BUEC 280 LECTURE 12
Quasi-Fixed Labour Costs and Their Effect on
Labour Demand
Labour Costs
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
The firm’s wage bill is a variable cost – it is proportional to the number
of hours worked by employees
Some labour costs are quasi-fixed: they are not proportional to the
number of hours worked by the employee.
 These are per-worker costs, rather than per-hour
 They are usually non-wage labour costs


e.g. some social insurance programs (CPP, EI) with caps
These generate an employment/hours tradeoff
Three kinds of non-wage labour costs

1.
2.
3.
We can divide non-wage labour costs into three
broad categories:
Hiring costs
Training costs
Employee benefits
Hiring Costs
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Hiring a new worker isn’t free.
Some examples of the expenses associated with hiring a
worker:
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Advertising a vacant position
Screening applicants to evaluate their qualifications
 interviews, checking references, etc.
Processing successful applicants
 Adding new employee to payroll, orientation, etc.
Some of these are hard to measure
Training costs
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
Training can be formal or informal
At least three kinds of training costs
1.
2.
3.
Direct monetary cost of employing trainers and of materials
used in training
Opportunity cost of labour and capital used in informal
training
 e.g., getting an experienced employee to demonstrate tasks
to a new employee reduces the productivity of the
experienced worker
Opportunity cost of trainee’s time
 In training, employee is less productive than they would be if
producing full time
Employee benefits

1.
Two kinds:
Mandated benefits

2.
CPP, EI, vacation pay
Privately provided benefits

pension, health/dental insurance, stock options, stock
purchase plans etc.
The quasi-fixed nature of most non-wage
costs




Notice that all of these costs are per worker rather than per hour
worked
Since they do not vary at the margin with the number of hours that an
employee works, we say they are quasi-fixed
 Once an employee is hired, the firm is committed to paying these costs
no matter how many hours the new employee works
Some non-wage benefits are exceptions
 Defined contribution pension plans (employer contributes percentage of
employee’s earnings to private pension fund)
Some are complicated
 CPP/EI etc. (payroll taxes) are proportional to earnings up to a cap
amount, then they are fixed
MPL revisited

So far, we’ve been a bit vague about the units we use to measure labour, but
usually we’ve implicitly been talking about labour hours hired by the firm

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With quasi-fixed labour costs, we need to be more precise about what we
mean by “one unit of labour”
Let M denote the number of employees
Let H denote the average hours worked by each employee
Then we have two marginal products of labour:

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e.g. we defined MPL as the extra output produced by hiring “one more unit of
labour”
MPM is the extra output produced by hiring one more worker (holding K,H constant)
MPH is the extra output produced by increasing the average hours per worker
(holding K,M constant)
As with MPL, assume that both are positive but decreasing
MEL revisited
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
If we’re going to distinguish between the number employees and the
number of hours they work, we also need to consider the MEL
Now we have two marginal expenses of labour:
 MEM is the marginal expense of hiring one more worker (holding K,H
constant)


A function of quasi-fixed costs plus the variable costs (including wages)
associated with 1 more employee working H hours
MEH is the marginal expense of increasing average hours of work
(holding K,M constant)

Equals (per-hour wage + per-hour benefit costs) x M
The employment-hours tradeoff

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Employer has to choose both M and H
Choosing the optimal employment and hours allocation is just like
choosing between any two inputs
To minimize cost of producing any level of output Q, the firm must adjust
its employment level and average work week so that the cost of
producing an extra unit of output is equalized:
 MEM/MPM = MEH/MPH
So, if per-worker quasi-fixed costs (MEM) increase, then substitute more
H, less M
If per-hour variable costs (MEH) increase, then substitute more M, less H
Example: Overtime pay
Q: Why do some employers consistently require their
employees to work more than 40 hrs/week, even though
they need to pay an overtime premium?
A: Because it is profit maximizing.



They face quasi-fixed hiring/training costs which makes
increasing M (instead of H) costly.
Therefore, they increase hours of work up to the point that
MEM/MPM = MEH/MPH.
Even though they need to pay a premium wage, they avoid the
quasi-fixed hiring/training costs associated with hiring more
workers.
Another example
Q: Would increasing the overtime premium to 2 times the
hourly wage be an effective way to reduce
unemployment?
A: The firm’s profit-max condition is MEM/MPM =
MEH/MPH.
 Increasing the overtime premium increases MEH (if the
firm requires workers to work overtime).
 The firm will therefore substitute more M, less H.
 Is this the whole story? What happens to total hours
worked in the economy?
More effects of increasing the overtime
premium
1.
2.
Increases labour costs. We know the firm could have chosen more
employment & less hours before, but didn’t because it was more
expensive. If increasing the overtime premium changes the employment
and hours mix at the firm, it must increase average per-hour labour costs.
In the long run, they will substitute K for L (use less labour hours).
Scale effects. The firm could have chosen to use more K and less L before
the overtime premium increased, but they didn’t. Hence doing so must be
more costly for the firm (otherwise they would have done it before). This
increases per-unit production costs, so the firm reduces output (supply
shifts up), and uses less labour hours.
Even more effects of increasing the overtime
premium
3.
4.
Substitutability of employed and unemployed workers. These may
be poor substitutes: maybe overtime workers are skilled and
unemployed workers are unskilled. This will make it difficult for the
firm to substitute more M and less H.
Wage adjustment. Maybe workers and firms agree on a “package”
of weekly hours and total compensation. An increase in the overtime
premium might just lead to a reduction in the (base) hourly wage,
leaving weekly hours and earnings unchanged.
Firms’ Labour Investments and Labour Demand
We have:

Introduced quasi-fixed labour costs




Leads to an employment/hours tradeoff by the firm
Profit-max condition:


Per-worker costs, like hiring, training and benefits
Don’t vary at the hours margin
MEM/MPM = MEH/MPH
Next: introduce some dynamics into our analysis of
labour demand
The time dimension

So far, our discussion of labour demand has been static

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
But many quasi-fixed costs need to be considered in a dynamic context
That is, hiring and training costs have a time dimension



Firms evaluate current marginal product and marginal costs
Hiring costs are incurred when the worker is hired, but not later
Training costs are incurred in the early part of an employment relationship, but have
benefits later (they increase future productivity)
We can think of these as investments that the firm makes in its labour force

Once the investment has been made, it is cheaper for the firm to continue using
current workers than it is to hire new ones at the same wage, because the trained
workers are more productive
A two-period model of training
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Imagine a firm that is choosing its
employment level over a two-period
MPL
horizon
To keep things simple, we’ll focus on
training and ignore any other quasifixed costs
Assume the firm operates in competitive
input and output markets
Period 0: training takes place, and MPL
= MP0
Period 1: training is complete, and MPL
= MP1
With no training, MPL = MP*
MP0 < MP* < MP1
MP1
MP*
MP0
L
Training costs and benefits
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Suppose the real cost (in units of the firm’s output) of training one
worker is Z
Assume the real wage (in units of the firm’s output) paid during training
is W0, after training it is W1
How is the employment level determined?
As always, the firm is a profit maximizer. It equates marginal benefits
with marginal costs.
Now, the costs and benefits are spread over two periods, and hence it
needs to compute the present value of the costs and benefits
If the interest rate is r, the present value of B dollars next period is
B0 = B/(1+r)
Present values and profit max
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The present value of the marginal product of a worker who gets trained is
PVMPL = MP0 + MP1/(1+r)
The present value of the marginal expense of a worker who gets trained is
PVMEL = W0 + Z + W1/(1+r)
The profit max condition is
PVMPL = PVMEL or,
MP0 + MP1/(1+r) = W0 + Z + W1/(1+r)
As always, this defines the optimal employment level: hire up to the point that
the profit max condition is satisfied
What’s new here is that current marginal product and expense need not be
equal! That is, it could be that
MP0 < W0 + Z
and
MP1/(1+r) > W1/(1+r)
Recouping investment costs
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Suppose that MP0 < W0 + Z so that the real marginal expense of employment
in the training period is greater than the worker’s marginal product
Then the firm needs to recoup their investment costs in period 1
That is, they need MP1/(1+r) > W1/(1+r) to “break even” on the training
We can rewrite the profit max condition as
W0 + Z - MP0 = (MP1 – W1)/(1+r)
(net expense of training = PV of net benefit)
Notice what we need in order for this to be true. If
MP0 < W0 + Z
(current cost of training exceeds current benefit)
then we need
MP1 > W1
that is, the trained worker must be paid less than their marginal product!!
How are wages determined in this model?
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We assumed the firm hires in a perfectly competitive labour market
Suppose the equilibrium wage is W*
Can the firm choose W0 and W1 to be different than W*?
Yes, if the firm and worker can sign a two-period wage contract
Just need the present value of the wage contract to equal the present
value of working two periods at the market wage:
W0 + W1/(1+r) = W* + W*/(1+r)
the worker is indifferent between these two income streams (assuming
they can borrow & save!)
General vs. Specific Training
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
Usually, we think there are two kinds of training
General training increases an individual’s productivity in many firms


Specific training raises productivity only in the firm offering the
training


General computer skills; learning to use a machine that is common to
many production processes, etc.
Proprietary software; learning to use a machine that is only used by this
firm
This is mostly a conceptual distinction because most training has both
general and specific aspects
Who should pay for general training?

In our two-period model, suppose the training is general


We saw that if MP0 < W0 + Z, the firm pays W1 < MP1 in the second period.
Can they do this?


The worker is worth MP1 to other firms, thus they can earn
W = MP1 at some other firm who didn’t incur the training cost
To keep the worker from quitting, they need to pay
W1 = MP1 after training unless they have some other way of making the
worker stay



After training, the worker’s marginal product is MP1 in any firm
Usually can’t sign contracts that prevent the worker from quitting (we have laws
against indentured servitude)
The firm might offer a credential to the worker if they stay until the end of the
second period (apprenticeships)
If they have to pay W1 = MP1 in the second period, then the firm will not pay
for general training, or they will reduce W0 until MP0 = W0 + Z (which is the
same as not paying – the worker bears the full cost of the training)
What if the training is specific?
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

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Then our original story is unchanged.
Why? Because the worker’s marginal product remains MP* < MP1 at
other firms. Hence the firm can pay W1 such that W* < W1 < MP1
The firm incurs some of the training costs
(W0 + Z > MP0)
Note the firm has two things to decide here: how much training to
invest in, and how to structure the wage profile
Defined by three conditions:
1. PVMPL = PVMEL
(profit max)
2. W0 + W1/(1+r) = W* + W*/(1+r)
(worker accepts)
3. W* < W1 < M
(firm recoups investment, worker stays)
The two period wage stream graphically
MP1
W1
W*=MP*
W0
MP0
Period 0
Period 1
Implications of the theory


This type of model has been suggested as one reason we see wages increase with job
tenure
Notice that both employees and employers have investments to protect:



Thus we might think that an “implicit contract” could be binding


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
Employers incur costs W0 + Z > MP0 in the first period, and need to recoup this investment in the
second period
Employees accept W0 < W* in the first period in anticipation of earning W1 > W*
An implicit contract is an informal agreement between the worker and firm
Here, the worker agrees to accept a low wage initially in return for a higher wage later (and
not getting laid off). The firm agrees to pay a higher wage later if the worker doesn’t quit.
Notice that W1 < MP1 provides the worker with some insurance against layoff in a
recession: the worker is worth more to the firm than he/she gets paid. Likewise, the firm
doesn’t want to lose their investment in the worker.
Remember labor hoarding during recessions?