### Elasticity of Demand and Revenue Function Analysis**Demand Function and Quantity Demanded**- **Demand Function:** $ p = 500 - 3x $- **Quantity Demanded:** $ x = 16 $**Objective:** Find the price elasticity of demand for the demand function at the indicated $ x $-value.**Question 1: Is the demand elastic, inelastic, or of unit elasticity at the indicated $ x $-value?**- $ \circ $ The demand is elastic at this $ x $-value.- $ \circ $ The demand is inelastic at this $ x $-value.- $ \circ $ The demand is of unit elasticity at this $ x $-value.**Graphical Analysis:** Use a graphing utility to graph the revenue function.#### Graph Descriptions1. **First Graph (Top Left): Linear Graph** - **Axes:** $ x $ and $ y $ - **Graph Description:** A downward sloping line graph showing a negative linear relationship between $ x $ and $ y $. As $ x $ increases, $ y $ decreases.2. **Second Graph (Top Right): Linear Graph** - **Axes:** $ x $ and $ y $ - **Graph Description:** Similar to the first graph, showcasing a negative linear trend with a steeper decline.3. **Third Graph (Bottom Left): Quadratic Graph** - **Axes:** $ x $ and $ y $ - **Graph Description:** A parabolic curve opening downward. The graph reaches a maximum value and then declines symmetrically.4. **Fourth Graph (Bottom Right): Quadratic Graph** - **Axes:** $ x $ and $ y $ - **Graph Description:** Another downward opening parabola with a higher peak and a wider spread compared to the previous quadratic graph.**Conclusion:** Understanding the type of elasticity (elastic, inelastic, or unitary) and analyzing revenue functions through graphs can aid in economic decision-making and pricing strategy optimization.

Given: p=500-3x x=166.667-0.3333p x=16

Consider the following. Quantity Demanded x = 16 Demand Function p = 500 – 3x Find the price elasticity of demand for the demand function at the indicated x-value. Is the demand elastic, inelastic, or of unit elasticity at the indicated x-value? O The demand is elastic at this x-value. The demand is inelastic at this x-value. The demand is of unit elasticity at this x-value. Use a graphing utility to graph the revenue function.

Consider the following. Quantity Demanded x = 16 Demand Function p = 500 – 3x Find the price elasticity of demand for the demand function at the indicated x-value. Is the demand elastic, inelastic, or of unit elasticity at the indicated x-value? O The demand is elastic at this x-value. The demand is inelastic at this x-value. The demand is of unit elasticity at this x-value. Use a graphing utility to graph the revenue function.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

### Elasticity of Demand and Revenue Function Analysis

**Demand Function and Quantity Demanded**

- **Demand Function:** $ p = 500 - 3x $
- **Quantity Demanded:** $ x = 16 $

**Objective:** Find the price elasticity of demand for the demand function at the indicated $ x $-value.

**Question 1: Is the demand elastic, inelastic, or of unit elasticity at the indicated $ x $-value?**

- $ \circ $ The demand is elastic at this $ x $-value.
- $ \circ $ The demand is inelastic at this $ x $-value.
- $ \circ $ The demand is of unit elasticity at this $ x $-value.

**Graphical Analysis:** Use a graphing utility to graph the revenue function.

#### Graph Descriptions

1. **First Graph (Top Left): Linear Graph**
- **Axes:** $ x $ and $ y $
- **Graph Description:** A downward sloping line graph showing a negative linear relationship between $ x $ and $ y $. As $ x $ increases, $ y $ decreases.

2. **Second Graph (Top Right): Linear Graph**
- **Axes:** $ x $ and $ y $
- **Graph Description:** Similar to the first graph, showcasing a negative linear trend with a steeper decline.

3. **Third Graph (Bottom Left): Quadratic Graph**
- **Axes:** $ x $ and $ y $
- **Graph Description:** A parabolic curve opening downward. The graph reaches a maximum value and then declines symmetrically.

4. **Fourth Graph (Bottom Right): Quadratic Graph**
- **Axes:** $ x $ and $ y $
- **Graph Description:** Another downward opening parabola with a higher peak and a wider spread compared to the previous quadratic graph.

**Conclusion:** Understanding the type of elasticity (elastic, inelastic, or unitary) and analyzing revenue functions through graphs can aid in economic decision-making and pricing strategy optimization.

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