Abstract
This
paper is sequel to the work by Abara (2010) who derived a mathematical model
showing that the optimal retirement age of a worker in Nigeria should be
determined based on the investment made on the worker in terms of education and
training and the extent to which the worker’s maintenance cost increases
annually.
Readers of the work observed that instead of isolating maintenance
cost alone, it would be necessary to consider and model factors such as human
resource productivity and capital in the determination of retirement age. The
author considered these observations seriously. Capital itself enhances human
efficiency or productivity, while the latter could influence the rate at which
human resource maintenance cost changes annually. Thus, the model was
reformulated using productivity as an independent variable in conjunction with
calculus to generate optimality conditions. The generated model shows that
retirement age is invariant to investment in human resource education and
training but variant (as a divisor) to productivity or any other variable. The
larger (smaller) the divisor the fewer (more) will be the optimal work years.
In essence, development of human capital through education and training, given
the level of productivity or changes in human maintenance cost, is the prima
fact that determines the longevity of human resource utilization. Thus,
retirement of a human resource is a function of the level of investments made
on it, and the rate at which its efficiency/productivity increases annually.
Stated differently, the model shows that the rate of growth (decline) in human
resource investment (further education, training and retraining, experience etc.)
should exceed (be less than) the rate at which human resource efficiency increases
(declines) on the job annually, if human resource must last long on the job.
Introduction
This
paper is sequel to the work by Abara (2010) who developed a mathematical model
capable of determining the optimal work years and hence the retirement age of
workers in the public and private sectors in Nigeria. The quest to evolve a
scientific approach to retirement age in Nigeria is today necessitated by the
scientific invalidity of the mandatory retirement age in Nigeria.
The
world economies today are intertwined in a somewhat vicious cycle arising from
that fact that what happens in one country, from the standpoint of
globalization, reverberates in others. This characteristics are shared more n
those economies as could be found in the western hemisphere and Eastern Europe
with similar micro-and macroeconomic policies. The financial turbulence which
has tended to destabilize world economies since the late 2010 is yet to abate,
as both world economies and for – profit organizations continue to realign
their limited production capabilities ad seemingly ever – expanding consumption
behaviours.
The
realignment of production possibilities and consumption patterns around the
world has further brought to the fore intense and often chaotic debate as to
the perceived and real efficacy and efficiency of human resource, especially
during periods of economic downturn. When corporate finances dwindle and
profits disappear, structural adjustments are necessitated. Even among national
economies with bloated internal and external debt as a large proportion of or
in excess of their average annual earnings or gross domestic product (GDP),
structural adjustment is necessitated. The implication of structural adjustment
in Nigeria or on private or public organizations in Nigeria with respect to
human resource recruitment, training, compensation, reevaluation, promotion,
retirement, etc. is a well –documented fact. Employee retirement is no longer a
“fixed” decision based on longevity of service or chronological age. The
dichotomy termed “longevity versus chronology” revolves around shrinking or
extending the services of human resources in response to the prevailing
financial and economic conditions of the economy or in the market place.
In
not too-distant past, heated debates on this dichotomy had taken place in
France, Belgium, and Greece, to mention but a few countries. Governments and
corporations that favor longevity do so only to the extent that long stay at
work would enhance, say, depleted cash reserves for unemployment benefits and
pension fund. On the contrary, early retirement could be seen as a strategy
that preserves a good proportion of saved – up earnings or profits as opposed
to paying their future values (with high expected interest rate). Labour unions
are not left out in this debate. Labour unions may canvass for early retirement
on the ground that human resources exert and expend lots of energy and hence
“depreciation” over a fairly long period of work time and therefore deserve a
quick break. Those on the other side of the isle would vote for late
retirement, especially if there is a dearth of human resource capacity. The
latter position has been adopted by the Academic Staff Union of Universities
(ASUU) in Nigeria.
The
retirement age of University professors in Nigeria is 70 years as signed into
law in 2012. This age is predicated on preserving the number of skilled and
experienced teachers and researchers in Nigerian Universities given the current
but overriding circumstances in Nigerian Universities. How ASUU arrived at age
70 to be the best, optimal, satisficing, or most efficient retirement age beats
science. Thus, there is need to empirically determine a general scientific way
of retiring workers taking different levels of education, training, etc. into
consideration. Nevertheless, the nexus of this study tended to address the
concern raised by readers of the previous work: How could productivity or efficiency
be applied to the model as opposed to human resource maintenance cost?
The Problem
This
paper has become necessary due to comments and observations made by readers
with respect to the work by Abara (2010). In the study, Abara found that the
retirement age of a worker is determined by two main variables namely the
initial education or training cost and the amount by which maintenance cost of
a human resource increases each year. Some readers of the work by Abara suggested that it might be necessary to
consider such variables as worker productivity (or technical efficiency) and
capital or technology that combines with human resource to influence the degree
of change in annual maintenance cost of human resource, as opposed to looking
at maintenance cost in isolation. While the observations are laudable, we make
bold to state that it may not be necessary to factor in capital as an
independent and separate variable as it is generally known that human resource
efficiency or productivity is enhanced or made possible by its interaction with
capital. therefore, the implication of capital on retirement age becomes
all-too-important to the extent that capital influences the productivity of
human resources, and human resource productivity determines the extent to which
a worker stays on the job. Furthermore, it was acknowledged in Abara (2010)
that the limitation the derived model might have had rested on the accurate but
difficult measurement of changes in human maintenance cost. Therefore, the
objective of this study was to determine the effect on the retirement model of
the introduction of productivity or any other variable into the human resource
cost function.
THEORETICAL FRAMEWORK
The
theoretical framework for this study revolves around asset replacement/retirement.
Employees invest in themselves through acquisition of education and skill.
Organizations invest in their employees through recruitment exercises and
employee development training programs. A human resource, like any other asset,
is continually used until its maximum productivity level is attained. The
decision to replace, retire, or continue using a productive asset such as human
resource is as important as the original decision to invest in it. The history
of asset retirement/replacement theory is a progression from qualitative
analysis to quantitative analysis and from simplicity to sophistication.
There
is one fundamental reason for either replacing/retiring or discarding
completely a human resource asset or any other durable asset for that matter.
It is that by doing so the organization makes greater profits (small loses).
Obviously an organization made its investment decision on the resource on this
principle in the first place. After this, most of the decisions are based on
the question of changes either in the resource itself or in its environment. Changes in the resource asset itself which
would affect the decision to retain or to retire/replace are, increasing need
for maintenance (such as training and retraining costs; costs of maintaining physical,
mental and psychological fitness, etc), declining efficiency (when the average physical productivity is
declining), or inability to perform the required functions satisfactorily and
over a fairly long period of time (such as old age). Changes in the environment
which affect the resource retirement/replacement decision are such things as
Obsolescence (availability of better trained and educated persons, either
technologically, economically, or socially)
and scarcity, the latter resulting often in out-sourcing for specialized skills
(labour).
The
analytical models of the behavior of some of the factors involved require
quantification and measurability. For example, the maintenance requirements of
many types of assets in which an organization deals are fairly predictable on a
statistical basis; and in most cases can be well enough handled by reducing
risk to certainty through using the average as a certain figure. The behaviour
of first (initial) cost (investment) and interest charges on this first cost or
on other costs present minor difficulties. At the other extreme, obsolescence
if applicable, due to major discontinuities such as the discovery processes are
almost totally unpredictable in any sort of long run. However, in between these
extremes are components of real world such as efficiency that present varying
degrees of difficulty in mathematical modeling. Generally, the mathematical
models derived are directly useful in a numerical calculation of the optimum
retirement/replacement point for a specific asset (Poage, 1981), human or
non-human. In addition, the models provide valid additional insights into
decisions regarding asset retirement/ in general.
THE LITERATURE
Theoretically,
the mathematical models for retiring/replacing assets consider various
performance variables such as profitability, or part thereof (costs), changes
in the environment, changes in the asset itself, interest rate/inflation,
maintenance, and productivity, to mention a few. In quantitative management,
inventory management/control theory is often adopted to consider optimum
replacement/retirement plans for assets.
Thuesen
and Fabrycky (1981) evaluated optimum asset retirement or replacement by
considering only the initial cost of the asset, annual operating costs, and the
annual increase in the maintenance cost. The
mathematical model expresses the
average annual cost of an asset with increasing
maintenance cost as:
C = I/n + Q + (n – 1) m/2 -------------
(1)
Where
C = average annual cost of asset, n = the useful life of asset in years, Q =
annual constant portion of the operating cost of the asset or the first year’s
operating cost including the total first year maintenance, I = the initial cost
of asset, and m = the amount by which maintenance cost increases each year. The
graphical presentation of Equation 1 is shown in Figure 1.
Figure 1:- The Human Resource
Retirement Model.
Three
cost curves are shown in Figure 1 as average initial investment (1/n), the
maintenance cost (n- 1) m/2, and the average annual cost
of the asset. In this case, Figure 1 shows total cost of an asset as a function
of time (t).
Figure 1 and Equation 1 reveal the
following characteristics of human productive assets:
a. The older the asset, the higher the
maintenance cost. As such, the maintenance
cost curve, (n – 1) m/2 raises or has a positive slope
over time.
b. The average initial investment (I/n)
is analogous to average fixed cost (AFC). Average fixed cost, and hence average
initial investment, declines as output from a resource or from its combination
with another resource increases (mass production) in the long run because the
AFC or I/n is spread over a large quantity of output over
a long period of time. In the short run, organizations are concerned with
returns to scale. In the long run, they are concerned with returns to size as
all fixed assets (resources such as specialized labor) or average initial investment
can be varied in a certain proportion. Thus, average initial investment
declines as size of an organization increases through more asset acquisition or
through enhanced human capital base (knowledge, experience, etc.)
The
optimal retirement period (years) of a human resource asset can be determined
by only applying the classical optimization procedure (calculus) which
differentiates Equation 1 with respect to n and then solving for n. The value
of n is the optimum life span (useful work years) of the asset. A major
limitation of Equation 1 is that it does not yield the same n value when the
equilibrium criterion is used to derive n.
Poage
(1981) observed that it is possible to derive some variations of Equation 1 by
including other terms or variables which are assumed to be either linearly
increasing with the life of the asset (n) such as obsolescence factors, or
which follow the average initial investment (I/n) in a reciprocal or inverse relationship
with the life of the asset (such as installation or recruitment charges). In
reality, however, the variations will be redefinitions as to what the initial
cost of the asset includes and what the annual increase in the maintenance cost
includes.
Bowman
and Fether (1981) also presented a more general model of only slightly more
mathematical complexity considering the cost of optimum life and the effect of
planning horizon on decision making. Their model can be stated as follows:
CV = ò0T [R (t) – E (t)] e –it
= dt + S (T) e – it - I -----------(2)
Where
CV is the current value of the total net return on the asset over the life of
the asset; I is the initial or first cost of the asset; T is the useful life of
the asset; S(t) is the salvage value function of the asset at time period t,
assuming continuity; e is base of natural logarithm usually equal to 2.71828; I
is the nominal annual interest rate; R(t) is the revenue rate function at time
t; and E(t) is the expense rate function at time t. Certainly, Equation 2 does
not yield optimum life of an asset. The equation of the mathematical condition
for the optimum life of the asset is achieved with some algebraic manipulation,
hence, Equation 2 is differentiated with respect to T, the derivative is set equal
to zero, and after dividing by e –it, the equation that meets the
condition for the optimum life of an asset becomes.
R(t) – E(t) = iS(t) – S/(t) -----------------------------(3)
Where
S/(t) is the function of the rate of increase of the salvage value.
The left – hand – side of Equation 3 is equivalent to profit (TT) or a similar
performance measure, while the right-hand-side is the real value of the salvage
value of an asset. For convenience, therefore, Equation 3 can be expressed as,
TT = iS(t) – S(t) -------------------------------------(4)
Theoretically,
we can make several observations about Equations 3, and hence 4. First, the
model is useful even if we don’t know the nature of the functions R(t), E(t),
S(t), and S/(t). The interpretation is simply that an asset should
be held (in use) until that time when the rate of profit or net income (TT or
R(t) – E(t) ] is just exactly equal to the interest on the salvage value minus
the rate of increase of the salvage value at that point in time. We should
note, however, that the rate of increase in the salvage value is usually a
declining (negative) figure. Therefore, -S/(t) is really equivalent
to plus the decrease in the salvage value. Second, the validity of Equations 3 and 4 depends rather strongly on
the assumption that the owners and users of the asset will dispose of or retire
the asset in question at the end of its life and possibly retire from that type
of business. Third, if the planning horizon is assumed to be infinite and where
each asset as it reaches the end of its optimum life is replaced by an
identical asset with a similar life
cycle, Equation 4 can be modified or remodeled using same methodology to
show an equation describing the condition of optimum life. This Equation can be
written as,
R(t) – E(t) = iS(t)
Therefore,
R(t) – E(t) = s(t)
+ i ò0T {[R (t) – E
(t)] e –i} dt + S(T) e – it - I
1-e -it
Consequently,
|
1 – e -it
Equation 5 is the same as Equation 4 with the
modification of the addition of a complex term which represents the interest on
the current worth (CV) of the total net return on the investment in all of the
assets in the infinite future. The inclusion of this term results in shortening
the optimal economic life of the asset before replacement when there is a chain
of competing assets waiting to replace the existing asset. This is very true in
relation to the availability of better competing human resources.
Notably, the Bowman and Fether model assumes that the
revenue, expense, and salvage value functions are continuous functions of time
way into the future. In consideration
of a short term condition, Morris (1986) provided a similar set of analysis
which showed that the revenue, expense, and salvage value changes are discrete
values occurring at the end of each year. The general conclusion was that, in most situations, it
could be shown that the total curve is relatively flat in the area of the
minimum, meaning that costs are relatively insensitive to errors in the
determination of the optimum life in the region near the optimum life.
METHODOLOGY:
THE MODEL
To generate the optimum work life (useful service
years) and the optimum retirement age for human resources, the Cost-Cost Model
Design (C-CMD) was used. The model design is explained as follows:
The Cost-Cost
Model Design (C-CMD)
This model employs an amalgam of mathematical designs
as shown in Poage (1981), Render and Stair, Jr. (188), Thuesen and Fabrycky
(1981), Bowman and Fetter (1981), and Abara (2009) with modifications made
where necessary. However, Thuesen and Fabrycky’s model was adapted discretely
on a cost – cost basis. As the human element (labour) is the focus of the study
and not non-human (machine), the model variables were modified and redefined.
More importantly, the Thuesen and Fabrycky’s model gives the condition for
determining optimal life of an asset only if calculus, through derivative or
first order condition, is employed. The model fails if cost components are
simply equated to each other. On the part of useful life or retirement period
for a human resource, a mathematical model that gives the condition for
optimality through the use of calculus and through cost equality condition was expressed
as follows:
TCL = T + I/n + n(m/2)
------------------------(6)
Where TCL = average annual education/training cost
of a human asset
T = first
year’s working cost including maintenance
I = initial
education/training cost of a human resource asset
m = the
amount by which maintenance cost of human
Resources
increases each year
n = the
useful work life of human resource asset (in years).
By interpretation, our working model states that the
average annual education/training cost of a human recourse is a function
of the total cost of education/training received by the person; the rate at
which his/her physical, mental, psychological, emotional, and mental
alertness//capability declines; and the number of years he/she is expected to
be usefully employed in a salaried position. For a physical asset, the average
maintenance cost increases by (n – I) in the Thuesen and Fabrycky’s model.
However, for a human asset, this cost increases by n (for as long as a job is
held) thus making it possible to achieve equilibrium between initial training
cost and maintenance cost. According to our model, these cost, I and m,
influence the total cost structure of a working human resource.
The
Productivity/Efficiency Factor
The major problem which we face is obtaining the real
quantified value for “m”. In our previous work on a related issue, we suggested
that “m” could be approximated as (a) the average estimated cost of improvement
in the work environment or the degree of comfort and convenience over the work
period (b) the average estimated cost of medical treatment, fitness, and other
physical, mental, and emotional care over the work period (c) a percent of the
investment capital (I) equal to the prevailing nominal opportunity cost of the
investment, or (d) average of the interest rate payments/nominal opportunity
cost of human resource investment over the wok period. As good as these
estimates may sound; they lack the physical attributes that are associated with
labour or human resources. While cost offers the opportunity to derive the
model, the appropriate value for “m” should not be in naira and kobo but in
physical terms.
A key physical measure of the value of labour is not
necessarily the investment in it nor the compensation it receives. Investment
is a stimulus to performance while compensation is a response to performance,
the latter being a response to the investment stimulus. If investment
necessitates performance, and performance necessitates compensation, then
investment or cost necessitates compensation which should be determined by
productivity. Productivity should therefore be a better measurable attribute of
“m” than any other measure. This is more so of a truth if we know that
productivity is a derivative from labour itself and therefore a good reflection
and measure of its source. This is in sharp contrast to use of any normative or
monetary measure. If technology is the key in every endeavour, then
productivity should be the key as well, especially as productivity is a general
measure of technology. In addition, the problem of definition (of “m”) and its measurability
is avoided since productivity is empirically definable and hence measurable.
Shroeder (2008) observed that measurability of
productivity has become a contentious issue in the field of management science,
even though knowledge of worker (labour) productivity is necessary for human
resource decision making such as recruitment, selection, promotion, “firing”,
and replacement/retirement. Management may logically retain labour if its
productivity rate is relatively high even though such labour might have
attained a mandatory retirement age or be “uperty”. Generally, productivity
(P’) is a measure of the relationship between labour input (L) or any other
input, and the quantity (and quality) of output (Y) resulting from the unit of
labour or any other input. This measure presupposes that human resource
(labour) is a factor of production. Thus, productivity of labour is an output –
input ratio describing the contribution to total output by a unit (usually
expressed as “man hour) of labour input used.
Traditionally, productivity or efficiency of labour is
measured as:
PrL = total
output = Y ------------ (7)
Total
labour used L
Where PrL is labour
productivity, Y is total output, and L is quantity of labour used.
To measure productivity, Shroeder (2008) combined
different effectiveness and efficiency measures by using a point system. Then
he defined productivity as a component of effectiveness and efficiency such
that productivity becomes the product of effectiveness multiplied by efficiency.
This can be mathematically, stated as,
PrL = effectiveness
x efficiency -------------------------- (8)
Where “efficiency” is the achievement of an outcome
with less than the proportionate factor input (synonymous with Y/L),
and “effectiveness” is the ability of an input or a factor to have noticeable
or desired impact on the desired outcome. Shroeder showed that where there is
no constant measure of output, outcome, or performance (designated as Y), the
effectiveness score could be multiplied by the more familiar traditional
efficiency or productivity (ratio) shown as Equation 7. Thus, Equation 8 could
be stated mathematically as.
P rL = effectiveness x Y
---------------------------------- (9)
L
Equation 9 is based on a caveat. It is based on the
traditional assumption that (1) human
resource efficiency is a linearly increasing function of time, and (2) the
quality of output or performance (Y) remains constant at the point of measurement.
When quality and productivity vary over time, as in the case of labour, a more
complicated productivity measure could be used. If we assume that effectiveness
equals unity (as its maximum) and we substitute Equation 9 into Equation 6, our
total labour (human resource) investment structure becomes a measure of the
effect of productivity on the total human resource cost function. Thus, the
human resource cost function incorporating human resource
efficiency/productivity becomes:
TCL =
T + n- I + 2-1
n L-1 Y ------------------------------- (10)
If we apply calculus and differentiate Equation 10 for
optimality with respect to n, or if we use the equilibrium method, it could be
shown that the optimal work years equals,
 |
|||
 |
|||
n = 2I/ Y/L -I = 2I
---------------------------- (11)
PrL
Equation 11 states that the optimal work life (not
retirement period) of a worker is estimated to be the square root of the ratio
of the cost of initial investment on a worker multiplied by two, and the rate
at which labor efficiency increases or decreases . Stated differently, the
optimal number of work years equals the square root of the ratio of the initial
investment on the worker education, training, etc. multiplied by 2, and the
worker’s level of productivity, on the average. As the value of the divisor (productivity)
in Equation 11 is expected to be very low (fraction), the quotient in Equation
11 is expected to be high. Therefore, the
higher (lower) the human resource efficiency the lower (higher) is the optimum
work life span of a worker, assuming perfect effectiveness holds
The optimal work life span of an employee is not the
retirement age. To obtain a worker’s retirement age, we add the chronological
age (K) of the worker when work was obtained to the optimal work life span (n).
Optimal retirement age becomes,
 |
R = K + 2I/PrL -------------------------------------------
(12)
Or
R = K + n ------------------------------------------------------(13)
Where R is the retirement age, K is the age of the
worker as at when usefully/productively employed, and n is the optimal work
years. Thus, human resource retirement is a function of investment made on it
and the rate at which its productivity/efficiency increases or decreases
annually.
DISCUSSION
It is expected that holding the denominator in
Equation 11 constant, the higher (lower) or more (less) educated/trained is the
employee, the higher (lower) or more (less) will be the optimal number of years
of work life. Thus, all the variables in the denominator (effectiveness and
efficiency or productivity) are linearly related. If the optimal work life span
is expected to be higher (lower) or more (less), so also will be the optimal
retirement age, ceteris paribus.
The advantage offered by Equation 12 is that the
optimal work life span (n) is now a function of only two variables: original
investment or cost of education/training (I) and productivity. Again the
variables, I and PrL are expected to be linearly related
with the time order beginning with I. An increase (decrease) in I is expected
to yield an increase (decrease) in PrL However, if I is
constant, which is usually the case after obtaining the required education
and/or training, an increase (decrease) in productivity will result in a
decrease (increase) in the optimal work life span. This suggests that for a human resource to
last long in an employ, the rate of growth in investment (further education,
training and retraining, experience, etc.) on the human resource should exceed
the rate at which human resource efficiency increases on the job annually. The
rate of change from time to time however is expected to increase or decrease
depending on the availability of further education, retraining, age, etc. This
is explained by the fact that in the youthful age, productivity is naturally
expected to be high in relation to older age. Moreover, the increased
productivity (at the early period of employment) comes with much enthusiasm and
“silent” STRESS. In the long run, enthusiasm gives way to boredom and loss of
zeal (especially where and when work is structured and there is little job
enrichment programs or strategies) accompanied with the manifestation of
stress. In the long run, it is difficult to sustain this increases in
productivity gained in the short run (early work life span), especially due to
age. Generally, the denominator in Equation 12 will decline in rate in the long
run after its peak somewhere along the line.
In the long run (latter years of work life) we should
expect productivity to decline due to several internal and external stimuli
including, but not limited to a) workforce factors (additional recruitment,
selection and placement, training, job design, organizational structure,
supervision, rewards/reinforcement, goals/MBO, and Unions) b) process factors
(process selection, automation, process flow, and facility layout), c) product
factors (research and development or “R & D”, product diversity, and value
engineering), d) capacity and inventory factors (capacity planning, inventory,
and purchasing) e) external factors (government investment policies, government
regulations, business competition, and customer demand). As a result of this
decline in absolute terms in productivity, one should expect the optimal work
life span to increase. This increase may not occur due to five major reasons:
first, the stress factor and other work constraints at the early stages will
cause a decline in n in the latter years of work.
Second, even if there was an increase in the work life
span in the latter years following a decline in productivity, n tends to
normalize or correct itself when the early and latter effects of work (zeal,
boredom, etc.) cancel out. In the end, n may not increase abnormally even
though there has been a decline in productivity. Third, the only way n can
increase is if productivity decline to a fractional level, holding I constant.
It is very likely to have 0< PrL<
0.9999. Normally, we should expect employee productivity to be strictly
positive although we should expect productivity of labour to decline after some
point for obvious natural reasons, Fourth, labour productivity may not
necessarily decline in the long run in absolute terms. The increase or decrease
in labour productivity depends on whether or not labour is combined with other
inputs. Growth in labour and its productivity over time has been shown to be
indirect; they were shown to increase due to the combined use of labour and
capital in an organization (Abara, 2009). Therefore, labour productivity will
decline faster when only labour is used, but will decline slowly (or even
increase) when labour is used in combination with other inputs especially
capital. A decline in the productivity of labour when used with other inputs
will indicate nonsubstitutability of those inputs in use, non transferability
(fixity) of hose inputs in use, and non improvement capability of the inputs in
use. Fifth, the productivity of labour, holding other variable inputs constant
but combined with fixed inputs, will decline at some point due to diminishing
returns effect. This could cause an increase in n. However, the marginal effect
of retaining, motivation programs, and other human capability enhancements late
in life could cause an increase in productivity, and hence a decline in n.
Actual determination of these scenarios is subject to empirical research.
SUMMARY AND
CONCLUSION
Retirement age is no longer guaranteed today according
to old paradigms or organizational culture. Economic and financial
circumstances have prevailed on nations and organizations to seek new work
tenure arrangements. Thus, there is no universal law or model today that could
serve as a benchmark for organizations or a nation like Nigeria to fall back on
when making decisions regarding retirement age.
This paper is sequel to the work by Abara (2010) who
developed a mathematical model showing that retirement age is influenced by the
original investment in education and training made on the work, and the rate of
increase in the maintenance of the worker. Critics argue that maintenance cost
may not be adequate to capture the implication of cost on retirement. Hence,
productivity was integrated into the model. The derivative showed that
investment in human capital through education and training is invariant to
changes in retirement age, but the latter varied as other factors considered in
ratio proportions. Thus, human capital development is the sin-qua-non for
longevity, organizational and national growth and development.
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MODEL FOR OPTIMIZING WORK YEARS AND
RETIREMENT AGE IN THE NIGERIAN PUBLIC AND PRIVATE SECTORS: A REVISIT
Author’s Name: Isaac. O.C. Abara, Ph.D.
Institutional Affiliation: Department of Business Management,
Faculty
of Management Sciences,
Ebonyi
State University, Abakaliki.