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Suppose two firms compete in micro-chip industry. Each period firm 1 produces q1 chips and firm two produces q2 chips and the firms face a
Suppose two firms compete in micro-chip industry. Each period firm 1 produces q1 chips and firm two produces q2 chips and the firms face a demand curve of P =100020Q, where Q=q1+q2. Both firms have a constant marginal cost of $40 per chip, C(qj)=40qi. Making the following change. Suppose the same industry exists for an infinite number of periods, the discount factor for profits is still =0.9. Firms are considering the following strategy: - As long as no firm has cheated, play according to the agreement to optimize joint profits and split the proceeds. - If either firm has cheated in any earlier period, play the static Nash equilibrium in every period from now on. 1. If both firms follow the proposed strategy, what is the present discounted value of each firm's profits? 2. If one firm decides it will cheat on the agreement and violate the strategy, what is the highest profit that firm can achieve? 3. Based on your previous answers in this question, is the proposed strategy an equi- librium? Why or why not? 4. What is the lowest discount factor, that the firms could have for the proposed strategy to be an equilibrium? Suppose two firms compete in micro-chip industry. Each period firm 1 produces q1 chips and firm two produces q2 chips and the firms face a demand curve of P =100020Q, where Q=q1+q2. Both firms have a constant marginal cost of $40 per chip, C(qj)=40qi. Making the following change. Suppose the same industry exists for an infinite number of periods, the discount factor for profits is still =0.9. Firms are considering the following strategy: - As long as no firm has cheated, play according to the agreement to optimize joint profits and split the proceeds. - If either firm has cheated in any earlier period, play the static Nash equilibrium in every period from now on. 1. If both firms follow the proposed strategy, what is the present discounted value of each firm's profits? 2. If one firm decides it will cheat on the agreement and violate the strategy, what is the highest profit that firm can achieve? 3. Based on your previous answers in this question, is the proposed strategy an equi- librium? Why or why not? 4. What is the lowest discount factor, that the firms could have for the proposed strategy to be an equilibrium
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