Models of Effort

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Models of Effort
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The Principal-Agent Problem Human Resource
Management is a separate field of study today.
But, we in economics have a take on the field and
that take is basically one of employers and
employees attempting to overcome the
principal-agent problem. The principal in this
context a employer or manager wants an agent
a worker here to behave in a certain way. But,
the agent has a set of priorities that does not
coincide with those of the principal and the
agent can usually conceal some aspects of their
behavior. Employers want workers to give effort
for pay. Workers want pay with minimum
effort. Next, lets turn to a model of effort.
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Here we have indifference curves for workers.
Wages, measured in dollars, are a good thing.
Effort is harder to quantify, but we think it is
a bad thing in that we would prefer not to exert
it. So, indifference curves here are upward
sloping because in order to take on more effort
workers need a higher wage to induce them to give
up other things to bring forth the effort.

w1
effort
E2 E1
Indifference curves to the northwest have higher
utility. One way to see this is that at a given
wage a worker would be happier exerting less
effort. Or, at a given effort level, higher
wages would make a worker happier.
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In this model workers choose the combination of a
wage and an effort level that gives the maximize
utility obtainable. Shirking Say a worker has
agreed to wage w1 and effort E1 in the graph on
the previous screen. If the worker gets the job
the worker has an incentive to only give effort
E2 because a higher level of utility would be
achieved. So far, this model suggests managers 1)
Need to be careful in hiring so that workers can
achieve E1, 2) Have to monitor work performance,
and 3) May have to dismiss workers have the
company give up any return on investment in the
employee.
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Here we have the firms perspective on things.
We assume the firm is a price taker in the output
market. w1 is the wage the firm offers. The
total revenue line (TR) is based on the idea that
with more effort more output results and the firm
can sell more. Thus, TR grows with effort. At
w1 the firm needs at least effort w1. At this
effort level the total revenue not only has to
cover the wage of the worker, but the TR must
also cover other expenses and allow for
TR

w1
effort
E1
normal profit. Normal profit is what the firm
would earn in its next best alternative.
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The TR line on the previous slide had P times Q.
In general, lets say for the individual that Q
aE v, where Q output E effort a a
parameter that connects effort to output v a
parameter that captures the effect on output from
factors other than effort an example is machine
down time. On the previous slide we had a 1 and
v 0, so Q E. When this isnt the case the
line gets more complicated.
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Here we bring the two previous graphs together.
Note at w1 I have a dashed line until the solid
part starts at E1. The idea is that the firm is
only offering w1 if the minimum effort is E1.
Workers who accept this type of job have utility
level represented by the middle indifference
curve. It is presumed that workers would take
this job if it is their best available
alternative.
TR


w1
w1
effort
effort
E1
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Concerns for manager with a fixed wage
model Shirking we see the potential to shirk
here. Cost of shirking to worker is an expected
cost. If the penalty form shirking is dismissal
from the job then the cost of shirking is the
probability of getting caught times the lost
income. The individual will shirk if the utility
gain is greater in value than the cost of
shirking. The probability of getting caught is
influenced by the firm. The firm can raise costs
of monitoring and raise the probability. The
worker has a trump card in that they can claim v
is the reason for poor performance. Another point
is that if w1 is the competitive wage workers may
not care as much about getting caught shirking
because they might think they can just go and get
another job.
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Another point is it does not appear that workers
will give more than E1 effort. But the firm
might like to see workers give more
effort. Extension of the model more effort more
pay Lets say the wage is tied to effort like
this w -B bE, where -B and b are parameters
that connect effort to the wage. This means that
we need to change our graph. Lets turn to that
next.
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w-B bE
In this graph the worker has the same feeling
about the fixed wage job and the job with
performance pay. They would earn w1 and put
forth effort E1 in either job. But, some workers
might have flatter indifference curves. Lets
see this on the next slide.
TR


w1
w1
effort
effort
E1
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Here the worker prefers the performance pay job.
A higher wage can be achieved compared to what is
offered in the fixed wage environment. Implication
s for this model The system encourages self
selection of workers. Workers decide which type
of job to take. Those that opt for the
performance pay have an incentive to put forth
more effort. Firms do not have to worry as much
about screening workers and shirking is less of
an issue because the worker can not hide the
amount of output produced.



w-B bE
TR


w2
w1
w1
effort
effort
E1 E2
With less spent on hiring and monitoring more can
be given to worker and maybe there will even be
more profit for the firm.
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Difficulties of implementing performance pay
jobs Many jobs have output that is hard to
measure so the link to effort and output is hard
to see. Some jobs have too many other factors
that influence output besides effort and thus the
link between effort and output is obscured. Some
jobs depend on team effort some workers could
shirk. That reminds me of a story about China.
Product would be shipped on the river. The more
trips that could be made the more workers could
make. SO, each day the workers would pick among
themselves the whipper. This person would
crack the whip on those who where not rowing the
boat hard enough.