Advances in Systems Science and Application (2015) Vol.15 No.3 220-232

Labour Market Model — Focused on Final Products

A.Oinarov1, S. Baizakov2, N.Baizakov3 and Jeffrey Forrest4

1 The Board of JSC “Kazakhstan Public-Private Partnership”
2 Economic Research Institute, Str. Temirkazyk 65, Astana, 0100000, Kazakhstan;

3 Association for “Leadership in Education Development”, 36 Saraishyk street, apt 105,
Astana, 0100000, Kazakhstan;

4 School of Business, Slippery Rock University, Slippery Rock, PA 16057, USA.

Abstract

This paper studied history of development of commodity and cash flows balanc-
ing models. Keynesian model , monetary model and Mundell-Fleming model are
investigated, the issues of mutual consistency of indicators of economic growth is
studied. At the same time , the mathematical formulation of market equilibrium
of levels of production, employment, incomes and prices is gives. A new model
of labour market focusing economy on the final product is established.
Keywords Labour market; Gross output; Labour-intensity of products; Interindus-
try balance; Final product

1 Market Imbalance Theory is an Instrument to Identify Macroeconomic
Imbalances

This section studied history of development of commodity and cash flows bal-
ancing models. There are assumptions that adequately reflected development of
market forces of economic development. Relationship between indicators of eco-
nomic growth in both sectors of the economy was established. If Keynesian model
developed a balance between real economy and financial economics by using only
one indicator, then monetary model used two, and Mundell-Fleming model used
three indicators of economic growth. It also studied the issues of mutual consis-
tency of indicators of economic growth.

Historically, analysis of production repeatability since 40-ies of the last century
was conducted based on Keynesian model, which assesses the market equilibrium
between commodity and cash flows. Using this model as an anti-crisis tool to
eliminate the consequences of the Great Depression of the US economy in the
1930s is associated with the name of the US President F. Roosevelt. Circuit
diagram of the replenishment cycle of this model is shown in Figure 1.

According to Keynesian model we may admit the constancy of prices for goods
and services, and consider investment growth and increase in other consumption
costs as an impetus for economic development by the state. As prices for goods
and services are constant, commodity and cash flows balancing based on this
model is carried out due to one indicator - nominal GDP. In other words, e-
conomic growth indicator is nominal GDP, which serves as an indicator of real



Advances in Systems Science and Application (2015) Vol.15 No.3 221

economic growth, as prices are constant, and volumes of real GDP and nominal
GDP are the same because of constant prices.

Fig.1 Principle circuit diagram of the replenishment cycle of Keynesian model

Fig.2 Principle circuit diagram of the replenishment cycle of monetary model

In the mid-80s of the last century a model of economic management has



222 A.Oinarov, S. Baizakov, N.Baizakov and Jeffrey Forrest: Labour Market Model — Focused...

changed. Keynesian model was replaced by more progressive model - a mod-
el of monetary policy. The reason of progressivity of monetary model was that
it considered variability of prices of goods and services that was clear in real life
and which is a key advantage of the market economy.Conditions of goods and
services are rapidly renewed because of the influence of market competition of
goods and services, and there will be their new prices, and prices of previous
goods and services will change due to scientific and technological progress.

Monetary model in production repeatability analysis started to be actively
used since the 1980s. Its appearance on practice of economic management of the
country is associated with the name of the President of R. Reagan. Monetary
model means constant money velocity and it uses two GDP indicators: nomi-
nal and real. A real GDP is defined in prices of basic year and characterizes
the dynamics of market forces of real economy. A nominal GDP is defined in
prices of the year and characterizes the dynamics of market forces of monetary
and financial system. GDP deflator connects their balancing between each other.
But later it is turned out that a weak point of the model of monetary policy
is assuming the constancy of money velocity, which is considered as a basis for
monetary model.

Fig.3 Principle circuit diagram of the replenishment cycle of monetary model



Advances in Systems Science and Application (2015) Vol.15 No.3 223

Multinational companies and companies with developed foreign trade relations
started to see the narrowness of this model during their economic analysis. In
this regard, since the 1990s of the last century Fleming - Mundell model was used,
which overcame limitations of the monetary model. The advantage of Fleming -
Mundell model is that it admits that money velocity is dynamic. However, this
model again assumes the constancy of prices for goods and services.

Production repeatability analysis according to Fleming - Mundell model (since
1990) considers dynamics of exchange rate, which serves as a reliable development
instrument of international relations of the world countries. It uses three GDP
indicators: nominal, real and GDP based on purchasing power parity; Figure 3
shows a principle circuit diagram based on Fleming - Mundell model.

Firstly, Mundell-Fleming model assumes that prices are constant, and sec-
ondly, it links three GDPs to each other. To ensure conceptual relationships of
three GDPs and stop assuming that prices for goods and services are constant,
market equilibrium of levels of production, employment, incomes and prices was
established.

Fig.4 Principle circuit diagram of the replenishment cycle of Kazakhstan model
of double regulation



224 A.Oinarov, S. Baizakov, N.Baizakov and Jeffrey Forrest: Labour Market Model — Focused...

A new model of market equilibrium of levels of production, employment, in-
comes and prices in employment terms summarizes Keynesian, monetary and
Fleming - Mundell models, and do not contradict their structure principles, but
develops them.

2 Economic Content of Kazakhstan Model of Double Regulation

This section gives mathematical formulation of market equilibrium of levels of
production, employment, incomes and prices.. A new model of labour market fo-
cusing economy on the final product is established, which is shown in the example
of the Republic of Kazakhstan. It explains why the market forces of labour and
capital are developing according to the laws of free competition despite wishes of
entrepreneurs to increase competitiveness of their companies.

An article of American Scientists was published in the column ”New World
Order” in magazine ”Foreign Affairs” about ”labour, capital and ideas in econo-
my of power laws”, which states that the future belongs not to those who provide
cheap labour or owns capital (they will be driven out by automation), but to
those who are willing to introduce innovations and create products, services and
business models based on them. New technologies do not only integrate existing
sources of labour and capital, but also generate products that replace both labour
and capital.

According to the authors of the article, innovations in the nearest future, will
lead to great changes, associated with distribution of incomes, as profit sources
will be represented by high technology and globalization, in which this process is
usually demonstrated as power laws. In this case, an employee in the USA will
receive the same salary as employees working in the industrial sector in China or
India. This is good news for developing countries, and problem for the United
States and Europe, where there are no possibilities of reducing production costs
and monetary growth.Can Kazakhstan take advantage of the situation in the new
world order?

Economic Research Institute (Kazakhstan) applies a system of techniques to
do forecasting and analysis. Innovative model of the labour market plays an im-
portant role in it, which is focused on the final result. Top modules of balance
labour model are coefficients of direct labour intensity of products. To measure
labour intensity we can use the unit of man-hours, man-years or jobs, and for
their calculation we can use the table ”Input - Output”, which are produced in
Kazakhstan every year:

ti =
Li

Xi
, i = 1, n (1)

where ti - coefficients of direct labour intensity of products; Li - number of people
employed in the economy; Xi - gross output.



Advances in Systems Science and Application (2015) Vol.15 No.3 225

To measure labour intensity we can use the unit of man-hours, man-years or
jobs.

Full coefficients of labour intensity per unit of production are calculated by
coefficients of direct labour intensity:

Tj =

n∑
i=1

aijTi + tj , i, j = 1, n (2)

where aij - input-output coefficient i type of economic activity for issue j type
of economic activity; Ti, Tj - full labour intensity coefficients for production of Yi
or Yj - component of final product - Y ;

If we consider that coefficients of direct t = (t1, t2, . . . , tn) and full T =
(T1, T2, . . . , Tn) labour intensities are raw vectors, then the ratio (2) can be writ-
ten in matrix form:

T = TA+ t (3)

or
T = t(E −A)−1 (4)

where E is identity matrix, A is matrix coefficient, representing production pro-
cess technology of this year. (E −A)−1 - input coefficient matrix of production
processes represented by full material costs in the table of interindustry balance.
Labour intensity turns into full material costs in accordance with duality princi-
ple of Koopmans and Kantorovich.
If we introduce a notation = (E −A)−1 then formula (4) can be rewritten as
follows:

T = tB (5)

As it is seen from the formula, the only link between direct and full labour
intensity indicators of products is still input coefficient matrix of production
processes. It means that coefficients of of full labour intensity of each goods and
services provided are very important, which reflect the influence of production
processes.

If we consider L as a number of jobs in all sectors of national economy and
apply module (1), we will get the following formula to calculate a number of
people employed in the economy:

L =

n∑
j=1

Lj =

n∑
j=1

tjXj = tX (6)

where X is gross output of goods and services.
If in formula (1) we marked a number of people employed in the economy by

the components of raw vector Li, then we can have the record shown in formula



226 A.Oinarov, S. Baizakov, N.Baizakov and Jeffrey Forrest: Labour Market Model — Focused...

(6) by representing the same number of people employed in the economy as that
of components of raw vector j.

If we multiply both sides of (5) by Y-final vector of production, we can have
the following model of the labour market:= tBY . And if we take into account
the formula (6), then balancing model will have a complete form, where the basic
law of labour market and capital is reflected:

tX = TY (7)

On the other hand, a similar assessment on the level of national economy of
the country represents the average value formed by the ratio of nominal GDP to
gross output:

c =
t

T
=

Y

X

Left side (7) is equal to TY where T according to formula (5) is full labour
intensity of products, nd Y is the final product. And the cost of the final product
is considered to be equal to nominal GDP. Right side (7) is equal to tX where
t according to the module (1) is direct labour intensity of products, nd is gross
output of goods and services provided. Based on this simple formula the yield of
GDP (CDP (t)) is estimated as per turnover unit - X(t).

In fact, the gross output value X(t), which was correctly identified by famous
American scientist Harrington Emerson in his main work “Twelve principles of
productivity” (1911), at business level it is ”total expenditure = material costs
+ labour costs + capital costs.

Or:
total expenditure =QP+TW+TR;

where compensation for intermediate materials, and other current material
resources, used during production of goods is QP; remuneration of labour
costs of employees is TW; remuneration of fixed capital is TR.

Thus, there is relationship between the final product and overall costs to create
it - X. So, by putting in place of t in the formula (7) its value from the formula
(1) we will have t = L/X. Then we will have L = TY . It means that a number of
people employed in the economy is equal to multiplication of full labour intensity
of products by nominal GDP. And full labour intensity of products is T , which
in turn, is determined by multiplication of direct labour intensity of products - t
to full costs matrix.B = (E −A)−1.

Multiplicationt X according to (6) alsomeans number of working time fund
used or number of jobs on economic activity, which are required to produce gross
output (X), necessarry for production of the final product (Y ).

On the one hand, development model of the labour market (7) defines the



Advances in Systems Science and Application (2015) Vol.15 No.3 227

marginal valuation of the ratio of direct and full labour intensity of products for
every type of economic activity, on the other - a similar assessment at the level
of national economy of the country represents the average value, formed by the
ratio of nominal GDP to gross output:

t/T = Y/X (8)

A number of people employed in the economy of state is similar to the total
number of employees in all economic activities. Therefore, new interpretation
of the main situation of the market in labour terms is calculated by the model
(7), which is completed by equation (8). In this case, the share of direct labour
intensity of goods and services in their full labour intensity is equal to the level
of production of the final product (Y ) in the gross output (X).

As a rule, destructive forces of laws of market equilibrium appear in macroeco-
nomic imbalances, which are easily detected by analytical tools built on the basis
of the table of interindustry balance. Thus, according to the above formula (5),
full material costs matrix allows to turn actual labour used during production of
gross output (X) into abstract labour. However, this abstract labour, expressed
in full labour intensity of products is needed to evaluate the effectiveness of pro-
duction of a particular amount of the final product (Y ).

As defined in formula (1), direct labour intensity is expressed by the ratio of
a number of people employed in every economic activity to the total volume of
gross output, issued in this sector. Multiplication of raw vector of direct labour
intensity of a particular type of human activity by inverse matrix of material
costs expresses a column vector of full labour intensity of production of the final
product (Y)). Figure 5 shows a piece of values of direct and full labour intensity
of products for certain types of economic activity of Kazakhstan for 2012.

As we can see from the diagram, the first indicator reflects the specific amount
of jobs (man-years, man-hours, man-days) required to produce 1 million tenge
worth of gross output. For example, in agriculture, hunting and forestry, it
amounted for 965 jobs, and in production area of crude oil and natural gas - only
10. Figure 5 also shows that full labour intensity is greater in number than direct
labour intensity.

This is due to the fact that the first indicator reflects abstract labour that
expresses the social form of unit cost of the final product produced, and the
second represents economy of a particular type of human activity. Here, the
“black box”, which allows you to transfer direct labour intensity (t) into full (T )
is represented by inverse matrix of interindustry balance (B), T = t ∗ B. It also
makes it possible to determine rapid development of technological improvement
of production, since it is its dynamics (τ) that is a factor defining the rapidness
of this process. That is why the advantages of new Kazakh model, focused on



228 A.Oinarov, S. Baizakov, N.Baizakov and Jeffrey Forrest: Labour Market Model — Focused...

the final result, are provided on the basis of analytical calculations, conducted
using reverse (τ)-matrix. The results are shown in Table 1.

Fig.5 Diagrams of the values of direct and full labour intensity, defined on the
basis of the table of interindustry balance of Kazakhstan for 2012.

The first three columns show the components of final demand, translated into
jobs, and the fourth column reflects total results. Thus, we see that to cover
final consumption, to have gross savings, and to attract export of the national
economy we will require 6903.22, 1907.75 and 2227.89 thousand jobs, respectively.
In general, the final demand (fourth column) can be satisfied if Kazakhstan will
have more than 11 million jobs. Since supply of the country’s economy, according
to the data of interindustry balance of 2012, is amounted to just tX = 8507000
jobs in total, then to cover the final demand of the economy additional capacity
will be fully required, which must be repaid by import financing of foreign goods
(the fifth column).

In general, as we can see from the sixth column, Kazakhstan’s jobs defined on
the basis of labour intensity of product in calculation equal to 1 million tenge
worth gross output ( by economic activity) significantly deviated from the jobs
defined on the basis of full labour intensity (Y ). However, their ratio (direct
labour intensity - 0,177 jobs, full - 0.298) in terms of the national economy is
equal to the ratio of scientific and technological excellence of real sector of the
country, because we have the equation:

c =
t

T
=

L

X
+

L

Y
=

Y

X
(9)



Advances in Systems Science and Application (2015) Vol.15 No.3 229

Index value of the level of scientific and technological excellence of real sector
of the country for Kazakhstan is 0.587. This equation (9) of market equilibrium
of levels of production, employment, incomes and prices in man terms is based
on the balance of aggregate demand and aggregate supply.

Final demand in the economy of the country is generally determined by total
costs of final consumption of households (Y 1), general government costs (Y 2),
non-profit organizations (Y 3), changes in inventories (Y 4), purchase minus re-
tirement of valuables (Y 5), gross saving of fixed capital (Y 6) and export (Y 7).

Final demand = Y 1 + Y 2 + Y 3 + Y 4 + Y 5 + Y 6 + Y 7

An aggregate supply, which is used to cover it, is defined as total of final demand
and import with a minus sign (−Y 8):

Final product =
∑

Y i− Y 8

Thus, market equilibrium of levels of production, employment, incomes and prices
is carried out by all agents of production, exchange, distribution and consump-
tion. For example, to measure performance of the economy in working time we
have the results of final demand in Kazakhstan: 11,005,000 people. (8.505 mil-
lion of which is covered by human resources within the country, and 2.5 million
- beyond the country). Volumes of aggregate demand and aggregate supply are
balanced, and they are equal to the work of 11,005,000 people, while direct labour
intensity of products for production of 1 million tenge worth gross products in
Kazakhstan in 2012 amounted to 177 people, and full labour intensity - 298 peo-
ple.

This equilibrium in formula (9) is defined in current prices and it expresses a
market equilibrium. To assess the level of economic development of the country
comparison base in comparable prices or quantum indexes should be determined
based on this level. Since nominal GDP (NGDP) is monetary terms of the final
product and is defined in prices of this year, then, multiplying both sides of a
well-known equation of GDP deflator: NGDP = b∗RGDP by purchasing power
(pp), real value of the final product (Q) can be defined, which corresponds to the
balance of supply and demand in the country:

Q = pp ∗NGDP = c ∗RGDP,

where c = pp ∗ pb = RGDP
X ∗ NGDP

RGDP = RGDP
X

(10)

The main indicator of equation (10) is an indicator of scientific and techno-
logical progress (STP) - c. Its multiplication by real GDP is identical to mul-
tiplication of nominal GDP with purchasing power. It turns out that STP’s
contribution helped to divide GDP deflator into two indicators. One of them



230 A.Oinarov, S. Baizakov, N.Baizakov and Jeffrey Forrest: Labour Market Model — Focused...

is purchasing power, the other is coefficient of scientific technological progress
itself. As a result, the formula (10) balances the final product both in terms of
money and terms of commodity. It is developed by generalizing and developing
the equation of exchange of monetarists, which do not contradict its structure
principles, but there are variables that are also represented by purchasing power
and an STP index at real GDP. It means that the cost of the final product is equal
to the nominal value of the product, i.e.Q = pp*NGDP. Therefore, multiplying
both sides of equation NGDP = pb ∗ RGDP by purchasing power, a balance
between nominal and real GDP can be set with weighing coefficient pp and c,
respectively:

pp ∗NGDP = c ∗ RGDP (11)

It explains the viability of creative formula of scientific and technological
progress:

ċ

c
=

Ẏ

Y
− Ẋ

X
(12)

Rapid change of STP coefficient in equation (12) depends on difference in speed
of the final product and gross output.

Let us assume that principle of using direct and full labour intensity to deter-
mine technical and technological excellence of the national economy is applied in
the countries all over the world, which have developed foreign economic relation-
s. Then value of the dollar, euro, Kazakhstani tenge and other currencies will
be established according to the level of economic development within the state
itself and its foreign relations. In this case, assessment principle of STP level
deviations between the countries can be preserved, and real exchange rates of the
national currencies will be set in accordance with rules of SDR design. Such an
approach can serve as an effective tool for building a methodology for sustainable
development of the global economy: measured economy is managed economy.

In conclusion, it can be summarized that it is possible to construct an analyti-
cal model for managing a market economy. It can be built in labour terms using
the principle of double regulation and the table “input-output”.

Thus, balances of commodity and cash flows on economic activity in labour
terms are formed with imbalances:

ti ∗Xi − Ti ∗ Yi = ±Θi

And at the level of the national economy of the state commodity and cash flows
are always balanced: ∑

ti ∗Xi −
∑

Ti ∗ Yi = 0

where components of final demand are Yi defined, and their total value is the
final demand, which corresponds to the final product of the country.



Advances in Systems Science and Application (2015) Vol.15 No.3 231

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232 A.Oinarov, S. Baizakov, N.Baizakov and Jeffrey Forrest: Labour Market Model — Focused...

These balance equations fully meet the conditions of globalization of the world
economy and can be used to ensure market equilibrium of the levels of production,
employment, incomes and prices anywhere in the world. The construction of an
analytical model of market forces for development of real sector and financial sys-
tem based on parity of their autonomous and parallel operation is the final result
of this study.

Corresponding author
S.Baizakov can be contacted at: baizakov37@mail.ru