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Suppose two firms compete simultaneously in quantities and face an inverse aggregate demand of P(Q)-100-2Q. Firm i has constant marginal costs equal to 12, while Firm 2 has constant marginal costs equal to 20 You are asked to solve for the Cournot equilibrium in two different ways. The long way: Calculate the firms payoffs for all possible quantity choices qi 10,11,12,13,14,15,16), i - [1,2). Display the pairs of profits in a payoff matrix (similar to Slide 5 from the file lb_stackelberg_equilibrium_evidence. (3 points) a. b. Use the payoff matrix to indicate each firms best-response function. That is, for each quantity of the rival firm, circle the firms optimal quantity. (2 points) What are the pair of equilibrium quantities and corresponding profits? (1 point) c. The short way: d. Solve algebraically for the equilibrium quantities, the equilibrium market price and each firms profit.(3 points

And how to calculate the numbers in matrix, please show the calculations step by step.

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