Firm 1 and firm 2 compete with each other by setting the price. For each firm i, its demand depends on its own price pi and the price of its opponent p−i . The demand function can be written as qi = 20 − pi + 1 2 p−i . The marginal cost is constant at $4 for both firms. There is no fixed cost. Firm 1 and firm 2 set their prices every year. In each year, there is probability 1 − δ that this market dies and their relationship ends. Assume no discounting. Answer the following questions. 1. Suppose δ = 0 (this is a one-shot simutaneous game), compute the equilibrium prices, quantities and profits for both firms. 2. Suppose δ = 0. If the two firms work together and collusively choose a price pC to maximize the joint profit, what is pC? 3. Consider the collusion where they both set the price as pC and split the joint profit evenly. For what values of δ will their collusion be sustainable by using a “Grim Trigger” strategy? 4. For what values of δ will their collusion be sustainable by using a “prefect Tit-for-Tat” strategy?
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Firm 1 and firm 2 compete with each other by setting the price. For each firm i, its demand depends on its own price pi and the price of its opponent p−i . The demand function can be written as qi = 20 − pi + 1 2 p−i . The marginal cost is constant at $4 for both firms. There is no fixed cost. Firm 1 and firm 2 set their prices every year. In each year, there is probability 1 − δ that this market dies and their relationship ends. Assume no discounting. Answer the following questions.
1. Suppose δ = 0 (this is a one-shot simutaneous game), compute the equilibrium prices, quantities and profits for both firms.
2. Suppose δ = 0. If the two firms work together and collusively choose a price pC to maximize the joint profit, what is pC?
3. Consider the collusion where they both set the price as pC and split the joint profit evenly. For what values of δ will their collusion be sustainable by using a “Grim Trigger” strategy?
4. For what values of δ will their collusion be sustainable by using a “prefect Tit-for-Tat” strategy?
