Tutorial 12: Non-competitive Labor Markets
Factor Markets with Wage-setting Power
In the last Tutorial we developed a model of the labor
market where firms hiring labor have no market power, i.e.,
they take the market-set wage rate as given. In Tutorial
12 we explore how that model is changed when individual
firms have enough market power to set the wage they pay
below the competitive equilibrium.
First an important reminder. In Tutorials 11 and 12 the
firm plays a new role as a buyer of inputs.
It is important that you keep this new role in mind.
Failure to to keep the firm's roles in mind can make it
easy to confuse models of input markets with models of product
markets.
Here are the assumptions made to keep this model
simple.
- The firm produces a product using only capital, K, and
labor, L.
- The amount of capital available is fixed (i.e., the
firm is producing in the short run).
- This firm is the only firm hiring labor in this area.
- All the workers hired by the firm have exactly the same
skill level.
Our single employer, called a monopsony, faces the
entire market supply of skilled labor. As a result, our
firm must offer higher wages if it wants to attract more
workers. [Remember, the quantity of labor supplied in the
market varies directly with wages -- people generally work
more at higher wages.] When it does raise wages, it will
do so for all its employees, not just the new ones.
[If this sounds far fetched, remember, if a firm does not
cover the opportunity costs of its workers, it will lose
those workers to better paying jobs...] Facing an upward
sloping labor market supply curve has significant implications
for the firm's marginal expenditures on labor.
Let's say the firm hires its first worker at $10 per hour.
If it wants to hire another worker, it will have to raise
wages to $12 per hour. The marginal expenditure,
ME, on the second worker includes the $12 per hour wage
plus an additional $2 per hour for the first worker.
So ME = $14, which exceeds the wage rate paid the second
worker. Continuing with this example, suppose a third worker
will accept no less than $14 per hour. The ME on this third
worker is $14 + $2 + $2 = $18. If you continue in the same
fashion you will discover that the rate of increase in ME
is twice as high as the rate of increase in wages.
Graphically, a model of a wage-setting firm is different
from that of a wage-taking firm in this one respect. Figure
1 illustrates this difference. The wage-setting firm faces
an upward sloping labor supply curve, S1, and a marginal
expenditure curve, ME1, that is also upward sloping,
but which rises twice as fast as supply.
Figure 1
The Input
Purchasing Decision of the Firm 
A profit-maximizing firm will hire labor
until the marginal benefit of the last worker hired equals
the marginal cost of employing her. That marginal cost,
referred to as marginal expenditure, ME1,
varies directly with the quantity of labor hired. The marginal
benefit to the firm of hiring each additional worker is
measured by how much revenue the output of that worker adds
to the total, which is called marginal revenue product (MRP1).
The intersection of MRP1 and ME1 determines the profit maximizing
level of labor for this firm to hire. In this case the firm
will hire L* = 20,000 labor days per period. The
last worker hired adds just as much to revenue as to cost,
but all previous workers added more to revenue than to cost
-- the difference going to the firm as additional profit.
Notice that there has been no mention of
how much the firm will pay these workers. That's because,
after the profit-maximizing level of hiring is determined,
the firm will know what the lowest wage that must be offered
to attract all L* workers. That "minimum willingness
to accept" is found on the labor supply curve, S1.
(Need a review
of reservation prices?) So at L*, draw a vertical line up
from the x-axis until it hits S1, then continue that line
horizontally until it intersects the vertical axis. Doing
so reveals that the firm need only offer a wage rate of
W* = $100 per day to fill their need for 20000 worker
days per period.
Wage-setting
Power
In Tutorial 10
we discovered that, for a price-setting firm in a product
market, MR = P + P·(1/Ed).
By a similar mathemagical derivation we can show that, for
a monopsony, ME = w + w·(1/Es).
[Ed and Es are used here to represent
price elasticity of demand and supply respectively.]
At the profit-maximizing level of hiring, ME = MRP, i.e.,
w + w·(1/Es)
= MRP.
Rearranging terms;
(MRP - w)/w
= 1/Es
with monopsony power, w < MRP (remember, w is determined
by the labor market supply, it is the lowest wage the last
hired worker is willing to accept). The difference between
MRP and w measures the "markdown" in wages (as a percent
of the wage rate). That is, how much below what a worker
is worth (as shown by MRP) a wage-setting firm can pay.
It is a tribute to the firm's wage-setting power... a sort
of Lerner's index of labor market power.
The size of the markdown is inversely related to Es;
- the more elastic labor supply, the smaller the
wage-setting power of the firm.
- the more inelastic S, the larger the wage-setting
power of the firm.
| Now it's time to
"do the thing".
Click on the following link
to download the Monopsony
Labor Market Workbook. Work through
Questions 1 - 7. This will let you improve
your understanding of how a wage-setting firm
chooses to hire inputs so as to maximize profit.
Return here when you have finished.
Need help
downloading the Excel file? |
|
In this Tutorial we explored a model of
the labor market where firms hiring labor have market
power, i.e., they set the wage rate below the marginal
revenue product of the workers. Inthe next part we explore
the social cost of having firms with wage-setting
power hire labor.
Continues...
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