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Suppose that there are three firms firm 1 firm 2 and firm 3

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:

Q_i = 250 -20P_i +5P_j + 5P_k.

Each firm has a marginal cost equal to 25. The profit function of firm i is given by:

Π_i = (P_i - 25)(250 - 20P_i +5P_i + 5P_k), (i, j,k)=(1,2,3)

Solve for the Nash equilibrium prices.
Suppose that firms 1 and 2 decide to merge.
If there are no cognizable efficiencies, calculate the UPPI for an increase in P₁.
Suppose that the merger makes possible a reduction in marginal cost of 10 percent with products 1 and 2 post merger. Calculate the UPPI for an increase in P₁.
Calculate the equilibrium prices after the merger, assuming 10 percent cognizable efficiencies for products 1 and 2.

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Business Management: Suppose that there are three firms firm 1 firm 2 and firm 3

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