ECON 2350: Intermediate Micro II Study Notes

Intermediate Micro II - Oligopoly

Instructor: Jun Zhao
University: York University
Term: Winter 2026
Assignment #3: Chapter 28: Oligopoly

SECTION 1: Bean Sprouts Market Analysis

Problem 1: Inverse Demand and Cost Functions

A. Demand Curve

• Inverse Demand Curve: Given by the formula $P(Y) = 100 - 2Y$ Where:

  • P: Price

  • Y: Total industry output

B. Cost Function

• Each firm has the same Total Cost Function: $TC(y) = 4y$ Where:

  • TC: Total Costs

  • y: Individual firm's output

Problem 1 (a): Reaction Functions

Reaction Function for Firm 1

1. Firm 1's Output: Let Firm 1 produce an output of y1.

2. Total Output in the Market:
   $Y = y1 + y2$

3. Price:
   $P = 100 - 2Y = 100 - 2(y1 + y2)$

4. Profit for Firm 1:
   $ext{Profit} = (P - 4)y1 = \big(100 - 2(y1 + y2) - 4\big)y1$

5. First Order Condition for optimal output (set derivative to 0 and solve):
   $rac{d}{dy1} ext{Profit} = 0$

6. Reaction Function for Firm 1 derived as a function of y2.

Reaction Function for Firm 2

1. Firm 2's Output: Let Firm 2 produce an output of y2.

2. Profit for Firm 2:
   $ext{Profit} = (P - 4)y2 = \big(100 - 2(y1 + y2) - 4\big)y2$

3. First Order Condition for optimal output (set derivative to 0):

4. Reaction Function for Firm 2 derived as a function of y1.

Problem 1 (b): Cournot Equilibrium

Total Industry Output

1. At Cournot Equilibrium:

   • Solve reaction functions simultaneously.

2. Total Industry Output (Y): Calculated based on equilibrium values of y1 and y2.

3. Market Price (P): Derived from total output using the demand curve.

Problem 1 (c): Collusion

Total Industry Output and Price

1. Total Industry Output:

   • Under collusion, firms maximize joint profits.

2. Market Price: Set based on collusive output behavior.

Problem 1 (d): Change in Output and Profits

1. Assumption: One firm increases output by one unit believing the other does not react.

2. Impact on Profits: Analyze profit changes based on demand elasticity and reaction of the non-adjusting firm.

Problem 1 (e): Stackelberg Competition

Leader-Follower Dynamics

1. Firm 1 as a Leader:

   • Determine output y1 based on expected reaction of Firm 2.

2. Firm 2 as a Follower:

   • Calculate output y2 based on leader's output.

3. Total Industry Output: Combined outputs of both firms.

4. Market Price: Derived from total output using the demand curve.

Problem 1 (f): Preferences of Firm 1

1. Comparison of Strategies: Analyze which role (leader or simultaneous) is preferred by Firm 1 based on profit maximization.

Problem 1 (g): Bertrand Competition

Outcomes of Price Competition

1. Industry Output and Price: Analyze how Bertrand competition affects market dynamics relative to Cournot and Stackelberg.

SECTION 2: Bread Market Analysis

Problem 2: Demand and Cost Structures for Bread

Demand Curve

• Demand for Bread: $Q = 600 - p$ Where:

  • Q: Total number of loaves of bread consumers willing to buy

  • p: Price per loaf

Baker Cost Structures

• Angela:

  • Constant marginal cost of $4 per loaf.

• Bianca:

  • Constant marginal cost of $8 per loaf.

Problem 2 (a): Angela’s Reaction Function

1. Angela's Output Decision

   • Explore her optimal output as a function of Bianca's expected output.

Problem 2 (b): Bianca’s Reaction Function

1. Bianca's Output Decision

   • Explore her optimal output as a function of Angela's expected output.

Problem 2 (c): Cournot Equilibrium for Bakers

1. Outputs: Calculate QA and QB at equilibrium.

2. Price of Bread: Derive based on outputs from the demand curve and sum of outputs.

Problem 2 (e): Stackelberg Equilibrium

1. Angela Bakes First: Analyze the outcomes based on observed decisions by Bianca.

2. Outputs for Each Baker: Given the sequential nature of decisions.

3. Market Price of Bread: Derive from the equilibrium outputs.

Problem 2 (g): Impact of Timing on Bianca

1. Evaluation of Effects: Consider whether Bianca is positively or negatively impacted by Angela’s decision to bake first.

2. Expected Reaction: Hypothesize potential strategic responses by Bianca based on changes in the competitive landscape.

Conclusion

• Key Takeaways: Understand the different strategic behaviors in oligopolistic markets such as Cournot, Stackelberg, and Bertrand competition and their impact on pricing and output decisions.