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Econ203 Intermediate Microeconomics 2022-23

Quiz 6

Each member chooses ONE of five essay questions. Submit answers in groups. The steps of calculation must be shown clearly. Write down your name and student number in each question.

1. Two firms (Firm 1 and Firm 2) selling a homogenous good face the market demand curve P = 400 – 2Q, where Q = Q₁ + Q₂, P = the market price, Q = total output from Firm 1 (Q₁) and Firm 2 (Q₂). The cost functions are given by C₁(Q₁) = 20 + 12Q₁ and C₂(Q₂) = 10 + 15Q₂. 

(A) Find the Cournot equilibrium, and profit for each firm.  (10 marks)

(B) If Firm 1 chooses output first, find the Stackelberg equilibrium and profit for each firm. (10 marks)

2. Two firms (Firm 1 and Firm 2) selling a homogenous good face the market demand curve P = 300 – 3Q, where Q = Q₁ + Q₂, P = the market price, Q = total output from Firm 1 (Q₁) and Firm 2 (Q₂). The cost functions are given by C₁(Q₁) = 30 + 20Q₁ and C₂(Q₂) = 40 + 10Q₂. 

(A) Find the Cournot equilibrium, and profit for each firm.  (10 marks)

(B) If Firm 1 chooses output first, find the Stackelberg equilibrium and profit for each firm. (10 marks)

3. Two firms (Firm 1 and Firm 2) selling a homogenous good have the cost functions given by C₁ = 20 Q₁ and C₂ = 30 Q₂, where Q₁ and Q₂ are outputs produced by Firm 1 and Firm 2 respectively. They face the market demand curve P = 200 – Q where Q = Q₁ + Q₂, P = the market price.

(C) Find the Cournot equilibrium, and profit for each firm.  (10 marks)

(D) If Firm 1 chooses output first, find the Stackelberg equilibrium and profit for each firm. (10 marks)

4. Two firms (Firm 1 and Firm 2) selling a homogenous good have the same constant average and marginal cost, AC = MC = $55. They face the market demand curve P = 452 – Q where Q = Q₁ + Q₂, P = the market price.

(A) Find the Cournot equilibrium, and profit for each firm.  (10 marks)

(B) If Firm 1 chooses output first, find the Stackelberg equilibrium and profit for each firm. (10 marks)