**Duopoly Competition and the Stackelberg Model**In this scenario, two firms compete in a single market, known as a duopoly, with demand given by the equation $ Q_D = 60 - P $. Both firms have identical cost functions, represented by $ C(q) = 2q $.### Stackelberg Model DynamicsThe Stackelberg model involves one firm (Firm 1) choosing its output first, followed by the second firm (Firm 2) making its decision. The interaction is sequential:- **Output:** - Firm 1 produces a certain number of units. - Firm 2 subsequently produces its output based on Firm 1's decision.- **Market Price:** - The price in the market is determined after both firms have chosen their outputs.- **Profits:** - Firm 1 earns a specified amount in profits. - Firm 2 earns its own profit based on the residual demand and its cost structure.### First-Mover AdvantageEvaluating whether Firm 1 has a first-mover advantage is crucial:- This examines if committing to an output level before Firm 2 provides Firm 1 with a strategic advantage, potentially leading to higher profits or more favorable market positioning compared to Firm 2.Understanding the interplay between the firms in this model sheds light on strategic decision-making and competitive behaviors in oligopolistic markets.

For the given game, firm 1 is a leader firm where it moves first and then the firm 2 moves which is the follower firm. Firm 1 produces 29 units. Firm 2 produces 14.5 units. The price in the market is 16.5 Firm 1 earns profit of 420.5 Firm 1 earns profit of 210.25 Yes, firm 1 has first mover advantage.

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Two firms compete in a single market (duopoly) with demand given by QD=60-P. The two firms have identical cost functions, C(q)=2q. Suppose firm 1 chooses its output first, following by firm 2 (Stackelberg model). In this case, firm 1 produces ✓ units and firm 2 produces ✓. Firm 1 earns ✓ units. The price in the market is ✓and firm 2 earns $ $ Does firm 1 have a first-mover advantage here?

Two firms compete in a single market (duopoly) with demand given by QD=60-P. The two firms have identical cost functions, C(q)=2q. Suppose firm 1 chooses its output first, following by firm 2 (Stackelberg model). In this case, firm 1 produces ✓ units and firm 2 produces ✓. Firm 1 earns ✓ units. The price in the market is ✓and firm 2 earns $ $ Does firm 1 have a first-mover advantage here?

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

**Duopoly Competition and the Stackelberg Model**

In this scenario, two firms compete in a single market, known as a duopoly, with demand given by the equation $ Q_D = 60 - P $. Both firms have identical cost functions, represented by $ C(q) = 2q $.

### Stackelberg Model Dynamics
The Stackelberg model involves one firm (Firm 1) choosing its output first, followed by the second firm (Firm 2) making its decision. The interaction is sequential:

- **Output:**
- Firm 1 produces a certain number of units.
- Firm 2 subsequently produces its output based on Firm 1's decision.

- **Market Price:**
- The price in the market is determined after both firms have chosen their outputs.

- **Profits:**
- Firm 1 earns a specified amount in profits.
- Firm 2 earns its own profit based on the residual demand and its cost structure.

### First-Mover Advantage
Evaluating whether Firm 1 has a first-mover advantage is crucial:

- This examines if committing to an output level before Firm 2 provides Firm 1 with a strategic advantage, potentially leading to higher profits or more favorable market positioning compared to Firm 2.

Understanding the interplay between the firms in this model sheds light on strategic decision-making and competitive behaviors in oligopolistic markets.

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