Measurement of Economic Growth, Development and Under Development: New Model and Application

📝 Abstract

This paper presents a simple model to measure the relative economic growth of economic systems. The model considers S-Shaped patterns of economic growth that, represented with a linear model, measure how an economic system grows in comparison with another one. In particular, this model introduces an approach which indicates if the economic system has a process of economic growth, development or under development. The application of the model is provided for regions and macro regions of the Italian economic system.

💡 Analysis

This paper presents a simple model to measure the relative economic growth of economic systems. The model considers S-Shaped patterns of economic growth that, represented with a linear model, measure how an economic system grows in comparison with another one. In particular, this model introduces an approach which indicates if the economic system has a process of economic growth, development or under development. The application of the model is provided for regions and macro regions of the Italian economic system.

📄 Content

CocciaLab Working Paper 2017 – No. 6

measurement of Economic Growth, development and under development: New Model and application Mario COCCIA ARIZONA STATE UNIVERSITY Center for Social Dynamics and Complexity Interdisciplinary Science and Technology Building 1 (ISBT1) 550 E. Orange Street, Tempe- AZ 85287-4804 USA and CNR – NATIONAL RESEARCH COUNCIL OF ITALY Via Real Collegio, 30-10024, Moncalieri (TO), Italy E-mail: mario.coccia@cnr.it A B To discover the causes of social, economic and technological change

1 | P a g e  

Coccia M. 2017. Measurement of economic growth, development and under development: New model and application

CocciaLab Working Paper 2017 – No. 6

MARIO COCCIA1 ARIZONA STATE UNIVERSITY & CNR – NATIONAL RESEARCH COUNCIL OF ITALY

E-mail: mario.coccia@cnr.it

Abstract. This paper presents a simple model to measure the relative economic growth of economic systems. The model considers S-Shaped patterns of economic growth that, represented with a linear model, measure how an economic system grows in comparison with another one. In particular, this model introduces an approach which indicates if the economic system has a process of economic growth, development or under development. The application of the model is provided for regions and macro regions of the Italian economic system.

KEYWORDS: Economic Growth; Convergence; Economic Development; Relative Growth; S-Shaped Pattern

JEL Codes: C02, F43, O40, O47.

1 Acknowledgements. I am grateful to Michele Mininni (University of Bari, Italy), Luigi Montrucchio (University of Torino, Italy), Alessandro Flamini (Graduate Institute of International Studies-Geneva, Switzerland), David Audretsch (Max Planck Institutes, Jena Germany), Jagannadha Pawan Tamvada (Max Planck Institutes, Jena Germany), and Angelo Reati (European Commission, Brussels) for valuable suggestions and discussion. I add that the responsibility for all views expressed is entirely mine.

measurement of Economic Growth, development and under development: New Model and application

2 | P a g e  

Coccia M. 2017. Measurement of economic growth, development and under development: New model and application

CocciaLab Working Paper 2017 – No. 6

MODEL

Let Y(t) be the total output at time t of the economic system Y’ and X(t) be the total output at the same time of the economic system X’;
let Y’X’, 1b and 2b be the rates of growth of total outputs Y and X, respectively, such that 1 2 1 b b B  ;
if Y and X increase, in the long run, according to some S-shaped pattern of growth, then 1 2 1 b b B  measures the relative economic growth of the economic system X’ in relation to the economic growth Y’.

In fact, if both Y and X increase in the long run according to some S-shaped pattern of growth (Lewis, 1955; Jarne et al., 2005), one way to represent such a pattern formally is in terms of the differential equation of the well- known logistic function. In the case of Y(t) we have:

  Y K K b dt dY Y   1 1 1 1

This equation can be rewritten as
  dt b dY Y K Y K 1 1 1 1  

dt b Y K dY Y dY 1 1 ) (    

Upon integrating we obtain   t b A Y K Y 1 1 1 log log    

dt b a Y Y K 1 1 1 log   

 t b a K Y 1 1 1 exp 1   

where dt b a 1 1  , and t1 is the abscissa of the point of inflection.
Thus the growth of Y and X can be described as:

3 | P a g e  

Coccia M. 2017. Measurement of economic growth, development and under development: New model and application

CocciaLab Working Paper 2017 – No. 6

t b a Y Y K 1 1 1 log   

[1] for X(t) we proceed in similar way of Y(t) and we have:

t b a X X K 2 2 2 log   

[2] respectively.

It can be readily verified that the logistic curve is a symmetrical S-shaped curve with a point of inflection at 0.5K2

Solving the equations [1] and [2] for t,
X X K b b a Y Y K b b a t       2 2 2 2 1 1 1 1 log 1 log 1

which immediately yields the expression 2 1 2 1 1 b b X K X C Y K Y         

[3] Clearly:
        2 2 1 1 2 1 exp b b a b a C , which can be written in a simplified form as
    1 2 1 1 exp t t b C   since, as noted earlier, 1 1 1 t b a  and 2 2 2 t b a  (cf. Eqs. [1] and [2]).
When X and Y are small in comparison with their final value, Eq. [3] reduces to
2 1 2 1 1 b b K X C K Y       

Hence the following simple model of economic growth is obtained 1 ) ( 1 B Y A X 

[4] where   1 1 2 1 1 2 C K K A b b  and 1 2 1 b b B 

The Eq. [4] was used by Huxley (1932) to describe the shape changes which animals and plans undergo during

2

This content is AI-processed based on ArXiv data.