Economics 151a
Spring 2008
Homework 3 – Solutions
111. 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 the union’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 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
.
The absolute value of the slope of the labor demand function is 0.01. Thus, utility maximization
requires that
.
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.
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112. 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 $8 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?
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 Spring '06
 Miller
 Economics, Supply And Demand, Utility, $3, $4

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