For a monopolist facing a linear demand function (P = a - bQ) for their product and a constant marginal cost (MC = c), how much would they raise the price they charge if a $6 per unit excise tax were to be imposed?
For a monopolist facing a linear demand function (P = a - bQ) for their product and a constant marginal cost (MC = c), how much would they raise the price they charge if a $6 per unit excise tax were to be imposed?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
100%
![### Excise Tax Impact on Monopoly Pricing
**Problem Statement:**
_For a monopolist facing a linear demand function \( P = a - bQ \) for their product and a constant marginal cost \( (MC = c) \), how much would they raise the price they charge if a $6 per unit excise tax were to be imposed?_
**Explanation:**
In this scenario, we are analyzing the impact of an excise tax on a monopolist's pricing strategy. Here's a step-by-step breakdown of the key concepts involved:
1. **Demand Function:**
- The demand function given is \( P = a - bQ \), where:
- \( P \) is the price of the product.
- \( Q \) is the quantity of the product.
- \( a \) and \( b \) are constants that describe the linear relationship between price and quantity.
2. **Marginal Cost:**
- It is provided that the marginal cost (MC) is constant and denoted as \( c \).
3. **Excise Tax:**
- The excise tax imposed is $6 per unit.
**Analysis:**
When an excise tax of $6 is imposed, the firm's marginal cost increases by the tax amount. Therefore, the new marginal cost becomes:
\[ MC_{\text{new}} = c + 6 \]
In a monopolistic market, the firm maximizes profit by setting marginal revenue (MR) equal to marginal cost (MC). The marginal revenue can be derived from the demand function. Without the excise tax, the profit-maximizing condition is:
\[ MR = MC \]
With the excise tax, the new condition becomes:
\[ MR = MC_{\text{new}} \]
Given that the only change is the increase in marginal cost by $6, the monopolist will adjust the price to reflect the higher cost.
**Conclusion:**
The price increase due to the $6 excise tax would be determined by the monopolist passing some or all of the tax onto consumers. The exact amount of the price increase would depend on the elasticity of demand and the specific values of \( a \) and \( b \). In a typical analysis, if the monopolist can pass the entire tax to consumers, the price would increase by $6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea0084d8-63e7-4f56-975c-add2c9289a98%2F1739599f-9602-4d74-a290-c64e05b1b814%2Fvr3aeun_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Excise Tax Impact on Monopoly Pricing
**Problem Statement:**
_For a monopolist facing a linear demand function \( P = a - bQ \) for their product and a constant marginal cost \( (MC = c) \), how much would they raise the price they charge if a $6 per unit excise tax were to be imposed?_
**Explanation:**
In this scenario, we are analyzing the impact of an excise tax on a monopolist's pricing strategy. Here's a step-by-step breakdown of the key concepts involved:
1. **Demand Function:**
- The demand function given is \( P = a - bQ \), where:
- \( P \) is the price of the product.
- \( Q \) is the quantity of the product.
- \( a \) and \( b \) are constants that describe the linear relationship between price and quantity.
2. **Marginal Cost:**
- It is provided that the marginal cost (MC) is constant and denoted as \( c \).
3. **Excise Tax:**
- The excise tax imposed is $6 per unit.
**Analysis:**
When an excise tax of $6 is imposed, the firm's marginal cost increases by the tax amount. Therefore, the new marginal cost becomes:
\[ MC_{\text{new}} = c + 6 \]
In a monopolistic market, the firm maximizes profit by setting marginal revenue (MR) equal to marginal cost (MC). The marginal revenue can be derived from the demand function. Without the excise tax, the profit-maximizing condition is:
\[ MR = MC \]
With the excise tax, the new condition becomes:
\[ MR = MC_{\text{new}} \]
Given that the only change is the increase in marginal cost by $6, the monopolist will adjust the price to reflect the higher cost.
**Conclusion:**
The price increase due to the $6 excise tax would be determined by the monopolist passing some or all of the tax onto consumers. The exact amount of the price increase would depend on the elasticity of demand and the specific values of \( a \) and \( b \). In a typical analysis, if the monopolist can pass the entire tax to consumers, the price would increase by $6.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education