Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Demand Curve and Monopolist Behavior
#### 1)
**a) Explanation of the Inelastic Portion of the Demand Curve:**
The inelastic portion of the demand curve refers to the range where the price elasticity of demand is less than one. In this range, the percentage change in quantity demanded is less than the percentage change in price, meaning consumers are relatively unresponsive to price changes.
A monopolist will never choose a level of output in this inelastic range because increasing output would lead to a relatively smaller increase in quantity demanded compared to the decrease in price, ultimately reducing total revenue. Consequently, it is more profitable for the monopolist to operate in the elastic portion of the demand curve (where the price elasticity of demand is greater than one).
**b) Inverse Demand Curve and the Change in Demand:**
Suppose the inverse demand curve is given by:
\[ p = 10 - \alpha y \]
where \( p \) is price and \( y \) is output demanded.
Consider a price change from \( p \) to \( p' \) and a corresponding change in demand from \( y \) to \( y' \). Using the notation:
\[ \Delta p = p' - p \]
and
\[ \Delta y' = y' - y \]
Calculate the value of:
\[ \frac{\Delta y}{\Delta p} \]
**c) Monopolist's Maximum Output:**
Given the answers to (a) and (b) above, suppose that \(\alpha = 2\). Determine the maximum level of output that the monopolist would produce.
---
### Explanation and Calculation for Educational Purposes:
1. **Understanding the Inelastic Demand:**
- **Inelastic Demand:** When the quantity demanded does not change significantly as price changes. Calculated as the percentage change in quantity divided by the percentage change in price results in a value less than one.
- **Monopolist's Choice:** Monopolists operate where marginal revenue equals marginal cost. Since reducing prices in the inelastic portion causes revenue to decrease faster than costs can be recovered, it's not optimal for a profit-maximizing monopolist to produce there.
2. **Given Inverse Demand Function:**
- If we have \[ p = 10 - \alpha y \], we understand that \(\alpha\) represents the rate at which price decreases as quantity increases.
- To compute \(\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfedcf45-36f9-41dd-be80-a8990833e266%2F5fbd7208-5c25-4ed1-95a0-1e133113ec31%2Fo199d8_processed.png&w=3840&q=75)
Transcribed Image Text:### Demand Curve and Monopolist Behavior
#### 1)
**a) Explanation of the Inelastic Portion of the Demand Curve:**
The inelastic portion of the demand curve refers to the range where the price elasticity of demand is less than one. In this range, the percentage change in quantity demanded is less than the percentage change in price, meaning consumers are relatively unresponsive to price changes.
A monopolist will never choose a level of output in this inelastic range because increasing output would lead to a relatively smaller increase in quantity demanded compared to the decrease in price, ultimately reducing total revenue. Consequently, it is more profitable for the monopolist to operate in the elastic portion of the demand curve (where the price elasticity of demand is greater than one).
**b) Inverse Demand Curve and the Change in Demand:**
Suppose the inverse demand curve is given by:
\[ p = 10 - \alpha y \]
where \( p \) is price and \( y \) is output demanded.
Consider a price change from \( p \) to \( p' \) and a corresponding change in demand from \( y \) to \( y' \). Using the notation:
\[ \Delta p = p' - p \]
and
\[ \Delta y' = y' - y \]
Calculate the value of:
\[ \frac{\Delta y}{\Delta p} \]
**c) Monopolist's Maximum Output:**
Given the answers to (a) and (b) above, suppose that \(\alpha = 2\). Determine the maximum level of output that the monopolist would produce.
---
### Explanation and Calculation for Educational Purposes:
1. **Understanding the Inelastic Demand:**
- **Inelastic Demand:** When the quantity demanded does not change significantly as price changes. Calculated as the percentage change in quantity divided by the percentage change in price results in a value less than one.
- **Monopolist's Choice:** Monopolists operate where marginal revenue equals marginal cost. Since reducing prices in the inelastic portion causes revenue to decrease faster than costs can be recovered, it's not optimal for a profit-maximizing monopolist to produce there.
2. **Given Inverse Demand Function:**
- If we have \[ p = 10 - \alpha y \], we understand that \(\alpha\) represents the rate at which price decreases as quantity increases.
- To compute \(\
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