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
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
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d5e88e6-b1af-4aea-9b08-2dadd85f5e2c%2Fe99e4747-86e9-42cb-b0b6-5ad8cd7ccab7%2Frjdcmr_processed.png&w=3840&q=75)
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.
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