Initially there are six firms producing differentiated products. The demand function for the good produced by firm i, i=1,2..,6, is given by qi = 10-2pi+0.3 summation pj where the sum is taken over the five prices other than firm i. Each firm has the same marginal cost c. The firms choose prices simultaneously; that is, they are differentiated products Bertrand competitors. (a) Solve for the symmetric Nash equilibrium prices. (b) Suppose that you observe each firm to set a price of 4.8. What must c be? (c) Suppose that two of the six firms merge to become a single firm. The firm continues to produce both goods. Using the marginal cost you found in (b), derive the new post-merger Nash equilibrium prices.
Initially there are six firms producing differentiated products. The
where the sum is taken over the five prices other than firm i. Each firm has the same marginal cost c. The firms choose prices simultaneously; that is, they are differentiated products Bertrand competitors.
(a) Solve for the symmetric Nash
(b) Suppose that you observe each firm to set a
(c) Suppose that two of the six firms merge to become a single firm. The firm continues to produce both goods. Using the marginal cost you found in (b), derive the new post-merger Nash equilibrium prices.
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