In some markets plumbers have a choice of joining unions or working as

In some markets plumbers have a choice of joining unions or working as nonunion plumbers. The total short-run supply of plumbers is perfectly inelastic at 500 workers per day.

The demands for nonunionized and unionized plumbers, respectively, are:
WNU = 30 – 0.04L WU = 30 – 0.10L.
The wage rate is W in $/hr. and the number of workers per day is L.

a. Determine the total demand for plumbers.
b. Calculate the total market wage rate of plumbers assuming that unionized and nonunionized plumbers get the same wage rate.
c. If the unionized workers succeeded in getting their wage increased to $20.00 per hour, how many unionized workers would lose their jobs?
d. If the unionized workers in (c) who lost their jobs take jobs as non-unionized workers, how much and in what direction would non-unionized wages change?

ANSWER

a.
The total demand for workers is the horizontal summation of the unionized and non-unionized demands. We rearrange the demands to get L in terms of wage.
The demand for non-unionized plumbers is now expressed as
LNU = 750 – 25W, and
the demand for unionized plumbers is now expressed as
LU = 300 – 10W
The sum of the two demands yields total demand.
L = 1,050 – 35W
or in terms of L: W = 30 – 0.0286L

b.
The market wage rate is
1,050 – 35W = 500
W = $15.71/hour

c.
At the higher wage of $20.00 per hour, LU = 300 – 10(20 ) = 100 per day. This is down from LU = 300 – 10(15.71 ) = 143 per day. A total of 43 workers would lose their unionized jobs.

d.
If the 43 workers take non-unionized jobs, the non-union wage rate would fall. The total non-unionized workers was
L = 750 – 25(15.71 ) = 357.25 or 357
Now, the total number of non-unionized workers becomes
L = 357 + 43
At 400 workers, the new non-unionized wage is
WNU = 30 – 0.04(400 ) = $14.00/hour