Suppose the inverse demand for a particular good is given by P = 1200 – 12Q. Furthermore, th are only two firms, A and B. Firm A's marginal cost is a constant $25, and Firm B's marginal cost is constant $20. Assume these two firms engage in Stackelberg competition, where Firm A moves first. If we assume that the firm with the lowest costs could supply the entire market, then the deadweight loss due to the market power these two firms exert through Stackelberg competition equals $______. [Round your answer to two decimals 1

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
icon
Related questions
Question
### Stackelberg Competition Example

**Problem Statement:**

Suppose the inverse demand for a particular good is given by \( P = 1200 - 12Q \). Furthermore, there are only two firms, A and B. Firm A's marginal cost is a constant $25, and Firm B's marginal cost is a constant $20.

Assume these two firms engage in Stackelberg competition, where Firm A moves first.

If we assume that the firm with the lowest costs could supply the entire market, then the deadweight loss due to the market power these two firms exert through Stackelberg competition equals $_____.

[Round your answer to two decimals.]

**Explanation:**

In the context of this problem, the Stackelberg competition model assumes that Firm A, as the leader, makes its output decision first. Firm B, as the follower, then makes its output decision based on Firm A's choice.

- **Inverse Demand Function:** \[ P = 1200 - 12Q \]
  - \( P \) is the price.
  - \( Q \) is the quantity.
- **Firm A's Marginal Cost:** \( MC_A = 25 \)
- **Firm B's Marginal Cost:** \( MC_B = 20 \)

### Steps to Determine the Deadweight Loss

1. **Determine the Reaction Function for Firm B:**
   - Firm B maximizes its profit given Firm A's output level \( q_A \).
   
2. **Determine the Optimal Output for Firm A:**
   - Knowing Firm B's reaction function, Firm A maximizes its profit.

3. **Calculate Equilibrium Quantities and Prices:**
   - Solve the simultaneous equations to find the optimal quantities \( q_A \) and \( q_B \).

4. **Calculate Total Output \( Q \) and Market Price \( P \):**

5. **Calculate Deadweight Loss:**
   - Compare the market outcome to the competitive equilibrium where price equals marginal cost.

This problem involves detailed calculations which can be part of an extensive exercise for understanding the implications of Stackelberg competition and market power on economic welfare.

___

**Note:** This explanation outlines the process and necessary equations. However, to find the precise numerical answer for deadweight loss, further calculation steps are required.
Transcribed Image Text:### Stackelberg Competition Example **Problem Statement:** Suppose the inverse demand for a particular good is given by \( P = 1200 - 12Q \). Furthermore, there are only two firms, A and B. Firm A's marginal cost is a constant $25, and Firm B's marginal cost is a constant $20. Assume these two firms engage in Stackelberg competition, where Firm A moves first. If we assume that the firm with the lowest costs could supply the entire market, then the deadweight loss due to the market power these two firms exert through Stackelberg competition equals $_____. [Round your answer to two decimals.] **Explanation:** In the context of this problem, the Stackelberg competition model assumes that Firm A, as the leader, makes its output decision first. Firm B, as the follower, then makes its output decision based on Firm A's choice. - **Inverse Demand Function:** \[ P = 1200 - 12Q \] - \( P \) is the price. - \( Q \) is the quantity. - **Firm A's Marginal Cost:** \( MC_A = 25 \) - **Firm B's Marginal Cost:** \( MC_B = 20 \) ### Steps to Determine the Deadweight Loss 1. **Determine the Reaction Function for Firm B:** - Firm B maximizes its profit given Firm A's output level \( q_A \). 2. **Determine the Optimal Output for Firm A:** - Knowing Firm B's reaction function, Firm A maximizes its profit. 3. **Calculate Equilibrium Quantities and Prices:** - Solve the simultaneous equations to find the optimal quantities \( q_A \) and \( q_B \). 4. **Calculate Total Output \( Q \) and Market Price \( P \):** 5. **Calculate Deadweight Loss:** - Compare the market outcome to the competitive equilibrium where price equals marginal cost. This problem involves detailed calculations which can be part of an extensive exercise for understanding the implications of Stackelberg competition and market power on economic welfare. ___ **Note:** This explanation outlines the process and necessary equations. However, to find the precise numerical answer for deadweight loss, further calculation steps are required.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Welfare Cost
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.
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