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Suppose that there are three firms, firm 1, firm 2 and firm 3, producing differentiated widgets. The demand curves facing each firm are symmetric and are given by the following equation:
Qi = 250 -20Pi +5Pj + 5Pk.
Each firm has a marginal cost equal to 25. The profit function of firm i is given by:
Πi = (Pi - 25)(250 - 20Pi +5Pi + 5Pk), (i, j,k)=(1,2,3)
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