Annals of the University of Petroșani, Economics, 14 (2), 2014, 2 53-260 253 [612409]

Annals of the University of Petroșani, Economics, 14 (2), 2014, 2 53-260 253

CONSIDERATIONS REGARDING THE CALCULATION
AND EVOLUTION OF LABOR PRODUCTIVITY IN TERMS
OF COMBINING TECHNICAL FACTOR – CAPITAL

DANIEL TOBĂ , DALIA SIMION *

ABSTRACT: The efficiency of labor , as evidenced by average productivity indicator
is linked to the existence of social conditions which relate to education , qualifications and
experience of staff , division of labor employment, labor discipline , but also the existence of
objective conditions , technical and technological, as modernization of produ ction and the
availability of equipment to employees. The content of the article we will highlight an analysis
of the calculation , and the evolution of labor productivity in terms of the elements related to the
value of labor used in relation to operationa l staff of the company. We will also reveal the
evolution of labor efficiency and profit when the company capital factor is constant , given the
need to increase production .

KEY WORDS: labor productivity, efficiency, degree of technical endowment ,
product ion, employees

JEL CLASSIFICATION: D01, M21 .

1. ANALYSIS CALCULATION LABOR PRODUCTIVITY UNDER ASPECTS
DEGREE OF TECHNICAL ENDOWMENT

In economic literature records that the average labor productivity is complex ,
the size and evolution are determined by a number of factors : economic , technical and
technological , natural, social, psychological , etc. [5]
In this context, the average annual labor productivity , labor efficiency as a
fundamental expression is directly related to the existence of general facto rs, valid for
any production system (modernization of production , staff qualifications and
experience , division of labor, natural conditions , etc) and the specific factors that acts

* Assoc. Prof., Ph.D., University of Craiova, Romania, danutob @yahoo.com
Assoc. Prof ., Ph.D., University of Craiova, Romania, [anonimizat]

254 Tobă, D.; Simion, D.

only at certain times and under certain circumstances (economic crisis, transition
economies , etc).
Thus , labor productivity must be analyzed in terms of factorial after causal
links that appear in its evolution .
The contents of this article, we systematize factor analysis the following
direction : approaching labor productivity in terms of the degree of technical
endowment to employees.
Between labor productivity and changes in the means of labor , production
technologies , raise the level of technical equipment there is a direct relationship,
resulting from the fact that high-level technical equipment results in relief work,
increasing production per unit time and increase quality .
We believe that the relationship can express labor productivity calculation
based on the degree of technical endowment , as follows:

eGFCA
NF
NCAW 

Where terms have the following meanings:
CA – turnover;
N – total number of staff;
F – average annual value of means of production used for the production;
FCAe
– the effectiveness of using fixed assets
NFG
– the degree of technical endowment .

By increasing technicality , increase the value of fixed assets used in the
production process , a situation which shows that labor productivity growth should
increase the efficiency of fixed assets more , that inequalities are satisfied :

g e Q iii

where : iQ – index of output growth ;
ie – use efficiency index of fixed assets;
ig – index of the degree of technical endowment.

Thus, to be certain labor productivity growth between the three indices must be
faster growth relationship production index to index the efficiency of using fixed
assets, and this in turn grow more pronounced compared to the index of technical
endowment .
The direct relationship between labor productivity and the the degree of
technical endowme nt can be expressed by the relation:

Considerations Regarding the Calculation and Evolution of Labor … 255

0011
0011
NFNF
NCANCA


where : CA 1,0 – turnover in the current period and the base ;
N1,0 – average number of staff employed in the current period and base ;
F1,0 – average annual value of means of production used in the c urrent and base
period .

The relationship above is actually the same content as follows:
01
01
GG
WW

which expresses the fact that:
g wii and that is a basic relationship highlights the
need for more rapid growth of labor produ ctivity than the availability of equipment .

Expression of the link between degree of technical endowment and labor
productivity can be achieved and relations :

1)
FCA
NF
NCA
op op

where : Nop – Number of operational staff .

This relationship express es the relationship between productivity , employment,
labor endowment degree and effectiveness of using fixed assets, customized for
operational staff , as follows:

e G Wop op

The content of this relationship they express that average labor pr oductivity is
calculated for operational staff determined the degree of endowment fixed assets of
personnel and efficiency of these assets .

2)
a opa op
FCA
NF
NN
NCA

where:
aF – value of fixed assets used in the production process .

This means that:

a aop op e G K W 

256 Tobă, D.; Simion, D.

ie labor productivity is determined by : the share of operational staff in total staff (Kop);
endowment degree of operational staff with fixed assets ( Gaop); effectiveness of using
active fixed assets (ea).

3)
a opa
op FCA
NF
FF
NCA

indicating that :
fa op fa op e G K W 

Labour productivity is determined by the following relationship :
– The share of fixed assets in total assets fixed assets (Kfa)
– The degree of endowment operational staff with fixed assets ( Gop)
– The effectiveness of active fixed assets (Efa).
To illustrate the determination of labor productivity relations based on the
availability of equipment to staff, we use the data for one year of activity , a company
producing domestic refined oil as follow s (Table 1):

Table 1.

Nr.crt Economic categories UM Amounts
1. Turnover – CA mii lei 4.000
2. Total number of staff – Nt pers. 100
3. Of wich: operational staff – Nop pers. 86
4. The total value of fixed assets – Ft thousands lei 4.500
5. Value of f ixed assets – Fa thousands lei 3.000
6. The average productivity per employee – W thousands
lei/pers. 40
7. The average productivity per worker force – Wop thousands
lei/pers 46,51
8. The degree of an employee endowment assets – G thousands
lei/pers. 45
9. The degree of endowment assets operative worker –
Gop thousands
lei/pers 52,32
10. The degree of endowment of an employee with fixed
assets – Ga thousands
lei/pers 30
11. The degree of a worker operating endowment with
fixed assets – Gaop thousands
lei/pers 34,88
12. The efficiency of fixed assets – Ef ef 0,888
13. he efficiency of active fixed assets – Efa efa 1,333

1) For the basic relationships :

99,39 8888,045 feG W thousands lei/pers.
2)
5,46 888,032,52 f op op e G W thousands lei/pers
3)
99,39 333,188,3410086fa aop op e G K W thousands lei/pers.

Considerations Regarding the Calculation and Evolution of Labor … 257

4)
5,46 333,132,5245003000fa op fa op eGK W thousands lei/pers.

2. THE CORRELATION BETWEEN PRODUCTIVITY GROWTH AND
PROFIT DEVELOPMENT , IN COMBINATION WITH THE TECHNICAL
FACTOR – CAPITAL

The combination of production factors is significantly i nfluenced by the
limited productive resources and essential criterion for assessing the effectiveness of
the combination is the very nature of economic activity. Moreover, the combination of
production factors, the developer based on the following two prem ises: the limited
factors and their properties .
In a short time , the volume of certain factors of production can not be changed
or adapted quickly to the needs of production of goods , due to changes in their market.
By their nature, these resources (factor s) have a fixed character , their short -term
demand is very inelastic . In this category we include : buildings , land, buildings,
facilities, equipment manufacturing and generally any other economic resource whose
amount cannot be changed immediately when the market requires an increase
(decrease) in production.
There are other economic resources, which is of a variable , such as certain
categories of staff , materials, equipment , fuel, electricity etc. and the volume of which
can be quickly adjusted according t o production needs change . It is assumed that the
factor most often variable light , short, is the work (labor ). This assertion does not
correspond to the theoretical needs , but an empirical findings : in general , an enterprise
can adjust the volume of work faster than that of capital ( it is easier to resort to hours
or additional employment , temporary work , technical unemployment or even layoffs ,
only to change production equipment and tools used in the enterprise ).
The combination of production factors (short term) is governed by a regular ,
known in economic literature as the law of diminishing marginal productivity (yields
disproportionate Act), under which , when combined fixed inputs with variable inputs
average productivity and the marginal increase to a peak and then begin to decline
gradually.
In other words, when using a fixed set of factors (capital, land) in combination
with a growing amount of a variable factor (labor ), the marginal productivity of this
factor will have an increasing trend at the beg inning and then , after will have reached a
point of maximum development will be decreasing . Here it should be noted that the
number of workers increases due to the need to increase production .
In the combination , we can distinguish synthesize and thus four stages (stages )
of the evolution of production (see figure no.1 ):
– Phase I, which is an increase of total production , media production and the
marginal , the latter being higher than average ; at the end of this phase, the maximum
output is marginal ;
– Phase II, where total and average production increase, but decreasing
increases as the marginal productivity begins to decrease, but maintaining higher than

258 Tobă, D.; Simion, D.

average ; This phase ends when the marginal productivity is equal to the average , the
latter thus achie ving maximum ;
– Phase III, corresponding to increasing developments still to total production
and decreasing productivity developments and marginal environments , the latter
becomes lower than average , but maintaining positive ; at the end of this phase
marg inal productivity is zero , at which total output is maximum ;
– Phase IV, called irrational phase , where total production is reduced due to
negative marginal productivity , ie the use of additional units of a variable factor not
result in an increase in prod uction , but with a drop of it.

Q

max

Qt

I II III IV W mL
L
0
WmgL

Figure 1.

For better illustration, we use the hypothetical data in Table 2.
Thus, assuming that in an economic activity, a trader has a certain amount of
capital (K) – as fixed factor and variable workload (L), microeconomic indicators (total
production – Qt; average productivity – Wm; marginal productivity – WMG, total cost –
Ct; marginal cost – CMG, marginal income – GMI, marginal profit – Pmg and tot al
profit – Pt) will be the trend evelopments in the table above. It should also be noted that
the market unit price of products is 100 um / tonne and the average cost of one unit of
labor salary is 2000 um / worker. For ease of analysis, in terms of costs with other
factors – land, capital, we considered conventionally, they are void.
The next question is : which of the variants combining shown in the table above
provides profit maximization (optimum manufacturer) ?
Optimum manufacturer is equivalent to steady state , because in this case he is
not forced to seek another solution. Specifically, it is the production version , which
provides the biggest difference between the proceeds and costs of production , so a
maximum profit .

Considerations Regarding the Calculation and Evolution of Labor … 259

Table 2.

K L
Qt
(tone) Wm
(tone) Wmg
(tone) Ct
(u.m.) Cmg
(u.m.) Vmg
(u.m.) Pmg
(u.m.) Pt
(u.m.)
10 2 30 15,0 – 4000 2000 – – -1000
10 3 53 17,6 23 6000 2000 2300 300 -700
10 4 78 19,5 25 8000 2000 2500 500 -200
10 5 105 21,0 27 10000 2000 2700 700 500
10 6 130 21,6 25 12000 2000 2500 500 1000
10 7 153 21,8 23 14000 2000 2300 300 1300
10 8 175 21,9 22 16000 2000 2200 200 1500
10 9 195 21,6 20 18000 2000 2000 0 1500
10 10 210 21,0 15 20000 2000 1500 -500 1000
10 11 223 20,2 13 22000 2000 1300 -700 300
10 12 233 19,4 10 24000 2000 1000 -1000 -700
10 13 233 17,9 0 26000 2000 0 -2000 -2700
10 14 230 16,4 -3 28000 2000 -300 -2300 -5000
10 15 228 15,2 -2 30000 2000 -200 -2200 -7200

In our case , the best option is the production where combines two units of
factor earth ( Ha) with 10 units of capital factor (K) and 9 units of labor factor (L). In
this case , it is observed that when the marginal cost and marginal revenue variable
factor obtained equalize , the total profit of the manufacturer is best. So when the
combination is betwe en a variable factor (usually labor) and one or more fixed factors
(capital, land), the condition of profit maximization is:
VMG = CMG or VMG – CMG = 0, ie Pmg = 0.
The analysis of the figures in the table allows to formulate some important
conclusions on economic behavior (rational) the manufacturer :
 Any increase in total production over the considered optimal (in our
case, 195 tons), under the circumstances , it is irrational in economic
terms , because it will result in a decrease in profit , leading to losses.
 As long as the marginal cost is lower salary amount from the sale of
marginal product (marginal revenue), the manufacturer is interested to
increase production by increasing the workload , as each additional unit
of labor brings a marginal profit , falling within composition of the
total profit .
 When marginal productivity is higher than average , the latter has an
upward trend, and when you are equalized (WMG = Wm), average
productivity peak. From this level, the marginal productivity falls
below average productivity , the latter starting to have a downward
trend .
 However, when the marginal productivity becomes invalid, total
production is at a maximum , and when the marginal productivity
becomes negative , total production begins to decline.

260 Tobă, D.; Simion, D.

3. ACKN OWLEDGEMENT

"This work was partially supported by the grant number 23C/2014, awarded in
the internal grant competition of the University of Craiova"

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