Suppose that two identical firms produce widgets and that they are the only firm

Question

Suppose that two identical firms produce widgets and that they are the only firms in the market. Their costs are given by:

C1 = 60Q1 and C2 = 60Q2

When competing, each firm will produce 480 units of output. In turn, each firm will earn profit of $230,400. If the firms form a cartel to maximize joint profits, each firm will produce 360 units of output. In turn, each firm will earn profit of $259,200.

If firm 1 were the only firm in the industry, Firm 1 would produce 720 units of output. Firm 1 would earn a profit of $518,400.

If they return to the duopoly and Firm 1 abides by the agreement, but Firm 2 cheats by increasing production, Then Firm 2 would produce 540 units of output. As a consequence, Firm 1 would earn profit of $194,400.

What would be the profit of Firm 2? Firm 2's profit would be $___.

Explanation / Answer

Under cartel, both firms works together and produces the monopoly output which is evident from the figures provided in the question

When both firms forms the cartel then the joint production = Q1 + Q2 = 360 + 360 = 720 and joint profit = 259200 + 259200 = 518400. These are the same numbers as if firm 1 behaves like a monopolist.

Now when both firms enterns into the cartel then maximum production would be 720 and maximum profit = 518400 and when firm 2 cheats and produces 540 units. The total profit of firm 1 reduces to 194400 (i.e. 3/4 of the cartel profit). Therefore it will produce 3/4 of the cartel production (i.e. 3/4 * 360 = 270). Thus rest of the 90 units (360 - 270) will be produced by firm 1 and earns a profit as per cartel

Hence firm 2's profit on 90 unit (as per cartel profit) = 90/360 * 259200 = 64800 ........... (1)

And on the rest of the production (i.e. 540 - 90 = 450) firm 2 will earn a profit as per competing profit = 450/480 * 230400 = 216000 ............ (2)

Thus total profit of firm 2 [Adding (1) and (2)] = 216000 + 64800 = 280800

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