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Problem: Consider the following duopoly with identical firms. Aggregate demand is given by P=20-Q and both firms have MC=8. Label the firms 1 and 2. Use the Cournot model to answer the following questions.
Question 1: Calculate the best response function (reaction curve) for firm 1?
Question 2: Calculate the best response function (reaction curve) for firm 2?
Question 3: Use the Cournot model to calculate the equilibrium quantity for firm 1 in this duopoly?
Question 4: Use the Cournot model to calculate the equilibrium price for firm 2 in this duopoly?
Question 5: Suppose that the firms in the Cournot question above do not choose quantity simultaneously. Instead, assume the Stackelberg model of oligopoly where firm 1 chooses its quantity first. Firm 2 then observes the choice of firm 1 and chooses its quantity. Redo parts a-c.
Question 6: Calculate producer surplus in the for each firm in the Cournot and Stackelberg Models. Which firm receives the larger producer surplus in the Stackelberg model? Is this amount greater than or less than the amount received int eh Cournot model?
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