Quasi-Fixed Costs and Labor
Demand
Quasi-Fixed Costs
• Costs that are not strictly proportional to the hours
of work and allocated on a per worker basis
• Non-wage labor costs such as required insurance
programs and employee benefits are important
components of labor costs.
• Quasi-fixed costs affect demand for labor but also
the nature of that demand, such as the choice
between hiring new employees and increasing
hours worked of existing employees.
• Q-F, such as costs of hiring and training, are
strategic investment decisions that firms must
make.
Non-wage Labor Costs
• Hiring and Training Costs
– Formal versus informal training
– Costs of Training
• Explicit costs
• Implicit or opportunity cost of the on-the-job trainer
• Implicit or opportunity cost of the on-the-job trainee
– Since many of the costs are implicit they are difficult to
measure. Studies cited in text say that 30% of an
employees time in the first 3 months are for training.
– Tradeoffs between high-wage/low-training and lowwage/high training strategies.
• Employee benefits
– Legally required benefits
– Privately provided benefits
– Non-wage benefits are about 30% of total
compensation
• Quasi-fixed costs
– Certain benefits are proportional to hours worked most
quasi-labor costs are proportional to the number of
workers.
• Workers’ comp. Are strictly proportional
• Social Security are for most employees
• Unemployment insurance is less so because it is charged up to
a relatively low max. level of income
• Health insurance and defined benefit retirement plans are per
worker
Employment/Hours Tradeoff
• So far, we have talked about labor as the number of hours
worked and ignored the distinction between hiring a new
worker and employing an existing worker for more hours.
• To determine what is the optimal mix of employees versus
hours worked we can redefine of profit-maximization and
cost-minimization rules.
• Two marginal products and two new marginal input
expenses:
– MPM - the marginal product of a new worker assuming that the
average work hours remain the same.
– MEM – the extra costs associated with hiring and employing a
worker given the going average hours worked
– MPH – the marginal product of increasing the average amount of
hours worked assuming that the number of workers is constant
– MEH – the extra costs associated with increasing the average hours
worked of existing employees
Optional Mix of Workers and Hours Worked
• Profit-maximization implies hiring workers and
employing them for a average number of hours
that satisfy the following conditions:
– MRPM = MEM, and
– MRPH = MEH
• Cost-minimization implies hiring workers and
employing them for a average number of hours
that satisfy the following condition:
– MEM /MPM = MEH/MPH
Figure 5.1
The Predicted Relationship
between MEM/MEH and Overtime
Hours
• Now assume that overtime pay is doubled as some lawmakers have
suggested as a way to increase employment
– MEH ↑ on M and H mix→
• Scale effect: MEH↑ → MCq|H↑ → Q↓
→ H↓ , M↓
• Substitution effect: (WH/WM) ↑ → Q constant → H↓ , M↑
– But average labor costs would rise, even if no overtime is scheduled
because they would have to hire more workers with the associated quasifixed costs. These costs must be higher than paying time and a half
because otherwise the firms wouldn’t have paid overtime. This causes
changes in the L and K mix
– MEL↑ → on L and K mix →
• Scale effect: MEL↑ → MCq|L↑ → Q↓
→ L↓, K↓
• Substitution effect: (Wl/C) ↑ → Q constant → L↓, K↑
• Will this increase employment? Perhaps, but there are offsets?
– Shift to more capital intensive production
– Substitutability might be low if overtime workers are skilled
– Employers and employees might reduce straight-time hours to keep
overall wage bills the same.
Part-time Employment and Mandated Benefits
• In the EROP, it was argued that manufacturing job losses
were overstated because of domestic outsourcing and parttime employees who are counted as service employment.
• Temporary help services have growing rapidly accounting
for one-fourth of all employment growth in the 1990’s.
• Those counted as employed part-time in the non-ag sector
has doubled in the last 50 years from about 10% to 22%.
– Supply-side reasons: increased participation rate of women, phased
retirement and students working to finance educations.
– The previous analysis of quasi-fixed costs suggest demand-side
explanation as well.
• Britain’s 1975 legislation slowed substitution and sectoral studies in
the US indicated that a low ratio of part-time wages to full-time
wages results in a higher ratio of part-time employees to full time
employees
– What would happen if all workers were covered by mandatory
health insurance?
Investments in Training and Hiring and
the Demand for Labor
• Training and hiring decision involve costs and benefits and
need to be included in understanding the demand for labor.
• Benefits of training and hiring are primarily higher
productivity by increasing human capital, lowering
turnover, and increasing motivation and/or effort.
• Costs of training and hiring include both explicit and
implicit costs.
– Examples of explicit costs are paying trainers, hiring head-hunters
– Examples of implicit costs are lost productivity from on the job
training either by the trainer or trainee.
• Training and hiring decisions also bring an intertemporal dimension to the employment decision.
The costs of training are usually incurred in the
present and their benefits are usually received in
the future.
• The concept of present value.
– Since costs and revenues in different time period can’t
simply be added together because of the time value of
money
– Calculation of future value vs. present value
– Using spreadsheets to analyze inter-temporal choices
Multi-period Employment Decisions
• To model inter-temporal employment decisions,
the following simplifying assumptions are made:
–
–
–
–
–
–
–
–
Two time period – (this year and next year)
Benefit costs are ignored
All workers work for the entire period
Firm’s sell output and hire inputs in competitive
markets
Training/hiring costs are incurred in the present and
their benefits are received in the future
MPDT<MP*<MPAT OR MPO<MP*<MP1
Z are the training costs in real terms
Real wages are paid WDT=Wo and WAT=W1
Figure 5.2
Effects of Training on Marginal
Product Schedules
Figure 5.3
Multiperiod Demand for Labor
•
•
•
•
Remember that we hire workers until the MEL=MRPL
PVMEL = W0 + Z + W1/(1+r)
PVMRPL = MP0 +MP1/(1+r)
So the profit-maximizing rule for hire labor in a multiperiod model with training costs is:
• PVMEL= PVMRPL or
• W0 + Z + W1/(1+r)=MP0 +MP1/(1+r)
• PV of Net Marginal Expenses of training = PVNMET=
W0 + Z - MP0 (all cost are borne in the first period)
• The assumption is that training creates a present
expense that is not compensated completely by
lower wages. This implies that the present value
of net marginal expenses are positive.
– PVNMET= (W0 + Z) – MP0 > 0
– (W0 + Z) > MP0
• Profit-maximizing firms subject to competition in
output markets cannot make losses. So, the
PVNMET must be covered by paying labor less
than their marginal product in the future. The
present value of the net marginal gain is:
– PVNMGT= MP1/(1+r) –W1/(1+r) = (MP1 – W1)/(1+r)>0
– MP1>W1
Multi-period Labor Agreements
• Covering training costs requires that a firm pay
less than a worker’s marginal product in the
future.
• Will a worker accept a wage below their marginal
product?
– Yes, if, W0 + W1/(1+r) > W* + W*/(1+r), where W* is
the single period wage
– But, when W0 and W1 are not the same the worker and
the employer may have competing interests that require
a formal or informal contract to come to agreement
– One can describe various payment plans that tradeoff
wages in the present for wages in the future but keep
the PV of payments the same.
– See table.
• Formal versus informal contract:
– Formal contracts: employer is more likely to be bound to future
payments than the employee is to accept them.
– Informal contracts: employees are worried that the employer may
break the agreement about future payments.
• Limitations on multi-period wage offers:
– High present wage and low future wage: employer worries that
employees may leave.
– Low present wage and higher future wage: employees are
concerned that the employer may break the agreement.
– Without binding contracts on both the employer and employee, the
dominant solution, in the absence of credentials or mobility costs,
is paying the same wage each period that is equal to the single
period wage.
– The inability to pay lower wages in the future discourages
employers from incurring training costs.
Training and Multiperiod Wage Offers
• An employer can afford to offer a wage package greater
than the single period wage scenario, if training/hiring
creates net marginal gains and if the employer is able to
capture some of that gain.
• General versus specific training
• General training – the employer appears to have little
incentive because, in the absence of credentials or mobility
costs or the possibility of brokering information, they may
not be able to capture a sufficient amount of the net
marginal gains. If they attempt to pay a future wage below
the employee’s new higher marginal wage, the employee
may quit and go elsewhere
Figure 5.4
A Two-Period Wage Stream
Associated with Specific
Training
Specific Training
• Because the training is specific to the firm, the
employee’s increased productivity is only relevant
to the firm. Therefore, employers can recuperate
by lower future wages the cost of training and also
possibly a surplus in future periods.
• Two questions arise:
– How much training should occur?
– How should wages be structured after training?
• Wages should be structured to take into account:
– Quit rates and costs of mobility
• As mobility costs decrease the present wage and the future
wage would converge to the single period wage.
• As mobility costs increase the present wage and the future
wage would diverge from the single period wage.
– Protecting investments – mutual benefit to employees
and employers to share the costs of specific training
• Employees want to increase their wages but reduce the possibility
they are fired.
– Lower present and future wages encourage firms to train workers.
– However, employees do not want to pay all the costs of training, even
though they could capture all the future surplus from training, because
employers would have no investment in training to protect and the
possibility of being let go would increase.
• Employers must decrease wages to pay for training but also reduce
the possibility that employees quit.
– Higher present and future wages encourage employees to undertake
training and to stay with the firm.
– However, if employers bear all the costs the lower future wage they
would pay would encourage quitting and the loss of their surplus from
the investment in training
Theoretical Implications
• Layoffs
• Labor productivity and the business cycle
• Cases where employers will pay for general
training
– Mobility costs
– Brokering information
Figure 5.5
Productivity and Wage Growth, First
Two Years on Job, by Occupation and
Initial Hours of Employer Training
Source: John Bishop, “The
Incidence of and Payoff to
Employer Training,” Cornell
University Center for Advanced
Human Resource Studies
Working Paper 94-17, July
1994, Table 1.
Figure 5.6
The Effect of a Decline in Demand on Employment with
General and Specific Training
Hiring Investments
• Credentials
• Internal labor markets
• Recouping hiring investments