Homework Help is Here – Start Your Trial Now!
Business
Economics
Acme is a monopolist for a good with inverse demand P = 4000 – 6Q, where P is the price in dollars and Q is the amount sold. Acme's variable costs are TVC(Q) = 4Q². With these functions, the marginal revenue is MR(Q) = 4000 – 120 and marginal cost is MC(Q) = 8Q. a) If Acme has no fixed costs, what is its profit maximizing price? b) If Acme has non-sunk fixed costs of $700,000, is it worth operating or should they shut down?

Acme is a monopolist for a good with inverse demand P = 4000 – 6Q, where P is the price in dollars and Q is the amount sold. Acme's variable costs are TVC(Q) = 4Q². With these functions, the marginal revenue is MR(Q) = 4000 – 120 and marginal cost is MC(Q) = 8Q. a) If Acme has no fixed costs, what is its profit maximizing price? b) If Acme has non-sunk fixed costs of $700,000, is it worth operating or should they shut down?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
See similar textbooks
icon
Related questions
Question
**Educational Content: Monopoly Pricing and Profit Maximization** **Scenario Analysis:** Acme is a monopolist for a good, facing the inverse demand function \( P = 4000 - 6Q \), where \( P \) represents the price in dollars and \( Q \) is the quantity sold. Acme's variable costs are represented by the equation \( TVC(Q) = 4Q^2 \). The marginal revenue function is given as \( MR(Q) = 4000 - 12Q \), and the marginal cost function is described by \( MC(Q) = 8Q \). **Questions:** a) **Profit Maximizing Price Without Fixed Costs:** - To determine the profit-maximizing price, set marginal revenue (MR) equal to marginal cost (MC) and solve for \( Q \). - \[ 4000 - 12Q = 8Q \] - \[ 4000 = 20Q \quad \Rightarrow \quad Q = 200 \] - Substitute \( Q = 200 \) back into the inverse demand equation to find \( P \): - \[ P = 4000 - 6(200) = 4000 - 1200 = 2800 \] - The profit-maximizing price is $2800. b) **Decision on Operation with Non-Sunk Fixed Costs of $700,000:** - Calculate total profit using the quantity found: - Total Revenue (TR) = \( P \times Q = 2800 \times 200 = 560,000 \) - Total Variable Cost (TVC) = \( 4Q^2 = 4(200)^2 = 160,000 \) - Total Cost (TC) including fixed costs = \( TVC + \text{fixed costs} = 160,000 + 700,000 = 860,000 \) - Profit = TR - TC = \( 560,000 - 860,000 = -300,000 \) Since the profit is negative even before considering fixed costs, Acme should consider shutting down because operating results in a loss.
Transcribed Image Text:**Educational Content: Monopoly Pricing and Profit Maximization** **Scenario Analysis:** Acme is a monopolist for a good, facing the inverse demand function \( P = 4000 - 6Q \), where \( P \) represents the price in dollars and \( Q \) is the quantity sold. Acme's variable costs are represented by the equation \( TVC(Q) = 4Q^2 \). The marginal revenue function is given as \( MR(Q) = 4000 - 12Q \), and the marginal cost function is described by \( MC(Q) = 8Q \). **Questions:** a) **Profit Maximizing Price Without Fixed Costs:** - To determine the profit-maximizing price, set marginal revenue (MR) equal to marginal cost (MC) and solve for \( Q \). - \[ 4000 - 12Q = 8Q \] - \[ 4000 = 20Q \quad \Rightarrow \quad Q = 200 \] - Substitute \( Q = 200 \) back into the inverse demand equation to find \( P \): - \[ P = 4000 - 6(200) = 4000 - 1200 = 2800 \] - The profit-maximizing price is $2800. b) **Decision on Operation with Non-Sunk Fixed Costs of $700,000:** - Calculate total profit using the quantity found: - Total Revenue (TR) = \( P \times Q = 2800 \times 200 = 560,000 \) - Total Variable Cost (TVC) = \( 4Q^2 = 4(200)^2 = 160,000 \) - Total Cost (TC) including fixed costs = \( TVC + \text{fixed costs} = 160,000 + 700,000 = 860,000 \) - Profit = TR - TC = \( 560,000 - 860,000 = -300,000 \) Since the profit is negative even before considering fixed costs, Acme should consider shutting down because operating results in a loss.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
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)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
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-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS