The Characteristics of the Evolution of the Economical Indicators

Munich Personal RePEc Archive

The Characteristics of the Evolution of the Economical Indicators

Stegaroiu, Carina-Elena

“Constantin Brâncuşi “ University of Târgu Jiu, Faculty of Economic Sciences

10 October 2008

Online at https://mpra.ub.uni-muenchen.de/12912/

MPRA Paper No. 12912, posted 22 Jan 2009 05:48 UTC

The Characteristics of the Evolution of the Economical Indicators

Carina-Elena STEGĂROIU

“Constantin Brâncuşi “ University of Târgu Jiu Faculty of Economic Sciences

Târgu Jiu, 24, Victoriei Street, Gorj, Romania carinastegaroiu@yahoo.com

Abstract: After the criterion of time to examine the evolution of the indicator values that can be given at the time (eg number of human population in year t) or the time (eg GDP in year t). The indicators characterizing economic development are absolute growth, growth rate, the rate increase.

Keywords: indicators economic, absolute growth, growth rate, rate increase.

INTRODUCTION

In order to extend the analysis methods applied in absolute economic growth indicators, the pace of growth, the pace of growth may be examined in the case continue. This allows the use of differential calculus.

In an economic analysis importance acceleration has a specific indicator, that is required to determine the acceleration of change indicator of the absolute growth.

Evolution absolute increase in time can be represented by a constant growth, increasing, decreasing, increasing the qualitative changes.

STRUCTURE RESEARCH

Evolution economic indicator Y can be represented as a function of time (Figure 1).

Fig.1. Indicator values are a function of time

The argument t may be represented intervals or, if the analysis is subject to retrospective and then ranges may be

(

^−∞;0

]

^;

(

^−∞;T

]

^;

[

−T1^;0

]

;

[

−T1;T2

]

;

[

−T₁;∞

)

. Y indicator values can be continuous or discrete. After the criterion of time to examine the evolution of the indicator values that can be given at the time (eg. number of human population in year t) or the time (eg. GDP in year t).

The indicators characterizing economic development are absolute growth, growth rate, the rate increase.

Absolute growth

(

^δ₁₀

)

is the difference between the indicator values Y in the base year t=0, ie

0 1 10 =Y −Y

δ (Figure 2).

Y(t)

Y(t)

t 0

Fig.2. Absolute increase in the (0; 1)

The pace of growth

(

η₁₀

)

he called indicator is a de facto economic index or growth factor that determines how often the Y₁ year t =1 exceeded the mean Y₀,

0 1

10 Y

= Y

η (Figure 3; 4; 5)

Fig.3 The pace of growth indicator

Fig.4 The pace of growth indicator

1

0 1 10 = >

Y

η Y 1

0 1 10 = <

Y η Y

Fig.5 The pace of growth indicator 1

0 1

10 = =

Y η Y

In other words, the pace of growth is equivalent to the percentage indicator Y₁ from Y ,₀

% 100

0 1

10= ⋅

Y

η Y .

The pace of growth

(

ρ₁₀

)

the increase is the absolute indicator ^Y₀ ie,

0 0 1

10 Y

Y Y −

ρ = (fig. 6; 7; 8)

Y(t) Y(t)

t = 0 t

0 1 10 =Y −Y

δ , absolute growth in the (0;1)

Y1

Y0 Y0

t = 1

t = 0 Y(t)

t = 1 t Y0

Y1

Y0

Y(t)

Y₀ Y₀

Y(t) Y1

t = 0 t = 1 t

Y(t)

Y0

Y₁ Y0

t = 0 t = 1 t

Fig. 6. The pace of positive growth Fig. 7. The pace of negative growth

Fig. 8. The pace of growth nul

The base year is an arbitrary and therefore he can maintain the same or may change. For each year considered, the previous year may have been an evolution for comparison. In this case the variable comparisons being made "in the chain". So characteristics: absolute growth, growth rate, growth rate can be calculated from the base year

(

t=0

)

, compared to the previous year

( )

t−1 .

Absolute growth, the pace of growth, the pace of growth indicator Y in , expressed in the prices of basic

(

,are:

)

t

=0 t

(

₀

)

0 Y_t Y

t = −

δ ;

0

0 Y

Y_t

t =

η ;

0 0

0 Y

Y Y_t

t

= −

ρ ;

expressed in the prices of the previous year –

1 1

,_t− = _t − _t−

t Y Y

δ ;

1 1 ,

−

− =

t t t

t Y

η Y ;

1 1 ,

1

−

−

− = ⁻

t Y t t

t Y

Y t

ρ .

Indicators, δ_t,t−1, η_t,t−1, ρ_t,t−1, compiled basic variable can be interpreted graphically (Fig.9).

Fig. 9. Indicators expressed "chain" discrete values

t = 0 Y(t)

t = 1 t Y0

Y1

Y0

Y(t)

Y0

Y1

t = 0 t = 1 t

t = 0 Y(t)

t = 1 t Y0 Y1 Y0

0 0

1−Y >

Y Y₁−Y₀ <0

0 0

1−Y

Y =

Y(t)

t = 0 1 t

Y0

Y1

Y0

0 1−Y Y

2 3 4

3

4 Y

Y −

2

3 Y

Y −

1

2 Y

Y −

Y4

Y3 Y3

Y2 Y2

Y1

Among the indicators δ_t0, η_t0, ρ_{tu ş}i δ_t,t−1, η_t,t−1, ρ_t,t−1 some may be established relationships:

The amount increases:

(

Y₁−Y₀

) (

+ Y₂ −Y₁

) (

+ Y₃−Y₂

) (

+ Y₄−Y₃

)

=Y₄ −Y₀ or

(

Y₁−Y₀

) (

+ Y₂−Y₁

)

+...+

(

Y_t −Y_t−1

)

+...+

(

Y_T −Y_T−1

)

=δ₁₀+δ₂₁+...+δ_t,t−1+

( )

∑ ∑

= − = −

− = ^T − = = −

t

T

t

T t t t

t T

T Y Y Y Y

1 1

0 1

, 1

1

, δ

δ +

+... ;

Differences:

(

^Y₂ −^Y₀

) (

− ^Y₁−^Y₀

)

=^Y₂ −^Y₁ or δ₂₀−δ₁₀ =δ₂₁

(

^Y₃−^Y₀

) (

− ^Y₂−^Y₀

)

=^Y₃−^Y₂ or δ₃₀−δ₂₀ =δ₃₂ Product:

0 1 1

2 3 1 2 0 1

Y Y Y

Y Y

Y Y

Y Y Y Y

Y _T

T T t

t ⋅ ⋅ =

⋅

⋅

⋅

⋅

−

−

K

K or

0 , 1 , 1

, 32

21

10 η η ηtt ηTT ηT

η ⋅ ⋅ ⋅K⋅ ₋ ⋅K⋅ ₋ = ; or

0 1 , 32 21

10 Y

Y_t

t

t =

⋅

⋅

⋅

⋅η η η ₋

η K where

1 , 32

21 10

0⋅ ⋅ ⋅ ⋅ ⋅ −

= _tt

t Y

Y η η η Kη ;

Catul:

1 2 0 1 0 2 :

Y Y Y Y Y

Y = or ₂₁

10

20 η

η η =

2 3 0 2 0 3 :

Y Y Y Y Y

Y = or ₃₂

20

30 η

η η ₌

...

1 0

1 0

:

−

− =

t t t t

Y Y Y Y Y

Y or _{, 1}

0 , 1

0 −

−

= _tt

t

t η

η η

...

1 0

1 0

:

−

− =

T T T

T

Y Y Y Y Y

Y or _{, 1}

0 , 1

0 −

−

= _TT

T

T η

η η

In order to extend the analysis methods applied in absolute economic growth indicators, the pace of growth, the pace of growth may be examined in the case continue. This allows the use of differential calculus.

Absolute increase in the case of discrete

1 1

,_t− = _t − _t−

t Y Y

δ or δ_t,t−Δt =Y_t −Y_t−Δt, at a time, ie

t Y Y t

t t t t

t t

Δ

= − Δ

Δ Δ −

,−

δ , the assumption that variable is still can move to limit:

Yt

( ) ( )

dt t dY t

Y t Y

t

t t t t t

t t

t =

Δ

= − Δ =

Δ

−

→ Δ Δ

−

→

Δ 0

,

0 lim

limδ δ

The pace of growth in case of discrete

1 1

,

− Δ

− −

= −

t t t t t

t Y

Y

ρ Y au

t t

t t t t t

t Y

Y Y

Δ

− Δ Δ −

−

= −

ρ, , calculated values proceed, can be written

( ) ( )

dt t Y d Y

t Y Y t

t t

t t t

t

lim ln

0 Δ =

−

=

Δ

− Δ

−

→

ρ Δ .

As an established , (figure 10) is the increase (or decrease) indicator in a unit of time, that is the speed of change.

t , 1 t+

δ δ_t,t−1 Y

Fig. 10. Speed, acceleration change indicator

Velocity difference

(

δt_+1,t −δt_,t₋₁

)

=ϕt is the acceleration of change indicator Y. The difference in unit time can be written:

t t t t t t t

tδ ϕ

δ =

Δ

− _−Δ

Δ

+ , ,

Since the assumption Y that a function is continuous

( )

( )

2 2 ,

, 0

lim dt

t Y d dt d t

t t

t t t t t t

t = = =

Δ

− _−Δ

Δ +

→ Δ

ϕ δ δ

δ

In an economic analysis importance acceleration has a specific indicator, that is required to determine the acceleration of change indicator of the absolute growth

t t

t t t t

Y Y −

−

+

− +

1 1 , ,

1 δ

δ (Fig. 11)

Fig. 11. Acceleration relative

From fig. 11:

( ) ( )

t t

t t t

t

t t t t t

t t t t t

Y Y

Y Y Y

Y

Y Y Y Y Y

Y −

− −

− =

−

−

= −

−

−

+

− +

− +

+

− +

1 1 1

1 1

1 1 , ,

1 δ 1

δ

Since assuming that Y is continuous variable gain:

( )

( ) ( )

dt t dlu t

dt t

d δ

δ δ

= .

CONCLUSIONS

In this case the economic intervals increases are growing in others - in decline.

Y(t)

t = 0 t + 1 t

1 t

t t+1,

δ

1 ,t−

δt

1 t – 1

Y(t)

t = 0 t + 1 t

1 t

1 ,− , +1_t− _tt

t δ

δ

t – 1

1 ,t−

δt

1 ,t−

δt t t+1,

δ

Bibliography:

1. Brian, W – Systems: Concepts, Methologies, and Applications, vol.1, John Wihley&Song, 2002;

2. Maximilian, S – Mathematical modeling of economic processes, Editura State University of Moldova, [Modelarea matematica a proceselor economice, Editura Universitatii de Stat din Moldova], Chisinau, 2006;

3. National Institute of Statistics, Statistical Yearbook 2007, Bucharest [Institutul National de Statistica, Anuarul statistic 2007], Bucuresti, 2008