Problem 4 Consider a market for a homogenous product with n identical firms that compete by...

Problem 4 Consider a market for a homogenous product with n identical firms that compete by setting quantities. The cost function of each firm is 8 per unit. The inverse demand function for the product is P = S/Q, where Q is the aggregate quantity and S is a positive parameter.

(a) Compute the symmetric Nash equilibrium in the market and the equilibrium profit of each firm.

(b) Suppose that one firm can break itself into two independent divisions that choose their output levels independently (this is like GM which has several divisions: Chevrolet, Buick, Cadillac, and GMC which are independent and compete against each other). That is, now there are effectively n+1 "firms" in the industry, though one of them consists of two separate divisions and hence earns twice the profit of all rival firms. Compute the new symmetric Nash equilibrium. What is the equilibrium profit of each firm now?

(c) How large should n be so that it will pay a firm to create 2 independent divisions? What is the intuition for your answer?

(d) Now suppose that starting from the equilibrium you computed in (a), 2 firms would like to merge and become one firm (this firm still has a cost of 8 per unit). What should n be such that the merger will be profitable? (Hint: to be profitable the merger should allow the merged firm to earn more than the combined profits of the two merging firms before the merger takes place).

Expert Solution

Rahul Sunny answered 1 year ago

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