Homework answers / question archive / ECON203 MICROECONOMIC ANALYSIS, S1 2013 TUTORIAL 10 (Week 13) Week beginning 3 June 2013) 1)What do the Cournot and Bertrand models have in common? What is the difference between the two models? Explain why in the Stackelberg model, the firm that sets output first has an advantage

ECON203 MICROECONOMIC ANALYSIS, S1 2013 TUTORIAL 10 (Week 13) Week beginning 3 June 2013) 1)What do the Cournot and Bertrand models have in common? What is the difference between the two models? Explain why in the Stackelberg model, the firm that sets output first has an advantage

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ECON203 MICROECONOMIC ANALYSIS, S1 2013

TUTORIAL 10 (Week 13)

Week beginning 3 June 2013)

1)What do the Cournot and Bertrand models have in common? What is the difference between the two models? Explain why in the Stackelberg model, the firm that sets output first has an advantage.  

 

2. Consider an industry including two firms only. They compete by choosing price and their demand functions are

   Q₁ = 20 – P₁ + P₂         and          Q₂ = 20 + P₁ – P₂ where P₁ and P₂ are the prices charged by each firm, respectively, and Q₁ and Q₂ are the resulting demands. Their costs are given by C₁ = 20Q₁ and C₂ = 20Q₂.

1. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be?

 

 

 

2. Suppose Firm 2 sets its price first and then Firm 1 sets its price. What price will each firm charge, how much will it sell, and what will its profit be?

 

 

3. Demonstrate the prices chosen by each firm in part a) and b) on a graph.

 

 

 

4. Based on the results in part a) and b), which strategy would the firm prefer? Explain. 

 

3. Suppose that two identical firms produce widgets and that they are the only firms in the market. Their costs are given by C₁ = 60Q₁ and C₂ = 60Q₂, where Q₁ is the output of Firm 1 and Q₂ the output of Firm 2.  Price is determined by the following demand curve:

            P = 300 – Q     where Q = Q₁ + Q₂.

a. Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium.

b. Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm’s profit.