ECON 2350 Lecture Notes - Lecture 2: Marginal Revenue, Marginal Cost, Demand Curve

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We saw earlier that the optimality condition for the cartel solution is. The marginal profits accruing to firm 1 will be . Suppose, for example that the two firms are operating at the outputs that maximize industry profits (y 1, y 2) and firm 1 considers producing a little more output, y1. 1 y1 = p(y 1 + y 2) + p y y 1 mc1(y 1). P(y 1 + y 2) + p y y 1 + p y y 2 mc1(y 1) = 0. P(y 1 + y 2) + p y y 1 mc1(y 1) = p y y 2 > 0. The last inequality follows since p/ y is negative, since the market demand curve has a negative slope. Inspecting equations we see that 1 y1 > 0. Thus, if firm 1 believes that firm 2 will keep its output fixed, then it will believe that it can increase profits by increasing its own production.

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