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Problem 3: Cournot CompetitionSuppose we have a duopoly market with two firms. Suppose first that firms 1 and 2 produce perfectly homogeneous products, in the sense that they sell their output at a price that depends only on the total amount produced in the market and not on who does the producing. Hence, the firms solve the following optimization problems:max x₁₂ = max (100 - 3x - 3x₂)x₁ - 10x₁max x₂₁ = max (100 - 3x - 3x₁ - 10x₂)x₁a) Find the equilibrium quantities of outpu
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SOLVED: Consider a duopoly that will last two more years in which each firm is currently suffering losses of c dollars per period. If one of the firms were to drop out, then the remaining firm would make a monopoly profit of T dollars per period for the remainder of the two years. Each firm can choose when to drop out: today (date 0), or a year from now (date 1), or it can stay till the end (date 2). Each firm only cares about profits. The payoff matrix is:| | Date 0 | Date 1 | Date 2 ||
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