Midpoints:** $ P_{mid} $ = $\frac{\$10 + \$5}{2}$ = \$7.50 $ Q_{mid} $ = $\frac{100 + 80}{2}$ = 90 units2. **Calculate Percentage Change in Quantity:** \[\% \Delta Q = \frac{Q_2 - Q_1}{\left(\frac{Q_2 + Q_1}{2}\right)} \times 100\] Where, - $ Q_1 = 100 $ (initial quantity at $ P = \$5 $) - $ Q_2 = 80 $ (new quantity at $ P = \$10 $) Now calculate: \[\% \Delta Q = \frac{80 - 100}{90} \times 100 = \frac{-20}{90} \times 100 \approx -22.22\%\]#### Demand LineTo summarize, the graph provides a visual representation of the initial and new quantities and prices. The percent change in quantity is approximately -22.22%. Students are encouraged to apply this method further to compute the price elasticity using the percent change in price.Ready to apply what you have learned? Calculate the

Answered: Use the midpoint method to compute the…

Use the midpoint method to compute the price elasticity on D1. $10 в $5 A D, D2 80 90 100 The percent change in quantity is:

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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