Economic growth models- these are economic and mathematical models that describe the change in time of economic indicators that characterize the development and growth of the economy as a whole, its branches, individual economic entities.

Economic growth models contain three main dependencies of the real (non-financial) sector of the economy: the production function, the labor supply function and the capital supply function, which set the trend for the growth of the country's production potential. When studying these models, an answer is sought to the question: how to ensure aggregate demand at the level of the economic growth trend?

Since the object of the study is changes in economic indicators over time, the parameters of the model turn out to be functions of time. In equations where all parameters refer to the same time period, the time period index t does not apply.

Modern models of economic growth were formed on the basis of two directions - the Keynesian theory of equilibrium and the neoclassical theory of production.

The simplest models of economic growth by R. Harrod (1939) and E. Domar (1947), built independently of each other, have become widespread, corresponding to the Keynesian concept of the functioning of the national economy ( neo-Keynesian).

They are based on the premises:

3) the growth of national income is only a function of capital accumulation, and all other factors influencing the growth of capital productivity (the degree of use of the achievements of scientific and technological progress, improving the organization of production) are excluded. In other words, it is assumed that the demand for capital for a given capital intensity depends only on the rate of growth of national income;

4) capital intensity does not depend on the ratio of prices of production factors, but is determined only by the technical conditions of production.

Domar model- a mathematical model of economic growth, which describes the dual role of investment in expanding aggregate demand and in increasing the production capacity of aggregate supply over time.

In formalized form, E. Domar's model is the equation:

Or ,

where I- annual net investment; k- return on capital (i.e.).

This model computes growth rate of net investment which provides full employment in the economy.

Harrod's model- a mathematical model of economic growth, which focuses on the rate at which national income must increase in order to satisfy the equilibrium condition in Keynesian economic theory.

R. Harrod's model is based on the Keynesian condition of macroeconomic equilibrium. It uses two formulas - the static equilibrium condition and the dynamic equilibrium condition.

,

where is the capital intensity; - the share of savings in national income.

,

where t- index of the time period.

In this model, the increase in national income in the period t- this is guaranteed growth rate that provides a dynamic balance between actual savings and anticipated investments. It is not achieved automatically, therefore, to achieve such a dynamic equilibrium, state regulation of the economy is necessary.

These models are largely theoretical and abstract in nature, i.e. reflect the most general dependencies of the production process: between accumulation, consumption and the rate of growth of the social product (national income) with an unchanged organic composition of capital.

The post-Keynesian direction (J. Robinson) based his analysis of the theory of economic growth on the idea that the growth rate of the social product depends on the distribution of national income. In this case, distribution is a function of capital accumulation, and the rate of its accumulation determines the rate of profit and its share in the national income.

The neoclassical trend is based on the idea of ​​self-regulation of the market system and its optimality, expressed in the most efficient use of production factors. Neoclassical economic growth models are based on the use of the Cobb-Douglas production function. As noted above, they include scientific and technological progress as a factor of economic growth. In this regard, a production function is distinguished with exogenous and endogenous NTP factor.

In the first case, since STP occurs in time, the time factor is introduced into the Cobb-Douglas production function, taking into account the pace of STP ( J. Tinbergen's function, 1942):

,

where r- growth rate of scientific and technological progress; t- time.

"Endogenous STP" is manifested in a change in the ratio between labor and capital. It is assumed that these factors of production are interchangeable, which leads to the need to calculate the elasticity of substitution of these factors. It indicates the percentage change in capital costs when labor costs change by 1%.

Solow's model (1957) - a model of economic growth depending on the level of technological progress. This model uses a production function in which output is a function of capital and labor. Labor can replace capital, but these factors are not completely fungible.

This model is characterized by a system of equations:

Y = f (K, L)- production function with two variables.

S = APS * Y- the function of savings on the value of national income.

? I =? K- net investment (capital gains).

I = S- the rule of balance.

L = L 0 e t- labor resources are growing at a constant pace.

? Y /? K = W- the wage rate is equal to the productivity of an additional unit of labor.

The natural growth rate is the increase in the number of labor force. If the supply of labor has increased as a result of natural population growth, then with the same structure of labor and capital, part of the labor force will remain unemployed. However, unemployment leads to lower wages, and entrepreneurs are already choosing a combination of resources with relatively less capital use, thereby restoring equilibrium.

The specific combination of labor and capital in accordance with the production function determines the level of total income, and this, in turn, determines the amount of savings. Since, under equilibrium conditions, savings are equal to investments, which are identical to capital gains, the economy will move to a new state. Thus, a new cycle of economic growth will receive an impetus from the natural growth of labor resources.

This classical model argues that there is not only the possibility of equilibrium economic growth - the development of the economy with full employment and the equality of aggregate demand and aggregate supply - but that this state is stable. In case of deviation from the equilibrium state, the mechanism of interchangeability of factors of production comes into play, capable of restoring equilibrium.

All models of economic growth allow for its effective forecasting, which makes it possible to more purposefully implement the state policy of regulating the economy.

Section 3. Macroeconomics

Topic 7. Dynamics of economic development

3.7.3. Economic growth models

The development of the theory of growth is carried out by economists of various directions.

In the modern economy, there are three main directions for modeling economic growth:

1. Keynesian models of economic growth;

2. neoclassical models;

3. historical and sociological models.

1. Keynesian the models are based on the dominant role of demand in ensuring macroeconomic equilibrium. The decisive element is investments, which increase profits by means of a multiplier. The simplest Keynesian model of growth is E. Domar's model - this model is a one-factor (demand) and one-product model. Therefore, it only takes into account investments and one product. According to this theory, there is an equilibrium rate of growth of real income at which production capacity is used. It is directly proportional to the savings rate and the marginal productivity of capital. Investment and income grow at an equally constant rate over time.

R. Harrod's model: economic growth rates are a function of the ratio of income growth and capital investment.

2. Neoclassical models consider economic growth in terms of factors of production (supply). The basic premise of this model is the assumption that each factor of production provides a share of the product produced. This model is called the production function: the volume of the product is determined by the sum of the products of each factor by its marginal product. Thus, economic growth is the sum total of such interchangeable factors: labor, capital, land and entrepreneurship.

3. Historical and sociological models.

R. Solow identified the stages of economic growth:

1. class society:

Static equilibrium of the economic system;

Limiting the use of scientific and technological progress;

Falling per capita income.

2. creating conditions for increasing growth by increasing production efficiency.

3. run-up stage- due to the growth in the share of investment in national income. All the achievements of science and technology are actively used.

4. mature society(path to maturity):

High rates of economic growth, at which the growth of production outstrips the growth of the population.

5. a society of high mass consumption:

Durable goods.

Previous

INTRODUCTION

GENERAL DESCRIPTION OF ECONOMIC GROWTH

2 Factors of economic growth

ECONOMIC GROWTH MODELS J. M. KEYNS AND HARROD-DOMAR

KEYNSIAN ECONOMIC GROWTH MODELS -

2 Big push theory

4 The theory of the transition to self-sustaining growth

R. SOLOW'S NEOCLASSIC GROWTH MODEL

THEORY OF ZERO ECONOMIC GROWTH

CONCLUSION

INTRODUCTION

Increasing the rate of economic growth, or at least maintaining it at the same level, is the most difficult and most important task that any state faces. The level of economic growth reflects the state of the state economy, the standard of living of the population, and so on. The policy of each state is aimed at stimulating economic growth in the country, increasing the welfare of the nation. The government is faced with the question of what methods to use in an attempt to increase this indicator.

There are many approaches to defining the concept of economic growth. Many indicators are compared, many formulas and factors are given, which shows how complex and contradictory this concept is and how difficult it is to predict and stimulate it.

The relevance of this topic is beyond doubt, because economic growth in the country has been a priority task since the creation of the first state and will be relevant as long as at least one state continues to function.

In this course work, the following goal was set: an in-depth study of the concept of economic growth, its factors and modern theories, as well as identification of the current tasks facing the government of the Republic of Belarus, the purpose of which is to increase the rate of economic growth.

In connection with the set goal, the following tasks were set:

.Study of the concept of economic growth and its factors;

.Analysis of existing modern concepts of economic growth;

To solve the set tasks, many sources of information were used, including Internet resources.

1. General characteristics of economic growth

1 The concept of economic growth

Economic growth is understood as such a development of the national economy in which the real volume of production (GDP<#"justify">The factors of economic growth are often grouped according to the types of economic growth.

There are intensive and extensive factors of economic growth:

· Extensive factor - growth due to an increase in the amount of resources (growth in the number of employees, buildings, resources, equipment). At the same time, labor productivity, quality of equipment, and quality of manufactured products do not change significantly. Extensive growth factors are characterized by the law of decreasing returns with an excessively large increase in the resource. For example, an unjustified increase in the number of machines will lead to the fact that some of them will be idle and cause a loss. The same will happen with an increase in labor, land, capital expenditures. These resources, however, do not include innovation, new production technologies, management technologies, and an increase in the quality of human capital.

· Intensive factors mean not quantitative, but qualitative change. Growth is achieved by improving indicators such as labor productivity, equipment quality, innovation, modernization. High quality human capital is recognized as the most important intensive factor.

Stable growth is mainly achieved by increasing labor productivity, stable inflow of investments, lower costs in comparison with competitors and in the economy as a whole. In the long term, economic growth is fueled by factors such as technological progress, capital accumulation, and the creation of infrastructure and economic institutions. All this contributes to an increase in labor productivity, modernization of physical capital and lower costs.

To summarize the above, we can say that the main factors affecting economic growth are:

1.The quantity and quality of labor resources;

.Efficiency of fixed capital;

.The quantity and quality of natural resources;

.Management efficiency;

.Technology efficiency;

.Institutional factors.

Now about all the factors in more detail.

The most important factor is labor costs. Determined primarily by the size of the country's population. It should be borne in mind that not all of the country's population can be considered able-bodied.

However, this method of calculating labor costs by the number of employees does not fully reflect the state of affairs. More accurate is the indicator of man-hours worked, which allows you to calculate the total cost of working time. Working hours take into account many factors, such as population growth rate, willingness to work, retirement benefits and unemployment benefits. All factors together differ from country to country, which creates the initial conditions for differences in the rates and levels of economic development.

Not only quantitative factors, but also the quality of the labor force are of great importance for economic development. The better the education and the higher the qualifications, the more productive the labor and the higher the economic growth. In other words, labor costs may increase not only due to an increase in the number of workers, but also as a result of an increase in the quality of the labor force.

The most important factor of growth, along with labor costs, is capital. The capital includes: equipment, buildings, inventories. Capital expenditures depend on the amount of accumulated capital. The accumulation of capital depends on the rate of accumulation: the higher the rate, the greater the amount of investment. Capital gains also depend on the scope of the company's accumulated assets - the larger they are, the lower the rate of capital increase.

It should not be overlooked that the amount of capital per worker, that is, the capital-to-labor ratio, is a decisive factor determining the dynamics of labor productivity. Those. with a uniform increase in capital investment, but a rapid growth rate of the labor force, the capital-labor ratio will fall, and labor productivity will decrease accordingly.

The third factor that has a decisive influence on economic growth is land, as well as the quantity and quality of natural resources. The more resources, the better their quality and variety, the higher the economic potential of the country. The presence of fertile lands and favorable climatic conditions are also of great importance.

However, all of the above conditions are not in themselves a self-sufficient factor of economic growth. Many backward countries have a large resource base and a good climate, but their use is ineffective and therefore does not lead to economic growth.

Scientific and technological progress is an important engine of economic growth. It includes not only the modernization of equipment, but also innovations, new methods and forms of management of the organization of production. Scientific and technological progress makes it possible to combine these resources in a new way in order to increase the final output of products. The consequence of this is the creation of new, more efficient industries. And an increase in efficient production leads to economic growth.

In addition to all of the above factors, there are a number of indicators that are of great importance in the economy. These indicators include institutional factors. Without them, it is impossible to rationally distribute. Institutional factors include:

.Effectively working government bodies;

.Rational legislation;

.Features of the social, cultural, religious situation in the country.

Models of economic growth by J.M. Keynes and Harrod-Domar

Consider the main theories of economic growth. Before proceeding with the consideration of models, it should be noted that any economic model is a simplified perception of the real state of affairs in the economy, represented by graphs and formulas, as well as having many assumptions that make the final result far from reality in advance. However, without these simplifications, it is not possible to analyze such a complex phenomenon as economic growth.

First of all, it is necessary to consider the model of J.M. Keynes, since many subsequent ones were built on the basis of the premises and conclusions of this particular model.

The Keynesian model reflects the state of equilibrium growth of the entire national economy as a whole. The main problem at the center of the whole theory is effective demand.

The two main metrics considered by Keynes are investment and savings. All total income is subdivided into investments I and savings S, that is, Y = I + S. The problem of large savings ("the paradox of thrift") is considered, when households prefer to spend less and save more, which leads to a decrease in demand and money outflow from the economy. The consequence of this is a slowdown in economic growth.

It should be borne in mind that an increase in income does not necessarily lead to an increase in investment, but causes an increase in savings. This is due to the fact that different business entities are responsible for investment savings. Keynes was the first to see savings in the economy. Before him, it was believed that savings have positive effects, are the basis of growth and progress.

Investment and savings are closely related. Keynes believes that it is the equality of investment and savings that ensures the sustainable economic development of the country. If savings exceed investments, the goods are not sold and stand idle in warehouses, a drop in production occurs, an increase in unemployment and, as a result, an oppression of the economy. The situation when investments exceed savings causes unsatisfied demand, higher prices, and an increase in production.

One of the key concepts in Keynes's model is the multiplier and acceleration effect. Consider the multiplier effect.

The investment multiplier shows the influence of an increase in investment on an increase in output and income. The multiplier and the growth in consumption are directly related, while the relationship between the multiplier and the growth in savings is inverse. The essence of the investment multiplier is that an increase in investment causes a multiplier effect of an increase in production and net domestic product. It is assumed that investments are autonomous, that is, independent of changes in production volumes.

where Mi is the investment multiplier; ? Y - growth of real income; ? Ia - growth of autonomous investments.

1 / (1 - MPC), Mi = 1 / MPS.

Thus, the autonomous investment multiplier is the reciprocal of the marginal propensity to save.

Y = Mi *? Ia = 1 / MPS *? Ia.

In accordance with the magnitude of the multiplier, income increases, which leads to an increase in demand, and as a result of production volumes. And the increase in production volumes contributes to the growth of induced investment. The growth of investments triggered by an increase in income is called the acceleration effect.

Two factors contribute decisively to the acceleration effect:

.Long period of equipment manufacturing, during which unsatisfied demand causes production expansion.

.Long period of operation of equipment, as a result of which the percentage increase in new investments to replacement (investments that compensate for equipment wear) is greater than the percentage increase in production. The demand for these products stimulates further investment.

The acceleration coefficient is the ratio of the increase in investments to the increase in income, consumer demand or the volume of finished goods that caused them in the previous period: V =? I /? Y.

The multiplier effect can only appear under certain conditions. It is important to take into account which industries are invested in, and an increase in taxes leads to a decrease in the real multiplier. With high imports, part of the income will flow abroad, increasing the likelihood of a deficit in the national balance.

Keynes believed that maintaining high investment in the economy is impossible without government intervention, and therefore proclaimed the best policy to stimulate effective demand. In turn, this caused an increase in government spending, which had to be supported by monetary policy, which led to an increase in money in circulation. This could not but affect the inflation rate in the country. However, Keynes's theories were widely applied in practice after World War II. Particular attention was paid to Keynes's opinion on the need for government intervention in the economy to manage demand through taxes and reduce unemployment. However, the model had several disadvantages due to its assumptions. First, the model was short-term and did not allow predicting the long-term changes in the economy caused by this policy. The next weak link in his theory, as noted above, was ignoring inflation, which is absolutely impossible in real conditions. However, we must not forget that at the time of the creation of the theory, the Great Depression was "raging" in the economy and the low unemployment rate at that time worried Keynes to a lesser extent than the growing inflation rate.

The static nature of the model, its short-term nature, and problems with inflation were an incentive to create new ideas based on the Keynesian model, taking into account all the listed disadvantages. One of the models of great importance for the economy was the Harrod-Domar model.

In this model, the theoretical and methodological foundations of Keynes's concept were used, but a number of its own assumptions were introduced. First of all, the static nature of the model was corrected. The Harrod-Domar concept was long-term and dynamic. Secondly, this model was one-factor, taking into account the main factor of economic growth capital. A few more assumptions: full involvement of all factors, equality of supply and demand and their incremental values. The source of the increase in supply and demand, as in the Keynesian model, is recognized as investment.

The original equation of R. Harrod's model (equation of the actual growth rate):

where g denotes the real increase in total output for any period, for example, for a year; or else: g =? Y / Y, that is, the actual growth rate - the ratio of the increment in income to the amount of income in the base period; c - capital ratio or capital intensity ratio; it shows the "investment price" of one unit of increase in income or production, in other words: c = I /? Y; finally, s is the share of savings in national income, or propensity to save: s = S / Y.

By reducing the common terms, the equation is reduced to simple equality, namely Keynes's equality: investment is equal to savings. However, Harrod and Domar were able to represent this model in dynamics: the left side of the equation (g · c) represents the accumulated part of the increase in production going to production purposes, and this part must be provided by a certain share of savings (s). Since both sides of the equation of the actual growth rate refer to the past period, this equality does not need special conditions for its implementation.

The next equation in Harrod's model is the guaranteed growth rate equation:

where gw is the guaranteed growth rate and cr is the required capital ratio.

The required capital ratio cr is the amount of new capital required to provide a unit of growth in output (standard capital intensity).

All indicators except s are predictive. They make the estimated amount of savings equal to the already existing savings. This equation equates future investment and actual savings.

According to Harrod, the guaranteed growth rate is constant. He explains it this way: the share of savings in national income is constant, since the motives that make people save are constant. The required capital ratio is also constant due to the existing neutral nature of scientific and technological progress: over time, labor-saving technologies and technologies are balanced by capital-saving technologies. Two exponents of the equation are constant, therefore, the third is also constant. If the actual growth rate (g) coincided with the predicted, guaranteed (gw) in a capitalist market economy, there would be sustainable continuous development.

But within the framework of the capitalist economy, there is no stability, and not only in the static (short-term), but also in the dynamic plan. To explain this fact, Harrod compares both equations in his model:

and notes that the indicators of the actual and guaranteed growth rates coincide by way of exception. Most often, there is a deviation of the actual growth rate from the guaranteed one. How are these situations characterized?

If the actual growth rate g begins to increase and exceeds gw, then s, due to its relative constancy, will not increase immediately to the same extent, then the actual capital intensity ratio c will necessarily decrease and become less than the required (forecast) capital intensity ratio, which entrepreneurs have tuned in. In other words, if g> gw, then (due to the constancy of s) with< cr. Но если с ниже cr, это означает, что в итоге предприниматели будут оценивать фактическую капиталоемкость как слишком низкую, и сочтут располагаемое количество товаров в каналах обращения или оборудования недостаточными для поддержания оборота. Предприниматели, следовательно, станут увеличивать свои товарно-материальные запасы, закупать новое оборудование. Другими словами, будут еще более способствовать превышению фактического темпа роста над гарантированным (равновесным).

Conversely, if the actual growth rate turns out to be less than the guaranteed one (g< gw), тогда в силу приведенных выше соображений требуемый (прогнозируемый) коэффициент капитала будет обязательно ниже фактического (с >cr), that is, entrepreneurs will consider the stocks of raw materials, equipment, materials excessive, reduce purchases, which will further reduce the actual growth rate in comparison with the guaranteed one.

This reasoning leads Harrod to two conclusions. First, he believes that, in principle, there is a growth rate that will keep producers satisfied with their performance and performance, and that will ensure that equilibrium is maintained in a growing economy. Second, however, “if the aggregate result of trial and error of multimillion-dollar producers gives a value for g that is different from gw, then not only does there not appear any tendency to adjust the size of of this value either upward or downward ”.

This conclusion is the quintessence of Keynesianism in the field of the theory of dynamics. It means that dynamic instability is inherent in a market economy, and if the actual growth rate runs away from the guaranteed one, then centrifugal forces work inside it, forcing the system to deviate further and further from the equilibrium line of development.

Deviations of the actual growth rate from the guaranteed one are explained, according to Harrod, mainly by short-term cyclical fluctuations. To interpret longer-term fluctuations in economic conditions, Harrod introduces a third equation - the natural growth rate:

where gn (from natural - natural) represents the maximum possible rate of movement of the economy for a given population growth and technical capabilities. The guaranteed rate - gw - meant the line of entrepreneurial equilibrium with full employment of cash capital and technical improvements. But gw, generally speaking, admitted the existence of “involuntary unemployment”. The natural pace - gn - does not allow it, being in the long term the maximum pace with the given resources. As Harrod notes, there may not be enough savings to ensure this rate of savings, so the equation of natural growth provides for the absence of mandatory equality between the left and right sides.

The full Harrod model considers the relationship between three quantities: natural (gn), guaranteed (gw) and actual (g) growth rates:

Let gw exceed gn (since guaranteed growth is a predictable, programmable value, such a combination is in principle possible). But if gw> gn, then gw> g (since natural growth is maximum for given resources, actual growth will be lower than natural, and therefore, for gw> gn, it will necessarily be lower than guaranteed). Then, taking into account the considerations given above, we have: cr< с, т. е. при чрезмерно завышенных прогнозах развития нормативная (требуемая) капиталоемкость будет обязательно ниже фактической, а это, как было показано ранее, есть условие длительной депрессии (чрезмерное перенапряжение сил порождает длительную фазу спада).

If gw< gn, тогда возможны по крайней мере два варианта. Первый (gw >g) we have already covered: it leads to long-term depression. But under the given conditions, the second option is also possible: gw< g, тогда cr >s, and this, as we know, is the condition for a long boom.

Hence, according to Harrod, "the ratio of gn and gw is of decisive importance in determining whether recovery or depression will prevail in economic life over a number of years."

In this regard, Harrod revises in a certain way Keynes's stance on savings. Keynes, as we know, was negative about saving, seeing it as a stimulus for depression. The neoclassicists, on the other hand, had an unambiguously positive attitude to savings, believing that they automatically turn into savings. Harrod takes a more balanced position here. He believed that savings are useful as long as gw is lower than gn, that is, when there is an economic boom. The fact is that Harrod considered equally dangerous both a situation where gw exceeded g, characterized by an economic recession, and a situation in which gw would be too low compared to gn. While this latter situation means a trend towards rapid economic recovery and full employment, this high employment will be inflationary and therefore unhealthy. In these conditions, saving is a virtue, since increasing gw makes it possible to achieve high employment without inflation.

Thus, Harrod drew attention to the danger of an inflationary boom, while Keynes did not consider inflation to be possible in an economic depression. However, among the problems of long-term growth for Harrod, as for Keynes, the first place was still the problem of depression and unemployment. Harrod clearly identifies two distinct sets of problems in theoretical analysis and economic policy:

) the discrepancy between gw and gn - the problem of chronic unemployment;

2) the tendency of g to move away from gw is an industrial cycle problem.

Hence, Harrod's practical program includes two groups of activities.

· Short-term countercyclical policy (directed against the “flight of the actual growth rate from the guaranteed one”). It assumes both traditional Keynesian methods - public works, interest rate regulation, and a specific tool proposed by Harrod to "fight the world crisis." This is the creation of so-called "buffer stocks" of non-perishable materials, raw materials, food. As a result, government agencies will be able to maintain prices for these types of goods at a relatively constant level, by massively purchasing inventory during a recession and selling them during a boom.

· A policy of long-term stimulation of economic development rates against chronic unemployment and long-term depression (in order to bring the guaranteed growth rate closer to the natural one and prevent mass unemployment). Such a policy involves the use of a reduction in interest - up to zero. This measure is not exhaustive, because it is impossible to achieve convergence of natural and guaranteed growth rates without government intervention. However, a decrease in the rate of interest should lead to an increase in capital intensity, an expansion of the demand for savings (by the amount d), and further - to a certain reduction in the share of savings in national income and an increase in the required capital coefficient c r ... According to Harrod, one should strive for such a progressive decrease in the interest rate, at which g w · C r = s - d = g n · C r ... The latter expression, according to Harrod, is the formula for "sustainable growth at full employment."

It is characteristic that, from Harrod's point of view, the withering away of interest can also serve the social progress of society. If there is no interest, the rentier class will die away (Harrod refers here to Keynes's ideas about the prospects for "euthanizing the rentier"). Along with interest, land rent will gradually disappear, and hence the class of landowners. However, in general, Harrod, like Keynes, was a supporter of the preservation of private property, considering it a guarantee of freedom, an incentive for entrepreneurship, etc.

3. Keynesian theories of economic growth

1 The theory of the "vicious circle of poverty"

The concept of "vicious circle of poverty" was proposed for the first time in 1949-1950. G. Singer and R. Prebisch. The concept of the “vicious circle of poverty” was invented at a time when third world countries were examined for economic equilibrium. Scientists have tried to explain the underdevelopment of countries by demographic and economic factors. In the post-war years, various variants of the “vicious circle of poverty” have emerged. They were based on the relationship between population and economic conditions. The general meaning of such concepts boiled down to the fact that an increase in the quality of life is quickly reduced to naught with an increase in population due to a decrease in the average per capita national income. As an example, let us give the theory of quasi-stable equilibrium by H. Leibenstein.

The “vicious circle” is that higher yields lead to better nutrition. Improved nutrition, in turn, leads to a decrease in mortality and an increase in life expectancy. All this leads to population growth. And the growing population is dividing the available resources among themselves. Land plots are being fragmented and, as a result, yield is falling.

In addition to "vicious circles", where the population in the country is taken as a basis, there are also options that explain the narrowness of the domestic market or the lack of resources for modernization. An example of such theories is the views of Columbia University professor Ragnar Nurke. According to his theory, a lack of capital leads to low labor productivity, which leads to a low level of income. As a result, there is weak purchasing power and insufficient incentive to invest. A typical feature of such a society is limited savings and lack of interest in investment.

In addition, there were a number of researchers linking backwardness with low qualifications of the labor force and the absence of a normal education system.

Scientists believed that to overcome such circles, a powerful external injection of capital was necessary, as a result of which self-sustaining growth would begin. But since it is unrealistic to invest these resources on a voluntary basis, it was assumed that compulsory savings were formed as a result of the monetary and tax policy of the state. The inefficiency of the institutional system could be compensated by the import of capital. The amount of injection must be sufficient to initiate irreversible movement; otherwise, there is a danger that it will go entirely to meet current needs, which have greatly increased due to demographic growth and / or demonstration effect. "Minimum critical effort", according to H. Leibenstein, should be such that the level of investment is at least 12-15% of national income. Such an impetus, he believes, on the one hand, will increase the growth rate of per capita income (that is, it will bring consumption out of stagnation), and on the other hand, it will expand the number of economic entities - entrepreneurs that will ensure further growth in per capita income.

According to Keynesian interpretation of the “vicious circle of poverty,” the economic underdevelopment of countries is closely related to low income. Low consumption and low savings generate inefficient demand, which contributes to a narrow domestic market and low investment growth. They, in turn, lead to low production efficiency, low profitability and low incentives to increase production, which explains the low income.

All theories of "vicious circles" had a number of flaws, the most obvious of which was the inability to achieve economic growth without huge injections of capital. Therefore, these theories are practically impossible to apply in practice. The consequence of this was the development of the "big push" theory.

3.2Big push theory

The founder of this theory is P. Rosenstein-Rodan, who formulated it back in 1943 for the underdeveloped countries of the European periphery. Later, the concept of the “big push” was used by Western scholars (R. Nurkse, H. Leibenstein, A. Hirschman, G. Singer, and others) to substantiate the conditions for the modernization of the liberated countries. At the center of their research were the problems of primary industrialization, which were interpreted in the spirit of neo-Keynesianism. Therefore, the main attention was paid to the role of autonomous investments, conditioned by the economic policy of the state, aimed at increasing national income.

Keynes's model could not help in solving such a problem, because it was, first of all, static and considered the economy in the short term. Harrod and Domar later expanded it for a long term.

The "big push" implies a massive injection of capital into the economy to get the country out of the backward state. However, unlike the “vicious circles of poverty,” “big push” theorists were highly critical of market self-regulation. Therefore, they focused on the distribution of investments in the necessary sectors to accelerate the growth of the national economy.

In contrast to the “vicious circles of poverty,” the idea of ​​the “big push” has found its followers. She found distribution in developing countries among leaders, as well as among the general population. Since the implementation of the modernization program was entrusted to state officials, over time, a social stratum was formed in these countries that was interested in its implementation - the state bureaucratic bourgeoisie. Large corporations looking for the most profitable capital investments were also interested. All this contributed not only to a high theoretical interest, but also to attempts at its practical implementation in Asia, Africa and Latin America.

However, despite all the attractiveness of this concept, there was a significant drawback. The theory was calculated on the use of limited capital in developing countries, and did not take into account such a clearly surplus resource as labor.

The big push concept has two different theories:

.Balanced Growth Theory;

.Unbalanced growth theory.

The first theory was developed by Ragnar Nurke. He believed that in order to modernize it is necessary to carry out a "balanced set of investments." Balance here is meant as equality of supply and demand. At the initial stage, there is no such correspondence, but the synchronous application of capital to a wide range of branches of material production will make it possible not only to achieve self-sustaining growth, but also to overcome the narrowness of the market, typical for most developing countries. At the same time, it is necessary to take into account the intervention of the state, which ensures the creation of a market infrastructure, the preparation of prerequisites for the deployment of private entrepreneurship. Forced savings will gradually be replaced by voluntary, autonomous investments - induced. All this will create conditions for the full-fledged operation of the market mechanism.

However, this approach had many disadvantages:

1.Implementation of the plan would lead to the superstructure of the new economic system over the old;

2.I did not take into account the time lag, because in the absence of centralized management, investments would hardly coincide in time and space;

3.An imbalance would lead to a slowdown in overall growth.

Therefore, other authors also proposed their ideas for this concept and the theory of unbalanced growth by Albert Hirschman appeared. The scientist noted that in order to implement the plan of the “theory of balanced growth” it is necessary to have huge capital, just the resource that is absent in the countries of the “third world”. Therefore, he offers developing countries the concept of unbalanced growth. The first investment, he believes, will inevitably upset the balance. However, this violation also plays a positive role, as it will stimulate new investments. New investments, correcting old imbalances, will cause imbalances in other sectors and in the economy as a whole. And it, in turn, will become an incentive for further investments.

However, this theory is not very realistic. Hirschman adheres to idealistic views on politics and economic processes in the third world countries. He assigns too much of a role to market mechanisms, which should respond to the slightest instability. In reality, instability causes even greater deficits in the economy.

In addition, Hirschman also idealizes the policy of the state in the "third world". He believes that it prioritizes modernization and increasing prosperity, while in fact it pursues its own selfish interests more.

Criticism of A. Hirschman's views contributed to the well-known rehabilitation and further development of the original concept. Hans Singer put forward the concept of modernization as “balanced growth through unbalanced investment”. A "big push" in industry, he rightly believes, is impossible without a "big push" in the agrarian sphere. Therefore, G. Singer pays special attention to the conditions of modernization - the preparation of a properly balanced path of development. To the fore, he puts forward an increase in agricultural productivity, an increase in labor productivity in agricultural sectors and stimulation of the development of traditional export industries. In a number of cases, in the course of modernization, it is advisable to develop import substitution and, in any case, to increase the absorption capacity of a developing society by developing its own production and social infrastructure. Only under these conditions does the "big push" reach its goal. We see that even this most developed concept is characterized by an orientation towards external resources. The topic of capital imports was further developed within the framework of the growth theory with two deficits.

3 Model of economic growth with two deficits

The economic growth model with two deficits was developed in the 60s and 70s. a group of American researchers - H. Chenery, M. Bruno, A. Straut, P. Extein, N. Carter and others.

It represents medium- and long-term regressive models in which the growth rate is determined depending on the deficit of domestic (savings deficit) or external (trade deficit) resources. The model includes three main elements: first, the calculation of the required resources received as the difference between savings (S) and investments (I); second, the calculation of the foreign trade deficit (exports (X) minus imports (M)); third, the definition of absorption (absorption) capacity, understood as the maximum amount of capital resources that a developing country is able to productively use at the moment. Therefore, in statics, the model can be written as follows:

S-I - savings deficit, X-M - trade deficit, where Y is income, Q is output, C is total consumption, S is gross savings, I is gross domestic investment, X is exports, M is imports.

The amount of foreign aid to meet the specified target growth rate of the modernization policy is determined by the largest of the two deficits. Aid is provided not only in order to reduce internal and external deficits, but also in order to over time either refuse foreign aid altogether, or significantly reduce its amount. The model assumes two periods. The second (long-term) includes two alternative stages.

In dynamics, the model considers 2 periods:

· medium-term (5-10 years);

· long-term (over 10 years).

In the medium term, the first stage stands out: the “big push”. In dynamics, the volume of foreign aid was calculated using the formula:

t - the required amount of assistance in period t,

The maximum possible investment growth rate,

k - incremental capital coefficient;

a - the marginal saving rate or marginal propensity to save. , where - potential domestic savings.

It is assumed that the first stage of modernization will end when the growth rate of investments equals the growth rate of GNP. Let us assume that this will happen at the moment of time t = m. Then I m = k * * Y m , where - target growth rate of GNP.

After the first stage, depending on which deficit prevails, the next stage begins (stage 2 - savings deficit, stage 3 - trade deficit).

Let's consider the second stage in more detail. As noted above, it is characterized by a savings deficit. To overcome this deficit, external sources are used, namely the import of foreign goods and services. However, the purpose of this stage is that this flow should be constantly decreasing. This is achieved when a > k ... Then S = I, and 0, where M is the required volume of imports of goods and services.

Now let's move on to the third stage. To eliminate the foreign trade deficit, it is necessary to redistribute domestic investments. If the third stage has begun, then Y t = Y n (1 + r) 1-n ... Moreover, M t = M n + µ (Y t - Y n ), and X t = X n (1+?) t-n, where µ - marginal propensity to import. ? - export growth rate, calculated exogenously (characterizes government measures to stimulate exports). In this case, the volume of foreign resources is calculated by the formula: Ft = Mt- Xt = Mn + µ (Yt- Yn) - Xn (I + x) t-n, where x is the growth rate of imports, calculated exogenously. Then the foreign trade deficit will be eliminated under the condition x >> r, and µ <<µWed , where µ Wed - average propensity to import; while S> I, where S - potential savings. The growth in potential savings will not only meet domestic investment needs, but will also allow foreign aid to be phased out over time. The calculation of a sufficient amount of savings is made as follows: S t = I t - F t = k r Yt- F t.

The described modernization model was developed for Israel. Later, it was significantly improved and was widely used to determine the amount of foreign aid in Asia and Latin America. The two-deficit model is a further concretization of the “big push” idea. Its purpose is to trace the relationship between the development of internal accumulation and external sources of financing. At the same time, this modernization concept has a number of significant disadvantages. First of all, it clearly underestimates the internal resources of developing countries, which objectively leads to an overestimation of the need for foreign aid and, ultimately, to a rapid increase in external debt. The considered concepts of modernization (theories of economic growth and the model with two deficits) were focused on the use of such a factor as capital, which is limited in developing countries, and clearly did not take into account the possibility of using such a relatively redundant factor as labor. This determined the fair criticism of the neo-Keynesian direction from the neoclassicists.
Another notable drawback of this model is the factual justification for the intervention of donor countries in the internal affairs of debtor countries. The very aggregated (approximate) nature of the model turned out to be a significant drawback. In the context of limited and unreliable statistical information, many important model indicators (for example, determining the absorption capacity of the economies of developing countries) are extremely conditional, which reduces the value of the forecasts and recommendations obtained with their help.

4 The theory of the transition to "self-sustaining growth"

Within the framework of the section "Keynesian theories of growth," it is also worth considering the model that was put forward in 1956 by W. Rostow. His theory was called "the concept of the transition to self-sustaining growth."

Rostow proposed to distinguish five stages of growth:

1.traditional society;

2.period of creation of prerequisites for;

3. takeoff;

.movement towards maturity;

5.the era of high mass consumption.

The criteria for identifying the stages were mainly technical and economic characteristics: the level of development of technology, the sectoral structure of the economy, the share of production accumulation in the national income, the structure of consumption, etc.

For the first stage of traditional society, it is characteristic that over 75% of the working-age population is engaged in food production. The national income is mainly used unproductively. This society is structured hierarchically, with political power vested in landowners or the central government.

The second stage is transitional to takeoff. During this period, important changes are being made in three non-industrial sectors of the economy: agriculture, transport and foreign trade.

The third stage - "take-off" - covers a relatively short period of time: 20-30 years. At this time, the rate of capital investment is growing, the output per capita is noticeably increasing, and the rapid introduction of new technology into industry and agriculture begins. Development initially encompasses a small group of industries (the "leading link") and only later spreads to the entire economy as a whole. In order for growth to become automatic, self-sustaining, several conditions must be met:

· a sharp increase in the share of industrial investment in national income (from 5% to at least 10%);

· the rapid development of one or more sectors of the industry;

· political victory of the supporters of economic modernization over the defenders of the traditional society.

The emergence of hotbeds of a new institutional structure should ensure, according to Rostow, the spread of the initial impulse of growth to the entire economic system (by mobilizing capital from internal sources, reinvesting profits, etc.).

The fourth stage - the period of "movement to maturity" - is characterized by W. Rostow as a long stage of technical progress. During this period, the process of urbanization develops, the share of skilled labor rises, and the management of industry is concentrated in the hands of qualified managers - managers.

During the fifth stage - "the era of high mass consumption" - there is a shift from supply to demand, from production to consumption. This period, for example, corresponded to the state of American society in the 1960s.

In his later work Politics and the Stages of Growth (1971), Rostow adds a sixth stage - the “stage of seeking quality” of life, in which the spiritual development of a person is brought to the fore. Thus, he tried to outline the prospects for the development of modern societies.

Development with this approach is understood, first of all, as a synonym for high growth rates. Deep social, institutional changes appear as if in the shadows, the ratio of investments and growth rates of the gross national product comes to the fore.

Rostow's theory of self-sustaining growth was a big step up from other theories of the 20th century. However, it did not have a number of shortcomings, primarily due to the fact that the model claims to explain historical processes.

1.Social and legal aspects are underestimated;

2.Absolutizes periods of modernization;

3.The Industrial Revolution is interpreted one-sidedly;

4.The abstract nature of the quantitative criteria by which the stages were distinguished. The theory that self-sustaining growth requires a doubling of the share of productive investment is not consistent with the historical experience of advanced capitalist countries.

economic growth theory model

4.R. Solow's neoclassical growth model

Unlike Keynesian models, Solow's economic model is multifactorial. The following factors are highlighted: technical progress, capital accumulation, growth of labor resources.

R. Solow showed that the instability of dynamic equilibrium in Keynesian models was a consequence of the non-fungibility of factors of production. Instead of the Leontief function, he used the Cobb-Douglas production function in his model, in which labor and capital are substitutes. Other prerequisites for analysis in the Solow model are: diminishing marginal productivity of capital, constant returns to scale, constant retirement rates, and the absence of investment lags.

The interchangeability of factors (change in capital-labor ratio) is explained not only by technological conditions, but also by the neoclassical premise of perfect competition in the factor markets.

A necessary condition for the equilibrium of the economic system is the equality of aggregate supply and demand. The proposal is described by a production function with constant returns to scale: Y = F (K, L), and for any positive z it is true: zF (K, L) = F (zK, zL). Then if z = 1 / L, then Y / L = F (K / L).

Let us denote Y / L by y, and K / L by k and rewrite the original function in the form of the relationship between productivity and capital-labor ratio (capital-to-labor ratio): y = f (k). The tangent of the slope of this production function corresponds to the marginal product of capital (MRC), which decreases with the growth of capital-labor ratio (k).

Aggregate demand in the Solow model is determined by investment and consumption: = i + c, where i and c are investments and consumption per employee.

Income is divided between consumption and savings in accordance with the savings rate, so that consumption can be represented as c = (l - s) y, where s is the savings (accumulation) rate, then y = c + i = (1 - s) y + i, whence i = sy. In equilibrium, investment is equal to savings and is proportional to income.

Conditions of equality of supply and demand can be represented as f (k) = c + i or f (k) = (1 - s) y + i

The production function determines the supply of goods in the market, and capital accumulation determines the demand for the product produced.

The dynamics of the volume of output depends on the volume of capital (in our case, capital per employee, or capital-labor ratio). The volume of capital changes under the influence of investment and disposal: investments increase the capital stock, disposal - decreases.

Investments depend on the capital-labor ratio and the rate of accumulation, which follows from the condition of equality of supply and demand in the economy: i = sf (k). The accumulation rate determines the division of the product into investment and consumption at any value of l (Figure 10).

Depreciation is accounted for as follows: if we assume that a fixed part d (the rate of disposal) is retired annually due to capital depreciation, then the amount of retirement will be proportional to the amount of capital and equal to dk. On the graph, this relationship is reflected by a straight line outgoing from the point of origin, with a slope d.

The influence of investment and disposal on the dynamics of capital stocks can be represented by the equation Аk = i - dk, or, using the equality of investments and savings, Аk = sf (k) - dk. The capital stock (k) will increase (Аk> 0) to a level at which investments will be equal to the amount of disposal, i.e. sf (k) = dk. After that, the capital stock per employee (capital-labor ratio) will not change over time, since the two forces acting on him will balance each other (Ak = 0). The level of capital stock at which investments are equal to retirement is called the equilibrium (stable) level of capital-labor ratio and is denoted by k *. When k * is reached, the economy is in a state of long-term equilibrium.

The equilibrium is stable, because regardless of the initial value of k, the economy will tend to the equilibrium state, i.e. to k *. If the initial k 1below k *, then gross investment (sf (k)) will be greater than disposal (dk) and the capital stock will increase by the amount of net investment. If k 2> k *, this means that investment is less than depreciation, which means that the capital stock will decrease, approaching the level k *.

The rate of accumulation (savings) directly affects the stable level of capital-labor ratio. Rising savings rate with s 1up to s 2shifts the investment curve upward from position s 1f (k) to s2 (j) (Fig. 12).

In the initial state, the economy had a stable capital stock to 1*, at which investment was equal to disposal. After the increase in the savings rate, investments increased by (i 1- i 1), and the capital stock (k 1*) and disposal (dk) remain the same. Under these conditions, investments begin to exceed disposal, which causes an increase in the capital stock to the level of the new equilibrium k 2*, which is characterized by higher values ​​of capital-labor ratio and labor productivity (output per employee, y).

Thus, the higher the rate of saving (accumulation), the higher the level of output and capital stock can be achieved in a state of stable equilibrium. However, an increase in the rate of accumulation leads to an acceleration of economic growth in the short term, until the economy reaches a point of a new stable equilibrium.

Obviously, neither the accumulation process itself, nor the increase in the saving rate can explain the mechanism of continuous economic growth. They show only the transition from one state of equilibrium to another.

For the further development of the Solow model, two prerequisites are alternately removed: the invariability of the population and its employed part (their dynamics is assumed to be the same) and the absence of technical progress.

Suppose the population is growing at a constant rate of n. This is a new factor that, together with investment and retirement, affects the capital-labor ratio. Now the equation showing the change in the capital stock per employee will look like this:

K = i - dk - nk or? K = i - (d + n) k.

Population growth, like retirement, reduces the capital-labor ratio, although in a different way - not through a decrease in the available capital stock, but by distributing it among the increased number of employed. In these conditions, such a volume of investment is necessary, which would not only cover the outflow of capital, but would also provide capital for new workers in the same volume. The product nk shows how much additional capital is required per employee so that the capital-labor ratio of new workers is at the same level as the previous ones.

The condition of stable equilibrium in the economy with a constant capital-labor ratio k * can now be written as follows:

K = sf (k) - (d + n) k = 0 or sf (k) = (d + n) k.

This state is characterized by full employment of resources. In a stable state of the economy, capital and output per person employed, i.e. capital-labor ratio (k) and labor productivity (y) remain unchanged. But in order for the capital-labor ratio to remain constant even with the growth of the population, capital must increase at the same rate as the population:

Thus, population growth becomes one of the reasons for continuous economic growth in equilibrium conditions.

Note that with an increase in the rate of population growth, the slope of the curve (d + n) k increases, which leads to a decrease in the equilibrium level of capital-labor ratio (k "*), and, consequently, to a fall in y.

Taking technological progress into account in the Solow model modifies the original production function. A labor-saving form of technological progress is assumed. The production function will be represented as Y - F (K, LE), where E is labor efficiency, a (LE) is the number of conventional units of labor with constant efficiency E. The higher E, the more products can be produced by a given number of workers. It is assumed that technological progress is carried out by increasing the efficiency of labor E at a constant rate g. The growth in labor efficiency in this case is similar to the results of the growth in the number of employees: if technological progress has a rate of g = 2%, then, for example, 100 workers can produce the same amount of products as 102 workers previously produced. If now the number of employed (L) is growing at a rate of n, and growing at a rate of g, then (LE) will increase at a rate (n + g).

The inclusion of technological progress also slightly changes the analysis of the state of stable equilibrium, although the line of reasoning remains. If we define k as the amount of capital per unit of labor with constant efficiency, then the results of the growth of effective units of labor are similar to the growth in the number of employees (an increase in the number of units of labor with constant efficiency reduces the amount of capital per unit). In a state of stable equilibrium, the level of capital-labor ratio k "* balances, on the one hand, the effect of investments that increase capital-labor ratio, and on the other hand, the effect of retirement, an increase in the number of employees and technological progress, which reduce the level of capital per effective unit of labor:

(s? k ") = (d + n + g) k".

In a steady state (k "*) in the presence of technological progress, the total volume of capital (K) and output (Y) will grow with the rate (n + g). But, unlike the case of population growth, now the capital-labor ratio K / L and output Y / L per person employed; the latter can serve as the basis for improving the well-being of the population.Technological progress in the Solow model is, therefore, the only condition for continuous growth in living standards, since only if it is available, there is a steady increase in per capita output ( y).

Thus, in the Solow model, an explanation has been found for the mechanism of continuous economic growth in the equilibrium mode with full employment of resources.

As is known, in Keynesian models, the saving rate was set exogenously and determined the value of the equilibrium income growth rate. In the neoclassical Solow model, for any saving rate, the market economy tends to an appropriate stable level of capital-labor ratio (k *) and balanced growth, when income and capital grow at a rate (n + g). The value of the rate of saving (accumulation) is an object of economic policy and is important in assessing various programs of economic growth.

Since equilibrium economic growth is compatible with different saving rates (as we have seen, an increase in s only accelerated economic growth for a short time, while in a long period the economy returned to a stable equilibrium and a constant growth rate depending on the value of n and g), the problem of choosing the optimal savings rates.

The optimal rate of accumulation, corresponding to the "golden rule" of E. Phelps, ensures equilibrium economic growth with the maximum level of consumption. The stable level of capital-labor ratio corresponding to this rate of accumulation will be denoted by k **, and consumption - by c **.

The level of consumption per one employed at any stable value of the capital-labor ratio A * is determined by a series of transformations of the initial identity: y = c + i. We express consumption c through y and i and substitute the values ​​of these parameters, which they take in a steady state:

Y - i, c * = f (k *) - dk *,

where c * is consumption in a state of sustainable growth, and i = sf (k) = dk by definition of a stable level of capital-labor ratio. Now, from various stable levels of capital-labor ratio (k *), corresponding to different values ​​of s, it is necessary to choose one at which consumption reaches its maximum.

If selected to *< к**, то объем выпуска увеличивается в большей степени, чем величина выбытия (линия f(k*) на графике круче, чем dk*), а значит, разница между ними, равная потреблению, растет. При к* >k ** the increase in the volume of output is less than the increase in disposals, i.e. consumption is falling. Consumption growth is possible only up to the point k **, where it reaches its maximum (the production function and the dk * curve here have the same slope). At this point, an increase in the stock of capital per unit will give an increase in output equal to the marginal product of capital (MRC) and will increase disposal by the amount d (depreciation per unit of capital). There will be no growth in consumption if the entire increase in output is used to increase investments to cover disposal. Thus, at the level of capital-labor ratio corresponding to the "golden rule" (k **), the following condition must be met: MRC = d (marginal product of capital is equal to the rate of retirement), and taking into account population growth and technological progress: MRK = d + n + g ...

If the economy initially has a capital stock that is greater than it follows according to the "golden rule", a program to reduce the rate of accumulation is needed. This program leads to an increase in consumption and a decrease in investment. At the same time, the economy goes out of balance and reaches it again at proportions corresponding to the "golden rule".

If the economy initially has a capital stock of less than k **, a program is needed to increase the savings rate. This program initially leads to an increase in investment and a drop in consumption, but as capital accumulates, from a certain point, consumption begins to grow again. As a result, the economy reaches a new equilibrium, but in accordance with the "golden rule", where consumption exceeds the initial level.

This program is usually considered unpopular due to the presence of a "transition period" characterized by a drop in consumption, therefore its adoption depends on the intertemporal preferences of politicians, their orientation towards short-term or long-term results.

The considered Solow model allows us to describe the mechanism of long-term economic growth that maintains equilibrium in the economy with full employment of factors. She singles out technological progress as the only basis for sustainable growth in well-being and allows you to find the optimal growth option that maximizes consumption.

5. Model of zero economic growth

In the early 70s of the XX century. some economists came up with the concept of the inevitability of a global catastrophe while maintaining the existing trends in the development of society. Thus, in the report of the Club of Rome "The Limits to Growth", prepared by the research group of the Massachusetts Institute of Technology, USA, led by prof. D. Meadows, noted that in connection with the aggravation of the contradictions between the rapidly growing population of the Earth, the rapid development of the production of investment goods and the rapidly depleting natural resources of the planet, every day of continued growth brings the world system closer and closer to the limits of this growth. Based on our current knowledge of the physical boundaries of the planet, it can be assumed that the growth phase should end within the next hundred years. Further, according to the author of the report, given the current trends, the achievement of "growth limits" will inevitably be accompanied by a spontaneous decline in the population and industrial production as a result of hunger, environmental destruction, depletion of resources, etc. In this situation, according to the authors of the report, the only way out is to maintain "zero growth".

Supporters of "zero growth" argue that technological progress and economic growth lead to a number of negative phenomena of modern life: environmental pollution, industrial noise, the release of toxic substances, the deterioration of the appearance of cities, etc. Since the production process only transforms natural resources, but does not completely utilize them, over time they return to the environment in the form of waste. Because of this, supporters of "zero growth" believe that economic growth should be purposefully contained. Recognizing that economic growth provides an increase in the volume of goods and services, supporters of "zero growth" come to the conclusion that economic growth cannot always create a high quality of life.

At the same time, opponents of D. Meadows and his like-minded people - supporters of economic growth - believe that this growth in itself softens the contradictions between unlimited needs and scarce resources, since in conditions of economic growth it is possible to maintain infrastructure at this level, implement aid programs the elderly, the sick and the poor, improve the education system and increase personal income.

As for the environment, proponents of economic growth believe that environmental pollution is not the result of economic growth, but the result of incorrect pricing, distorted by externalities.

To solve this problem, it is necessary both to introduce legislative restrictions or special taxes, and to form a market for pollution rights.

CONCLUSION

Economic growth is one of the main goals of society, since on its basis it is possible to increase the well-being of the population and solve new socio-economic problems. The combination of factors of economic growth is subordinated to the solution of the problem of maximizing marginal productivity. Today, the most promising is the use of long-term factors of economic growth associated with the use of scientific and technological progress and investment in human capital.

Economic growth depends on many factors, such as land, labor, capital, scientific and technological progress, and institutional factors. It is incredibly difficult to take into account all of the above, so it is incredibly difficult to predict how the economy will behave, and even more so to correctly apply methods to stimulate economic growth. That is why economists make many assumptions when creating models, which simplifies the model, but also pushes the result away from reality.

The first considered in this course work was Keynes's model, as it had a huge impact on the economy of both the past and the present. Many omissions were noted that prevent the full application of those concepts in modern practice.

Subsequent economists Harrod and Domar refined Keynes's model, making it dynamic, but the model still remains univariate and works more in theory.

The concepts of the “vicious circle of poverty”, “big push” and “model with two deficits” had a great influence on the development of the countries of the “third world”. However, the “big push” model has achieved the greatest recognition among the leaders of states. It cannot be said unequivocally that this model is perfect and will solve the problems of the third world countries. There are still many shortcomings, provisions that exist only in theory, but in practice everything is much more complicated.

Therefore, despite the enormous contribution that scientists have made to economic science, one cannot rely only on these theoretical propositions, it is necessary, among other things, to take into account the real state of affairs, the peculiarities of each state separately.

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Economic growth concept

Definition 1

Economic growth is the central object of research in modern macroeconomics, which is the basis for solving most of the social and economic problems in society.

Economic growth is the main factor of civilizational progress and the result of the development of technology and science in the state. The main parameters of economic growth, including its dynamics, are widely used to characterize the development of the national economy and state regulation of the economy.

In general terms, economic growth is represented by an increase in the gross domestic product per capita, and an increase in the rate leads to an increase in the level of income of the population, a decrease in unemployment, and an increase in budget revenues. For this reason, promoting growth is one of the main tasks of the economy of any country, which has been facilitated by various theories of economic growth applied in practice.

Economic growth is born at the production stage and gains sustainable development at other stages. The types of economic growth are represented by the extensive and intensive types.

The essence of the extensive type is to increase the national product through the growth of quantitative factors of production, that is, the attraction of additional factors.

Remark 1

The intensive type is a more complex type, which is carried out through the qualitative improvement of technologies and an increase in the main production factors.

In order to characterize economic growth, a large number of indicators are used, which are divided into qualitative and quantitative, as well as dynamic and static.

Dynamic indicators characterize the macroeconomic development of the state economy. Static indicators are able to reflect the existing equilibrium conditions for various processes.

The basis of the economic growth model

Modern economic growth models were formed on the basis of the classical and Keynesian approach to the development of the economy and the economy. If we consider the Keynesian model of economic growth, then it was based on the study of the national economy as a whole.

Keynesians considered the main problem of macroeconomics to be the factors that determined the level and dynamics of national income, including its distribution. The theory considered these factors from the standpoint of the formation of effective demand, referring to the implementation of the study of the main parts of demand, as well as the factors on which the parts and demand as a whole depend.

The volume and dynamics of national incomes, according to Keynes's research, depended on the movement of consumption and accumulation.

Neo-Keynesianism studied the problem of the dynamics of effective demand, the concept of the multiplier and the use of investments. Other aspects of Keynes's theory were related to the monetary sphere and were considered insignificant in models of economic growth.

The theoretical basis of neo-Keynesian concepts was based on the views of Keynes, especially on the position that the spontaneous mechanism of the market is not able to ensure an equilibrium of supply and demand, during which underemployment of citizens and material resources may arise.

To achieve market stability, there is a problem of effective demand and state regulation of the economy, which affect the factors that make up effective demand, which is able to ensure stability.

Based on these provisions, the American economists Domar and the English Harrod came up with their theories of economic growth.

The central problem of neo-Keynesianism was the problem of implementation, that is, the movement that promoted the full use of production resources. In this case, the economy will be in a state of dynamic equilibrium.

With the help of changes in effective demand, it was possible to determine the actual level of production, as well as its deviation in a certain direction from the potentially possible level.

The theory accepts the importance of economic growth to consider the quantitative relationships between accumulation and consumption, as well as the principle of the multiplier-accelerator. The main driver of economic growth has been investment, which is viewed in conjunction with savings.

Subsequently, the Keynesian and neo-Keynesian models were brought closer to reality and somewhat complicated, but, as before, the increase in production growth was considered only as a function of new investments.

Neoclassical model of economic growth

The neoclassical model of economic growth considered the idea of ​​an optimal market system as a perfect and self-regulating mechanism that allowed the best use of all factors not only for each economic entity, but also for the economy as a whole.

Through market prices, free competition could provide general equilibrium or a state of optimality by creating conditions for obtaining utility. Depending on this, the system of optimal growth was modeled in conditions of perfect competition, for which a number of prerequisites were subsequently introduced: the need for complete information about the conditions of supply and demand, as well as the technical and production capabilities of all markets.

When analyzing economic growth, neoclassicists paid attention to the following prerequisites:

• value creation of production factors,
• the contribution by each factor to the creation of the value of the product depending on the marginal products and the receipt of income, which is equal to the marginal product,
• the quantitative relationship of products and resources that are needed for production, as well as the relationship between the resources themselves,
• independence of production factors and interchangeability.

Remark 2

This neoclassical model is a multivariate model. Whereas the neo-Keynesian and Keynesian models were univariate. The scientific and technological revolution gave a powerful impetus to new research in the field of economic growth theory.

Economic growth, its modeling, taking into account the state of ecology and social sphere in economic and mathematical models

Economic growth models are widely represented in economic research. On the basis of these models, various problems of analysis and forecasting of the development of national economies are solved.

Modern models of economic growth take into account the possibility of investing not only in physical capital, but also in a number of other productive resources. This is due to the recognition that a large number of technological, organizational and other factors contribute to the increase in the efficiency of the use of production resources, the totality of which is covered by the concept of scientific and technological progress (STP).

In addition, in recent years, more and more works have appeared in which it is investigated how the growth of production affects the ecological situation, how ecology affects the possibility of growth, how the level of economic development is associated with various indicators characterizing the state of the social sphere. However, due attention is not paid to the mutual influence of the economy, ecology and social sphere, despite the desire of many countries of the world for sustainable development, which is understood as development that meets the needs of both the present and future generations for economic and environmental benefits. This means an increase in gross domestic product (GDP) while reducing the anthropogenic load on the environment. The concept of sustainable development also includes the problems of narrowing the gap in the levels of economic development of different countries and the welfare of their population, security, etc.

The solution of these problems requires the use of methods of economic and mathematical modeling of economic growth, taking into account environmental and social factors.

Exogenous - external; endogenous - internal.

Development of economic growth models

Growth theory has experienced three major waves of development. The first was associated with the work of E. Lundberg and developed by Harrod and Domar. These works appeared in the late 30s and 40s. In the mid-1950s, the emergence of the neoclassical growth model of Solow and Swann sparked a second, longer wave of interest among economists in this topic. The third wave of research began in the mid-1980s with the work of Romer and Lucas and continues to this day.

Harrod and Domar tried to combine Keynesian analysis with elements of economic growth. They used production functions with little substitutability to argue that the capitalist system is inherently unstable. Because they wrote during and immediately after the Great Depression, their arguments were accepted by many economists. Their results played a role in the development of the theory, but their analysis is very rarely used today.

The next and more important achievement belongs to Solow and Swan, who published their work in 1956. A key aspect of the Solow-Swan model is the neoclassical form of production function, which assumes constant returns to scale, diminishing returns from each factor, and positive elasticity of factor substitution. This production function, together with a constant rate of accumulation, is used to create the simplest general equilibrium model in the economy.

One of the consequences of this model has only come to be used as an empirical hypothesis in recent years. We are talking about conditional convergence. A lower starting level of real GDP per capita relative to the long-term or equilibrium state causes a higher growth rate. This property follows from the assumption of diminishing returns to capital. Economies with less capital per worker tend to grow at higher rates. The convergence of the relative equilibrium level of capital and output per unit of labor depends in the Solow-Swan model on the rate of accumulation, the rate of population growth and the state of the production function, i.e. characteristics that can vary from economy to economy. Modern research makes it possible to take into account the differences between countries, especially in public policy and the initial state of human capital. However, the concept of conditional convergence - the main feature of the Solow-Swan model - largely explains economic growth in different countries and regions.

Another implication of the Solow-Swan model is that there is no endless improvement in technology, growth (in terms of capital-labor ratio) should gradually stop. This is also a consequence of diminishing returns on capital.

Neoclassical growth theorists of the late 50s - early 60s. recognized such modeling as insufficient and often supplemented it with the assumption of the exogenous nature of scientific and technological progress. This made it possible to speak of a positive, possibly constant, growth rate in the long run, and this growth depends on the rate of scientific and technological progress, which is determined outside the model.

Perhaps due to the lack of empirical relevance, growth theory practically ceased to develop as an area of ​​active research in the early 70s. on the eve of the revolution of rational expectations and oil shocks. For about fifteen years, macroeconomic development has focused on short-term fluctuations. Major advances included the incorporation of rational expectations into business cycle theory, improved approaches to political development, and the application of general equilibrium analysis techniques to real business cycle theory.

Since the mid-1980s, research on economic growth has experienced a new boom, beginning with the work of Romer and Lucas. The reason for this is that the drivers of long-term economic growth are much more important than the mechanism of the business cycle or the results of the government's monetary or fiscal policy aimed at countering cyclical fluctuations. But realizing the importance of long-term growth is only the first step. To go further, it is necessary to avoid the limitations of the neoclassical growth model, in which the rate of long-term growth of capital-labor ratio is tied to the rate of exogenous scientific and technological progress. Thus, it is imperative that new advances determine the long-term growth rate within the model. Therefore, the creation of models of endogenous growth is required.

New research also includes technology diffusion models. Since discoveries are made mainly in more developed countries, the study of diffusion raises the question of how other economies imitate these discoveries. Since imitation is cheaper than innovation, diffuse models yield a form of conditional convergence similar to that arising from the neoclassical model.

Another key exogenous parameter in the neoclassical growth model is population growth rate. A higher rate of population growth reduces the equilibrium level of capital and output per unit of labor and thus reduces the rate of growth of capital-labor ratio for a given level of output. However, the Standard Model does not address the impact of return on capital and wage rates on population growth. Other researchers consider endogenous population growth by incorporating analysis of household choice in relation to childbearing in a neoclassical model. There have also been published works that examine the endogenous growth of the labor force as a result of migration and the choice of workers in favor of work or rest.

Theoretical conclusions from the presented growth models with endogenous technological progress are confirmed by many trends in world development associated with the deepening of globalization processes. However, vulnerabilities in the new theory have been identified, especially with respect to economies of scale, which are not supported by empirical evidence at the country level. This applies, in particular, to the predicted in these models the dependence of growth rates on the number of specialists employed in R&D.

The fundamental or underlying sources of growth include variables that affect the ability of a national economy to accumulate factors of production and invest in knowledge production. Factors affecting economic growth include population growth, the state of the financial sector and the environment, natural resources, trade rules, the size of the state, and indicators of political and social development. In addition, a number of researchers Abramovitz, Dawson, Baumol and others consider the influence of such factors as the institutional structure of the economy, "social potential", "social infrastructure" or "auxiliary variables". Many authors view human capital as a key driver of economic growth.