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Managerial and Business Economics (12quiz Quiz 6: Capacity constrained industries

Numerical

Alpha Inc. and Beta Corp. compete in the market for smallgoods (processed meats). The smallgoods produced by the two firms are homogeneous, and the firms compete in Cournot (quantity) competition. Inverse demand in the market for smallgoods is given by the function, 𝑃 = 100 − 𝑄 𝐴 24 − 𝑄 𝐵 24 , where 𝑄 𝐴 is the quantity of smallgoods produced by Alpha, and 𝑄 𝐵 is the quantity of smallgoods produced by Beta. Alpha Inc.'s marginal cost is 𝑀 𝐶 𝐴 = $ 20 , and Beta Corp.'s marginal cost is 𝑀 𝐶 𝐵 = $ 10 . How many kilograms of smallgoods does Beta produce in a Cournot equilibrium in which both firms compete? Hint: Keep a record of your answer for use in later questions.

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We start by expressing the market demand and profits for each firm in Cournot competition. The inverse demand is P = 100 - (Q_A)/24 - (Q_B)/24, where Q_A and Q_B are Alpha and Beta outputs respectively. Alpha’s marginal cost is 20 and Beta’s is 10, so their per-unit profits depend on price minus these costs, multiplied by their quantities. Fo......Login to view full explanation

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