# How to Express and to Measure Whether an Economic System Develops Intensively

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Comprehensive Analysis of Relations between Inputs, Productivity of Inputs, and Outputs of a System

^{α}·L

^{(1 − α)}

- Pure developments, which are situated on coordinate axes of Figure 3. The product only grows or declines as a result of one of the factors under consideration, either purely extensively or purely intensively. The other one remains unchanged, i.e., I(TIF) = 1 (for a purely intensive change) or I(TFP) = 1 (for a purely extensive change). Pure developments can be further distinguished to pure growth and pure decline. Pure extensive growth (I(TIF) > 1 and I(TFP) = 1) is indicated by the positive ray of axis x, while pure extensive decline (I(TIF) < 1 and I(TFP) = 1) is indicated by the negative ray of axis x. Similarly: purely intensive growth (I(TFP) > 1 and I(TIF) = 1) is indicated by the positive ray of axis y, while purely intensive decline (I(TFP) < 1 and I(TIF) = 1) is indicated by the negative ray of axis y.
- Balanced developments. Both factors under consideration have the same effect, i.e., I(TIF) = I(TFP). In Figure 3, these developments are situated in quadrants I and III on a straight line at the angle of 45 degrees, which intersects the origin of coordinate axes. The developments can be further distinguished to intensive–extensive growth and intensive–extensive decline. The former is represented by the positive section of the straight line at the angle of 45 degrees, the later by negative section of this straight line.
- Compensatory developments. Both factors fully compensate each other into product stagnation, i.e., I(Y) = 1, and thus I(TFP) = 1/I(TIF). These developments lie on the hyperbolic isoquant of product stagnation (see above). The upper half of the hyperbola represents intensive–extensive compensation where I(TFP) > 1 and I(TIF) < 1. The lower half of hyperbola represents extensive–intensive compensation—where I(TFP) < 1 and I(TIF) > 1.

- The nomenclature must cover all types of developments.
- If the system product (output) grows, we use the word “growth”; if it declines, we use the word “decline”; if it remains unchanged, we use the words “pure compensation”.
- We refer to all basic developments as “pure”.
- When referring to consonant developments, i.e., those where both factors drive growth or both factors drive decline in system output, but they do so unequally, we use the word “predominantly”, and use the name of the predominant factor. This means that predominantly intensive growth indicates the situation where both factors (I(TIF) and I(TFP)) drive growth, but the impact of intensive factors is greater than that of extensive factors. Likewise, predominantly extensive decline depicts the situation where both factors (I(TIF) and I(TFP)) drive decline, but the impact of extensive factors is greater than that of intensive factors.
- When referring to dissonant developments, i.e., those where one factor drives growth and the other drives decline in system output, we use the word “compensation” or “compensatory”.
- If the names of combined compensatory or purely compensatory developments concurrently include the words “intensive” and “extensive”, we use—as the first of the words intensive and extensive—the one which drives growth, followed by the one that drives decline. For instance, the term intensive–extensive compensatory growth refers to the situation where the intensive factors grow so rapidly that they partly compensate a decline in the extensive factors, thus making the system grow in the end (see the situation above, where I(Y) > 1 and at the same time I(TFP) > 1/I(TIF)), with I(TIF) < 1 and at the same time I(TFP) > 1. Likewise, an intensive–extensive compensatory decline indicates the situation where the intensive factors grow while the extensive factors decline, making system output decline in the end. In this logic, a pure intensive–extensive compensation shows the situation where the intensive factors drive growth and the extensive factors concurrently drive decline, making the system output stagnate in the end (a pure extensive–intensive compensation defines the opposite situation, where the extensive factors drive growth, the intensive factors drive decline, making system output stagnate again).

## 3. Dynamic Parameters of Intensity and Extensity

## 4. Comparison Our Approach with Other Methods to Quantify Impact Intensive and Extensive Factors

_{k}K + MPP

_{l}L

_{k}is the marginal product of capital and MPP

_{l}is the marginal product of labor.

_{f}, they divide the TFP growth rate by the rate of GDP growth G(Y). For the share of the impact of intensive factors, we will thus obtain the expression

## 5. Results

- Using the three initial growth rates, we calculate the average growth rate for the entire period.
- We calculate the growth rate of capital labour equipment G(K/L) using the equation$$G\left(\frac{K}{L}\right)=\frac{G\left(K\right)+1}{G\left(L\right)+1}-1.$$
- We calculate the growth rate of the aggregate input factor G(TIF) using the equation$$G\left(TIF\right)=\sqrt{\left(G\left(K\right)+1\right)\xb7\left(G\left(L\right)+1\right)}-1.$$
- We calculate the growth rate of aggregate productivity G(TFP) using the equation$$G\left(TFP\right)=\frac{G\left(Y\right)+1}{G\left(TIF\right)+1}-1$$
- The dynamic parameters of intensity and extensity and dynamic parameters of the share of the influence of the labor or capital development on the TIF development are calculated according to Equations (8) and (9).

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Different values of Equation (11) and the dynamic parameter of intensity for purely intensive–extensive growth or decline (in %). Source: authors.

Purely Intensive–Extensive Growth | Purely Intensive–Extensive Decline | ||||||||
---|---|---|---|---|---|---|---|---|---|

G(SPF) | G(SIF) | G(Y) | i_{f} | i | G(SPF) | G(SIF) | G(Y) | i_{f} | i |

1 | 1 | 2 | 50 | 50 | −1 | −1 | −2 | 50 | −50 |

5 | 5 | 10 | 49 | 50 | −5 | −5 | −10 | 51 | −50 |

10 | 10 | 21 | 48 | 50 | −10 | −10 | −19 | 53 | −50 |

15 | 15 | 32 | 47 | 50 | −15 | −15 | −28 | 54 | −50 |

20 | 20 | 44 | 45 | 50 | −20 | −20 | −36 | 56 | −50 |

**Table A2.**Different values of Equation (11) and the dynamic parameter of intensity for purely extensive–intensive compensation or purely intensive–extensive compensation (in %). Source: authors.

Purely Extensive–Intensive Compensation | Purely Intensive–Extensive Compensation | ||||||||
---|---|---|---|---|---|---|---|---|---|

G(SPF) | G(SIF) | G(Y) | i_{f} | i | G(SPF) | G(SIF) | G(Y) | i_{f} | i |

1 | −1 | −0.01 | −10,000 | 50 | −1 | 1 | −0.01 | 10,000 | −50 |

5 | −5 | −0.25 | −2000 | 50 | −5 | 5 | −0.25 | 2000 | −50 |

10 | −10 | −1.00 | −1000 | 50 | −10 | 10 | −1.00 | 1000 | −50 |

15 | −15 | −2.25 | −667 | 50 | −15 | 15 | −2.25 | 667 | −50 |

20 | −20 | −4.00 | −500 | 50 | −20 | 20 | −4.00 | 500 | −50 |

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**Figure 1.**System output as the product of system total input factor and system total factor productivity. Source: authors.

**Figure 2.**Plot of the area for development typology of I(Y), I(TIF) and I(TFP. Source: authors. The scope of indices for both factors (I(TFP) and I(TIF)) is selected within the range of (0; 2) i.e., from the output decrease, through output stagnation, to output growth to a double.

**Figure 3.**Detailed description of basic types of development I(Y), I(TIF) and I(TFP). Source: authors.

**Figure 4.**Representation of basic and combined types of development I(Y), I(TIF), and I(TFP). Source: authors.

**Figure 5.**The complex nomenclature of all basic and mixed relationships among I(Y), I(TIF), and I(TFP). Source: authors.

**Figure 6.**Comparison of expressions of development intensity using expressions (5) and (11). Source: authors. RÚ = growth accounting values according to expression (11), DP = values of dynamic parameter of intensity according to expression (5). Quadrant assignments: 0 to 90: quadrant I (top right), 90 to 180: quadrant II (top left), 180 to 270: quadrant III (bottom left), 270 to 360: quadrant IV (bottom right).

**Table 1.**Overview of individual types of development I(TIF) and I(TFP) and values of dynamic parameters of intensity and extensity. Source: authors.

Change of Extensive Factors (I(TIF)) | Change of Intensive Factors (I(TFP)) | Change of Output (I(Y)) | Values of Intensity (i) and Extensity (e) | Type of Development | |
---|---|---|---|---|---|

11 | growth, (I(TIF) > 1) | unchanged, (I(TFP) = 1) | growth, (I(Y) > 1) | e = 1; i = 0 | pure extensive growth |

22 | unchanged, (I(TIF) = 1) | growth, (I(TFP) > 1) | growth, (I(Y) > 1) | e = 0; i = 1 | pure intensive growth |

33 | same growth as intensive ones, (I(TIF) > 1, I(TIF) = I(TFP)) | same growth as extensive ones, (I(TFP) > 1, I(TFP) = I(TIF)) | growth, (I(Y) > 1) | e = 0.5; i = 0.5 | pure intensive–extensive growth |

44 | faster growth than intensive ones, (I(TIF) > 1, I(TIF) > I(TFP)) | slower growth than extensive ones, (I(TFP) > 1, I(TFP) < I(TIF)) | growth, (I(Y) > 1) | e > 0; i > 0; e > i | predominantly extensive growth |

55 | slower growth than intensive ones, (I(TIF) > 1, I(TIF) < I(TFP)) | faster growth than extensive ones, (I(TFP) > 1, I(TFP) > I(TIF)) | growth, (I(Y) > 1) | e > 0; i > 0; i > e | predominantly intensive growth |

66 | is greater than inverted value of intensive ones, (I(TIF) > 1, I(TIF) > 1/I(TFP)) | is greater than inverted value of extensive ones, (I(TFP) < 1, I(TFP) > 1/I(TIF)) | growth, (I(Y) > 1) | e > 0; i < 0; e > |i| | extensive–intensive compensatory growth |

77 | is greater than inverted value of intensive ones, (I(TIF) < 1, I(TIF) > 1/I(TFP)) | is greater than inverted value of extensive ones, (I(TFP) > 1, I(TFP) > 1/I(TIF)) | growth, (I(Y) > 1) | e <0; i> 0; i > |e| | intensive–extensive compensatory growth |

88 | equal to inverted value of intensive ones, (I(TIF) > 1, I(TIF) = 1/I(TFP)) | equal to inverted value of extensive ones, (I(TFP) < 1, I(TFP) = 1/I(TIF)) | no change (stagnation), (I(Y) = 1) | e = 0.5; i = −0.5 | pure extensive–intensive compensation |

99 | equal to inverted value of intensive ones, (I(TIF) < 1, I(TIF) = 1/I(TFP)) | equal to inverted value of extensive ones, (I(TFP) > 1, I(TFP) = 1/I(TIF)) | no change (stagnation), (I(Y) = 1) | e = −0.5; i = 0.5 | pure intensive–extensive compensation |

110 | is less than inverted value of intensive ones, (I(TIF) < 1, I(TIF) < 1/I(TFP)) | is less than inverted value of extensive ones, (I(TFP) > 1, I(TFP) < 1/I(TIF)) | decline, (I(Y) < 1) | e < 0; i > 0; i < |e| | intensive–extensive compensatory decline |

111 | is less than inverted value of intensive ones, (I(TIF) > 1, I(TIF) < 1/I(TFP)) | is less than inverted value of extensive ones, (I(TFP) < 1, I(TFP) < 1/I(TIF)) | decline, (I(Y) < 1) | e > 0; i < 0; e < |i| | extensive–intensive compensatory decline |

112 | faster decline than intensive ones, (I(TIF) < 1, I(TIF) < I(TFP)) | slower decline than extensive ones, (I(TFP) < 1, I(TFP) > I(TIF)) | decline, (I(Y) < 1) | e < 0; i < 0; |e| > |i| | predominantly extensive decline |

113 | slower decline than intensive ones, (I(TIF) < 1, I(TIF) > I(TFP)) | faster decline than extensive ones, (I(TFP) < 1, I(TFP) < I(TIF)) | decline, (I(Y) < 1) | e < 0; i < 0; |i| > |e| | predominantly intensive decline |

114 | same decline as intensive ones, (I(TIF) < 1, I(TIF) = I(TFP)) | same decline as extensive ones, (I(TFP) < 1, I(TFP) = I(TIF)) | decline, (I(Y) < 1) | e = −0.5; i = −0.5 | pure intensive–extensive decline |

115 | declining, (I(TIF) < 1) | unchanged, (I(TFP) = 1) | decline, (I(Y) < 1) | e = −1; i = 0 | pure extensive decline |

116 | unchanged, (I(TIF) = 1) | declining, (I(TFP) < 1) | decline, (I(Y) < 1) | e = 0; i = −1 | pure intensive decline |

Year | G(Y) | G(L) | G(K) | G(K/L) | G(TIF) | G(TFP) | Intensity i | Extensity e | Share l | Share k |
---|---|---|---|---|---|---|---|---|---|---|

1991 | 5.1 | 2.8 | 5.3 | 2.4 | 4.0 | 1.0 | 20 | 80 | 35 | 65 |

1992 | 1.9 | −1.3 | 4.1 | 5.5 | 1.4 | 0.5 | 28 | 72 | −25 | 75 |

1993 | −1 | −1.3 | −4.2 | −2.9 | −2.8 | 1.8 | 39 | −61 | −23 | −77 |

1994 | 2.5 | 0 | 3.6 | 3.6 | 1.8 | 0.7 | 28 | 72 | 0 | 100 |

1995 | 1.7 | 0.4 | 0 | −0.4 | 0.2 | 1.5 | 88 | 12 | 100 | 0 |

1996 | 0.8 | 0 | −0.5 | −0.5 | −0.3 | 1.1 | 81 | −19 | 0 | −100 |

1997 | 1.8 | −0.1 | 0.8 | 0.9 | 0.3 | 1.4 | 80 | 20 | −11 | 89 |

1998 | 2 | 1.2 | 3.9 | 2.7 | 2.5 | −0.5 | −17 | 83 | 24 | 76 |

1999 | 2 | 1.6 | 4.6 | 3.0 | 3.1 | −1.1 | −26 | 74 | 26 | 74 |

2000 | 3 | 2.3 | 2.3 | 0.0 | 2.3 | 0.7 | 23 | 77 | 50 | 50 |

2001 | 1.7 | −0.3 | −2.5 | −2.2 | −1.4 | 3.2 | 69 | −31 | −11 | −89 |

2002 | 0 | −0.4 | −5.8 | −5.4 | −3.1 | 3.2 | 50 | −50 | −6 | −94 |

2003 | −0.7 | −1.1 | −1.3 | −0.2 | −1.2 | 0.5 | 29 | −71 | −46 | −54 |

2004 | 1.2 | 0.3 | 0 | −0.3 | 0.1 | 1.0 | 87 | 13 | 100 | 0 |

2005 | 0.7 | 0 | 0.7 | 0.7 | 0.3 | 0.3 | 50 | 50 | 0 | 100 |

2006 | 3.7 | 0.8 | 7.5 | 6.6 | 4.1 | −0.4 | −9 | 91 | 10 | 90 |

2007 | 3.3 | 1.7 | 4.1 | 2.4 | 2.9 | 0.4 | 12 | 88 | 30 | 70 |

2008 | 1.1 | 1.3 | 1.5 | 0.2 | 1.4 | −0.3 | −18 | 82 | 46 | 54 |

2009 | −5.6 | 0.1 | −10.1 | −10.2 | −5.1 | −0.5 | −8 | −92 | 1 | −99 |

2010 | 4.1 | 0.3 | 5.4 | 5.1 | 2.8 | 1.2 | 31 | 69 | 5 | 95 |

2011 | 3.7 | 1.4 | 7.2 | 5.7 | 4.3 | −0.5 | −11 | 89 | 17 | 83 |

2012 | 0.4 | 1.2 | −0.4 | −1.6 | 0.4 | 0.0 | 1 | 99 | 75 | −25 |

2013 | 0.3 | 0.6 | −1.3 | −1.9 | −0.4 | 0.7 | 65 | −35 | 31 | −69 |

2014 | 1.6 | 0.9 | 3.5 | 2.6 | 2.2 | −0.6 | −21 | 79 | 21 | 79 |

2015 | 1.7 | 0.8 | 2.2 | 1.4 | 1.5 | 0.2 | 12 | 88 | 27 | 73 |

2016 | 1.6 | 1.1 | 2.5 | 1.4 | 1.8 | −0.2 | −10 | 90 | 31 | 69 |

2017 | 1.6 | 0.8 | 2.7 | 1.9 | 1.7 | −0.1 | −8 | 92 | 23 | 77 |

1991–2017 | 1.47 | 0.55 | 1.25 | 0.7 | 0.9 | 0.6 | 38 | 62 | 31 | 69 |

Year | G(Y) | G(L) | G(K) | G(K/L) | G(TIF) | G(TFP) | Intensity i | Extensity e | Share l | Share k |
---|---|---|---|---|---|---|---|---|---|---|

1991 | −11.6 | −5.5 | −27.3 | −23.1 | −17.1 | 6.6 | 26 | −74 | −15 | −85 |

1992 | −0.5 | −2.6 | 16.5 | 19.6 | 6.5 | −6.6 | −52 | 48 | −15 | 85 |

1993 | 0.1 | −1.6 | 0.2 | 1.8 | −0.7 | 0.8 | 53 | −47 | −89 | 11 |

1994 | 2.9 | 1.1 | 11.7 | 10.5 | 6.3 | −3.2 | −35 | 65 | 9 | 91 |

1995 | 6.2 | 0.7 | 23.3 | 22.4 | 11.4 | −4.7 | −31 | 69 | 3 | 97 |

1996 | 4.3 | 0.5 | 9.8 | 9.3 | 5.0 | −0.7 | −13 | 87 | 5 | 95 |

1997 | −0.7 | −0.7 | −5.2 | −4.5 | −3.0 | 2.3 | 43 | −57 | −12 | −88 |

1998 | −0.3 | −1.7 | −1.1 | 0.6 | −1.4 | 1.1 | 44 | −56 | −61 | −39 |

1999 | 1.4 | −2.2 | −2.6 | −0.4 | −2.4 | 3.9 | 61 | −39 | −46 | −54 |

2000 | 4.3 | −0.8 | 8.4 | 9.3 | 3.7 | 0.6 | 14 | 86 | −9 | 91 |

2001 | 3.1 | −0.3 | 5.6 | 5.9 | 2.6 | 0.5 | 16 | 84 | −5 | 95 |

2002 | 1.6 | 0.6 | 2.2 | 1.6 | 1.4 | 0.2 | 13 | 87 | 22 | 78 |

2003 | 3.6 | −0.8 | 1.8 | 2.6 | 0.5 | 3.1 | 86 | 14 | −31 | 69 |

2004 | 4.9 | −0.2 | 3.9 | 4.1 | 1.8 | 3.0 | 62 | 38 | −5 | 95 |

2005 | 6.4 | 1.9 | 6.4 | 4.4 | 4.1 | 2.2 | 35 | 65 | 23 | 77 |

2006 | 6.9 | 1.3 | 5.9 | 4.5 | 3.6 | 3.2 | 47 | 53 | 18 | 82 |

2007 | 5.5 | 2.1 | 13.5 | 11.2 | 7.6 | −2.0 | −21 | 79 | 14 | 86 |

2008 | 2.7 | 2.2 | 2.5 | 0.3 | 2.3 | 0.3 | 13 | 87 | 47 | 53 |

2009 | −4.8 | −1.8 | −10.1 | −8.5 | −6.0 | 1.3 | 17 | −83 | −15 | −85 |

2010 | 2.3 | −1 | 1.3 | 2.3 | 0.1 | 2.2 | 94 | 6 | −44 | 56 |

2011 | 2 | −0.3 | 1.1 | 1.4 | 0.4 | 1.6 | 80 | 20 | −22 | 78 |

2012 | −0.9 | 0.4 | −3.2 | −3.6 | −1.4 | 0.5 | 27 | −73 | 11 | −89 |

2013 | −0.5 | 0.3 | −2.7 | −3.0 | −1.2 | 0.7 | 37 | −63 | 10 | −90 |

2014 | 2 | 0.6 | 2 | 1.4 | 1.3 | 0.7 | 35 | 65 | 23 | 77 |

2015 | 4.2 | 1.2 | 7.3 | 6.0 | 4.2 | 0.0 | 0 | 100 | 14 | 86 |

2016 | 2.1 | 0.4 | −0.5 | −0.9 | −0.1 | 2.2 | 98 | −2 | 44 | -56 |

2017 | 2.6 | 0.3 | 3 | 2.7 | 1.6 | 0.9 | 37 | 63 | 9 | 91 |

1991–2017 | 1.77 | −0.23 | 2.30 | 2.5 | 1.0 | 0.7 | 42 | 58 | −9 | 91 |

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**MDPI and ACS Style**

Wawrosz, P.; Mihola, J.; Kotěšovcová, J.
How to Express and to Measure Whether an Economic System Develops Intensively. *Systems* **2018**, *6*, 24.
https://doi.org/10.3390/systems6020024

**AMA Style**

Wawrosz P, Mihola J, Kotěšovcová J.
How to Express and to Measure Whether an Economic System Develops Intensively. *Systems*. 2018; 6(2):24.
https://doi.org/10.3390/systems6020024

**Chicago/Turabian Style**

Wawrosz, Petr, Jiří Mihola, and Jana Kotěšovcová.
2018. "How to Express and to Measure Whether an Economic System Develops Intensively" *Systems* 6, no. 2: 24.
https://doi.org/10.3390/systems6020024