11-1. Suppose the firms 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 the unions 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 the marginal utility of
employment is w. What wage would a monopoly union demand? How many workers will be
employed under the union contract?
Utility maximization requires the absolute value of the slope of the indifference curve equal the absolute
value of the slope of the labor demand curve. For the indifference curve, we have that
MU E = w .
MU w E
The absolute value of the slope of the labor demand function is 0.01. Thus, utility maximization requires
E = .01.
Substituting for E with the labor demand function, the wage that maximizes utility must solve
which implies that the union sets a wage of $10, at which price the firm hires 1,000 workers.
11-2. Suppose the union in problem 1 has a different utility function. In particular, its utility
function is given by:
U = (w - w) E
where w *is the competitive wage. The marginal utility of a wage increase is still E, but the marginal
utility of employment is now w w . Suppose the competitive wage is $10 per hour. What wage
would a monopoly union demand? How many workers will be employed under the union contract?
Contrast your answers to those in problem 1. Can you explain why they are different?
76 Again equate the absolute value of the slope of the indifference curve to the absolute value of the slope of
the labor demand curve:
MU E = w w = 0.01 .
Setting w* = $10 and using the labor demand equation yields:
2,000 00 w
Thus, the union demands a wage of $15, at which price the firm hires 500 workers.
In problem 1, the union maximized the total wage bill. In problem 2 the utility function depends on the
difference between the union wage and the competitive wage. That is, the union maximizes its rent. Since
the alternative employment pays $10, the union is willing to suffer a cut in employment in order to obtain
a greater rent.
11-3. Using the model of monopoly unionism, present examples of economic or political activities
that the union can pursue to manipulate the firms elasticity of labor demand. Relate your
examples to Marshalls rules of derived demand.
Marshalls rules state that the elasticity of labor demand is lower the
1. lower is the elasticity of substitution;
2. lower is the elasticity of demand for the output;
3. lower is labors share of total costs; and
4. lower is the supply elasticity of other factors of production.
Consider two examples: innovations and picket lines. Unions are notoriously bad at allowing firms to
introduce (labor saving) innovations in their factories. The long shoremen on the west coast recently
struck, because they were unwilling to let cargo crates be identified with bar codes. (The union wanted a
union worker to record all movements of crates with pencil and paper.) Thus, the union was pursuing a
policy of limiting the supply of other factors of production (rule 4). In a similar vein, when on strike,
unions picket the firm in order to decrease the ability of the firm to hire scabs (rule 1).
7711-4. Suppose the union only cares about the wage and not about the level of employment. Derive
the contract curve and discuss the implications of this contract curve.
The utility function U = U(w) implies that the unions indifference curves are horizontal lines, so that the
contract curve coincides exactly with the firms labor demand curve (D).
11-5. A bank has $5 million in capital that it can invest at a 5 percent annual interest rate. A group
of 50 workers comes to the bank wishing to borrow the $5 million. Each worker in the group has an
outside job available to him or her paying $50,000 per year. If the group of workers borrows the $5
million from the bank, however, they can set up a business (in place of working their outside jobs)
that returns $3 million in addition to maintaining the original investment.
(a) If the bank has all of the bargaining power (that is, the bank ca