again. A suitable development process in a certain period can be understood in many different ways. With each specific point of view, one can build one or a set of criteria to evaluate this suitability. From a modeling point of view, to quantify or model each point of view on the suitability of the population-economic development process, it is necessary to have a model system with a relatively complete structure, reflecting the relationship of the aspects in the unified movement of a socio-economic entity. Basically, two main approaches can be proposed, which are: Modeling and determining a trajectory of the optimal system in a certain sense under conditions of complete information or evaluating suitability based on comparing possible trajectories thanks to a criterion expressing suitability for a given goal. First of all, to see the process of economic and population integration with mathematical modeling approach, and at the same time create the basis for establishing specific models, the following thesis will systematize with more specific analysis the process of developing the population-economic modeling system.
IV- DEVELOPMENT OF POPULATION-ECONOMIC MODELING SYSTEM
Mathematical modeling and analysis is one of the modern tools in socio-economic research. With population-economy, many classes of models have been established and the results obtained from these models are very remarkable. This part systematizes the development of population-economic models. Analyzes the basic ideas of the classes of models that have been formed in history. On that basis, outlines the basic viewpoints when approaching the economic-population relationship in the study of a major field of social development in general. In addition, the thesis also presents some results that the researcher discovered in the process of analyzing the development of this system.
The research process and works related to economic-population modeling can be divided into the following periods:
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Classical Malthusian model class: includes models of Thomas Robert Malthus and his students.
Class of models with exogenous capital and technical progress: this class of models is rich but can be represented by Solow in the neoclassical school.
Class of models with endogenous capital and technical progress: the major representatives of this class of models in the third period are Boserup, Phelps, Simon, Steimann, Lucas, Romer... .
The following is a systematic review of the above model classes with separate analyses to serve the purpose of the thesis.
4.1- The role of food and the first idea of economic population modeling
4.1.1- Malthus model
Thomas Robert Malthus (1756-1834) wrote his first work, "Elementary Principles of Demography" (1798). This work caused much controversy in demography and economics. However, it can be said that it was in this work that TR Malthus modeled the population-economic relationship in its simplest form.
The three outlines regarding the role of food (economic factor) in population process that TR Malthus put forward are as follows:
The first model: Food increases faster than population, creating conditions for population growth. This is the period of development in which population becomes the strength of a country. However, the growth and prosperity in the condition of population growth and food already contain a potential state of poverty. With 50-year data of the United Kingdom, TR Malthus describes this model through the curves of food quantity - food, population and together with these two curves is the curve describing the phenomenon of decreasing food - food per capita, even in the case of food
9
8
7 LTTP
6
5 Population
4
3
2
1 LTPT/person
0
1 3 5 7 9 11 13 15 17 19 21 23 25
food increases faster than population. With this model, he argues that: even in the period when food increases faster than population, food output per capita can decrease. This is a result that is not easily seen without the help of modeling, even at a relatively simple level (see chart 1).
Chart 1: Increase in per capita food in the condition that food production increases faster than population
A mathematical model can explain this situation better:
Let Y(t), P(t) be functions indicating the level of food and the number of people (population) over time. For simplicity, we can assume that these functions have derivatives with respect to t and P(t) >0.
The condition Y'(t) >P'(t) >0 reflects that food and foodstuffs increase faster than population growth.
Establish the food function per capita and the derivative of this function over time:
a – Results of the thesis author.
y(t) Y(t)
P(t)
Y '(t)P(t) P '(t)Y(t)
(1.1)
y '(t)
The condition for y'(t) <0 is:
Y '(t) P '(t) Y(t) P(t)
P(t)2
(2.1)
That is: population growth faster than food growth is a factor showing the decline in average income per capita.
b- Second model: The worse case is that due to natural limitations and labor efficiency, food production per capita decreases faster because population increases rapidly while food production increases slowly, illustrated in Chart 2.
9
8
7
6
5
4
3
2
1
0
LTTP
Population
LTTP/capita
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
Chart 2: Increase in per capita food production is limited by natural conditions and labor efficiency
c- Model 3 (population growth and poverty): If in case a, population and food double after 25 years, then in model b, in the next 25 years, population doubles (4 times compared to the beginning) while food only increases 1.5 times. In model 3, he found that
After 25 years, the population doubled again (8 times the original) while food only increased 1.25 times. Poverty or in Malthus' language, the law of poverty (poor laws) is inevitable.
To explain cases b and c, he uses the labor efficiency model.
dynamic, illustrated in chart 3. LTTP output
Labor Chart 3: Labor efficiency
The above analysis is based on the population economic model proposed by Malthus at the same time. It is a production function model called the Malthusian model of growth. In this model, he assumed that the usable land area is fixed and labor changes depending on the birth and death rates of the population. Agricultural products depend only on labor.
The production function has the form: Y =f(L,N)
Where Y is output, L is total labor and N is a fixed quantity indicating total
exploitable land
Because labor only differs in organization while land capital remains unchanged, therefore when labor increases, productivity and efficiency gradually decrease. Even if labor is increased, the increase in product is much smaller than the increase in the number of additional laborers for field work.
TR Malthus used an example in the current state of full exploitation of potential, which is the production function Y= L0.5N0.5. With this example he described two cases N=100 and N=200 (illustrated in Chart 4).
50
N=200
40
30
20
N=100
10
0
1 2 3 4 5 6 7 8 9 10 11
Figure 4: Average food growth with different resource levels
The above situation shows that regardless of the amount of land, a gradual decline in per capita food production is inevitable.
4.1.2- Malthusian equilibrium
With the above model, Thomas Robert Malthus describes the economic-population equilibrium in two cases as follows:
a- LTTP/capita limit and population growth
y1
y2
y3
P/P
Y/P=y
Chart 5: Average food quota per capita
With Y being food, P being population, P being population growth rate, y=Y/P being average food per capita.
His conclusion is: with y=y2 then P/P must be 0, that is, the birth rate equals the death rate or the population does not grow. Only in this case can the average food level per capita be kept stable (chart 5).
b- Equilibrium and the formation of equilibrium
In this analysis he assumes a proportion w of the population participating in labor and so the production function has the form: Y=Y(wP,N). Diagram 6 depicts the equilibrium formation.
Y
C
A
B
P
Chart 6: Formation of per capita food quota
According to the graph above, when the average food-wage level per capita (LTTP/capita) is higher than the equilibrium level (point B), determined at a constant population, the population continues to increase and a corresponding amount of labor is attracted to the production areas, leading to the average income per capita increasing more slowly and reaching equilibrium at A. Conversely, if the population increases faster than output (point C), equilibrium can only be achieved when the population decreases and equilibrium is established at A.
The conclusion is: In case the population does not decrease or continues to increase, the average income per capita will gradually decrease and poverty is inevitable.
4.1.3- Scientific ideas and limitations of Thomas Robert Malthus' growth model
It can be seen that TR Malthus's model, although established very simply, allows for the analysis of dynamic relations and changing trends, the quantifiable influence of population-economic relations. Modeling becomes a tool to explain socio-economic phenomena, poverty and the characteristics of the formation of economic-population balance, through a constant population, called "Malthusian population" and the amount of products limited by natural conditions.
Thomas Robert Malthus's model considers population as a factor of social production, although only agricultural population. That is still true today, when people have gone a long way on the path of approaching economics and development with models.
The biggest limitation of TR Malthus's model is from the assumption and scope of consideration, which can be considered a historical limitation, that is, only considering agriculture and there he realized the limitation to the extent that is very clear but not complete: limited natural resources. It is said that T. R Malthus painted a gloomy picture for mankind in the gloomy period of history. In the period after TR Malthus, with the remarkable development of productive forces, the circulation of goods and resources in creating material wealth; especially the achievements of science and technology applied to life and production, the world economy has gradually overcome poverty described as the main consequence of population growth. However, the image he built from his model still exists somewhere on the continents and countries of the third world.
How did history happen?
+ England 1539-1809