In Q&A 13.4, suppose that A = 12 but that profits under the current wage and high output are 14 for Firm 1 and 11 for Firm 2. Which wage would Firm 1 choose?

Q&A 13.4

In a duopoly market, to produce a given amount of output, Firm 1 uses relatively more capital but less labor than does Firm 2. Both firms hire labor from the same labor union, which sets the same wage for both firms. Firm 1 is about to bargain with the union. Whatever wage it negotiates, Firm 2 has to pay the same wage. Because this industry is suffering from a downturn in demand, the union is willing to accept the current (lower) wage. However, if Firm 1 agrees to a higher wage, its cost of production will rise by less than Firm 2’s cost. The game tree shows the profits corresponding to the various actions by the firms. Firm 1’s profit is A if it chooses the high wage and Firm 2 chooses the low output level. Under what condition should Firm 1 offer to pay a high wage?

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Firm 1 Firm 2 Profits Negotiates Sets Output High output (8, 4) High wage Firm 2 Low output (A, 5) Firm 1 High output (10, 10) Current wage Firm 2 Low output (12, 7)