Suppose the firm’s labor demand curve is given by w = 20 - 0.01 E where w is the hourly wage and E is the level of employment. Suppose also that theunion’s utility function is given by U = w * E It is easy to show that the marginal utility of the wage for the union is E and themarginal utility of employment is w. What wage would a monopoly union demand?How many workers will be employed under the union contract?

1,000 workers, each at $10 per hour.

Explanation:

w = 20 - 0.01E

The absolute value of the slope of the labor demand function is 0.01. Thus, utility maximization  requires that

= 0.01

Substituting for w with the labor demand function, the employment level that maximizes utility  solves

= 0.01

20 – 0.01E = 0.01E

20 = 0.02E

E = 1,000 workers

20 – 0.01(1000) = $10.

Hence, the monopoly union requires the firm to hire 1,000 workers, each at $10 per hour.

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