Consider a market with an inverse demand Function p = 60-4*Q. There are two firms, an incumbent and an entrant. There is a constant variable cost of 6 and a unit capacity cost of 6. In the first stage, the incumbent chooses capacity. In the second stage, the entrant decides whether or not to enter and all active firms choose quantities (where the entrant also has to simultaneously choose its capacity in the second stage, if it enters). a. For a capacity of 5 units, what is the best response function of the incumbent in the second period? b. What is the Cournot-Nash equilibrium of the second stage if the incumbent chose a capacity of 5 units in the first stage conditional on the entrant entering? c. For a capacity of an arbitrary k units, what is the best response function of the incumbent? d. What is the Cournot-Nash equilibrium of the second stage if the incumbent chose a capacity of k units in the first stage conditional on the entrant entering? e. Solve for the subgame perfect equilibrium of the game when the entry costs are 25. f. Solve for the subgame perfect equilibrium of the game when the entry costs are 64.
Consider a market with an inverse demand Function p = 60-4*Q. There are two firms, an incumbent and an entrant. There is a constant variable cost of 6 and a unit capacity cost of 6. In the first stage, the incumbent chooses capacity. In the second stage, the entrant decides whether or not to enter and all active firms choose quantities (where the entrant also has to simultaneously choose its capacity in the second stage, if it enters). a. For a capacity of 5 units, what is the best response function of the incumbent in the second period? b. What is the Cournot-Nash equilibrium of the second stage if the incumbent chose a capacity of 5 units in the first stage conditional on the entrant entering? c. For a capacity of an arbitrary k units, what is the best response function of the incumbent? d. What is the Cournot-Nash equilibrium of the second stage if the incumbent chose a capacity of k units in the first stage conditional on the entrant entering? e. Solve for the subgame perfect equilibrium of the game when the entry costs are 25. f. Solve for the subgame perfect equilibrium of the game when the entry costs are 64.
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.3P
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Step 1: Define game theory
VIEWStep 2: a. Calculate Best Response Function for Incumbent (capacity = 5 units):
VIEWStep 3: b. Calculate Cournot-Nash Equilibrium (capacity = 5 units):
VIEWStep 4: c. Calculate Best Response Function for Incumbent (capacity = k units):
VIEWStep 5: d. Calculate Cournot-Nash Equilibrium (capacity = k units):
VIEWStep 6: e. Calculate Subgame Perfect Equilibrium (entry costs = 25):
VIEWStep 7: f. Calculate Subgame Perfect Equilibrium (entry costs = 64):
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