Consider a market containing four firms, each of which produces an identical product. The inverse demand for this product is p = 100 ? Q. The production cost for each firm is identical and given by C(qi) = 20qi , i = 1, 2, 3, 4. This means that for each of these firms, marginal costs are constant at $20 per unit.
a. Identify the Cournot-Nash equilibrium output for each firm, the product price, and the profit to each firm.
b. Suppose that firms 1 and 2 merge and that all firms continue to act as Cournot competitors after the merger. Show that this merger is bad for consumers.
c. Confirm that the merger between firms 1 and 2 is unprofitable.