Suppose that the only two firms in an industry face the market (inverse) demand

Question

Suppose that the only two firms in an industry face the market (inverse) demand curve p=160-Q. Each has constant marginal cost equal to 16 and no fixed costs. Initially the two firms compete as Cournot rivals (Chapter 11) and each produces an output of 48. Why might these firms want to merge to form a monopoly? What reason would antitrust authonities have for opposing the merger? (Hint Calculate price, profits, and total surplus before and after the merger) The firms would favor the merger because combined prot would increase by sand the profl-maximizing price would increase by s(Enter your response rounded to two decimal places) Text t Shar

Explanation / Answer

Initially, two firms compete as cournot rivals and each produce an output of 48 units.

So, total market output is (48+48) 96 units.

Profit-maximizing price, P = 160 - Q = 160 - 96 = $64

Combined profit = (P*Q) - (MC*Q) = (64*96) - (16*96) = $6,144 - $1,536 = $4,608

The profit-maximzing price in case of Cournot outcome is $64 per unit.

The combined profit in case of cournot outcome is $4,608.

Now, firms merge and becomes a monopolist.

Demand curve is as follows -

P = 160 - Q

TR = P * Q = (160 - Q) * Q = 160Q - Q2

MR = dTR/dQ = d(160Q - Q2)/dQ = 160 - 2Q

A monopolist maximizes profit when it produce that level of output corresponding to which MR equals MC

MR = MC

160 - 2Q = 16

2Q = 144

Q = 72

P = 160 - Q = 160 - 72 = $88 per unit

Profit = (P*Q) - (MC*Q) = ($88 * 72) - ($16 * 72) = $6,336 - $1,152 = $5,184

In case of monopoly,

The profit-maximizing price is $88 per unit.

The combined profit is $5,184.

So,

The firms would favor the merger because combined profit would increase by $576 and the profit-maximizing price would increase by $24.

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