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The Solow model shows how savings, population growth, and technological change affect economic growth over time, and it helps to identify some of the reasons why countries differ so much in living standards.

Solow proceeds from the fact that a necessary condition for the macroeconomic equilibrium of an economic system is the equality of aggregate demand and aggregate supply.

Solow considered a closed economy without the participation of the state, therefore, in his model, aggregate demand is equal to the sum of consumer and investment demand.

To determine the stability of the state.ec. in the Solow model, it is necessary to consider the problem of capital accumulation. The dynamics of the volume of output depends on the volume (reserve) of capital, which depends on the volume of investments and the rate of disposal of capital: invest. increase the stock of capital, while disposals decrease it.

Let's designate the rate of disposal - d, then arb. Capital accumulation can be written - D k - i-dk.Because investment \u003d savings, then the change in capital stocks can be expressed: D k = sf(k) - qk. Daneur-e is a conv. Capital accumulation.

The Solo y model shows that the savings (accumulation) rate is the main factor determining the level of sustainable capital-labor ratio. A higher savings rate provides a larger capital stock and more high level output per capita. An increase in the savings rate shifts the investment curve upward and the economy moves to a new equilibrium state.

An important source of economic growth is population growth, or rather, an increase in the number of employed (workers). In order for the capital-labor ratio to remain even with population growth, the capital stock must increase at the same rate as it. This is possible if the growth rates of investments turn out to be the same. The growth of the latter will lead to an increase in the level of output of the national product at a harmonized pace.

The third source of economic growth after investment and employment growth is technological progress.

The Solow model shows that sustainable equilibrium economic growth is compatible with different savings rates. Therefore, the problem of choosing the optimal savings rate arises. E.FLeps formulated a condition and called it the golden rule of accumulation: consumption in a growing eq. reaches max. with equality of the marginal productivity of capital and the rate of disposal, and taking into account the growth of population. And technol. progress marginalproduction. Capital should be equal to the rate of economic growth: MPk=d+n+g. This is the very rule of capital accumulation.

The highest level of consumption is achieved at such a fixed level of capital-arms ratio, at which there is the greatest difference between the volume of output and the volume of required investments. The level of consumption corresponding to the evil rule is called sustainable consumption. The stock of capital that provides the mouth. State at max. consumption - golden level of capital accumulation. The fulfillment of the conditions for achieving the maximum consumption per capita is possible with a certain stock of capital. Finding the value of the stock according to the golden rule means choosing the optimal savings rate.

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Federal State Educational Budgetary Institution of Higher Education

"Financial University under the Government Russian Federation»

Department of Economic Theory

COURSE WORK

on the topic « Golden Rule accumulation" by E. Phelps

in the discipline "Macroeconomics"

Completed by a student of the GMF group 2 - 4

Faculty of Finance and Economics

Kosteva Korina Ivanovna

supervisor

assistant Efimova O.N.

Introduction

1. Theoretical aspects of economic growth

1.1 The concept of economic growth

1.2 Extensive and intensive types of economic growth

1.3 Drivers of economic growth

2. The essence and basic concepts of the "Golden Rule of Accumulation" by E. Phelps

2.1 Neoclassical growth model

2.2 E. Phelps' golden rule of accumulation

Conclusion

List of sources used

Introduction

economic growth accumulation phelps

One of the most important long-term goals of the economic policy of the government of any country is to stimulate economic growth, to maintain its pace at a stable and optimal level. Therefore, it is so important to have a clear idea of what economic growth is, what factors stimulate it, and what, on the contrary, hold it back. In economic theory, dynamic models of economic growth are developed that help to explore the conditions for achieving an equilibrium economic growth rate for each specific country and develop an effective long-term economic policy.

The purpose of the course work - is to consider the golden rule of accumulation E. Phelps.

In the course of this goal, it is necessary to solve the following tasks of the course work:

- consider the concept of economic growth;

- to define extensive and intensive types of economic growth;

- to study the factors of economic growth;

- consider the neoclassical model of economic growth;

- reveal the golden rule of accumulation of E. Phelps.

The object of the course work is the golden rule of accumulation.

The subject of the course work is macroeconomics.

The methodological and theoretical basis of the study are the works of leading domestic experts in the field of macroeconomics, namely Anisimov A.A., Anosova A.V., Anosova A.V., Antipina O.N., Antipina O.N., Balabanova A.V. ., Basovsky L.E., Blanchard O., Brodsky B.E. and etc.

1. Theoretical aspects of economic growth

1.1 The concept of economic growth

In the economic literature, the concept of economic growth is interpreted ambiguously.

Some economists understand economic growth as an increase in potential and real gross national product (GNP), an increase in the country's economic power.

Other economists characterize economic growth as:

- increase in production capacities;

- increase in the real volume of production (GNP);

- an increase in real output per capita.

In domestic economic literature, economic growth is understood as the quantitative and qualitative improvement of the social product and its factors of production.

Economic growth has:

- its content (social reproduction);

- movement mechanism (interaction of workers, means of production, nature, technology);

- economic growth cycle phase;

- quantitative and qualitative signs of this movement, reflected in the growth rate of the product;

- socio-economic result (national wealth);

- goal (public welfare).

Economic growth is measured in two ways:

- annual growth rates of the gross national product (GNP);

- annual growth rates of the net national product (NNP).

The second method is more preferred.

Distinguish between potential and actual economic growth. Potential economic growth refers to the total NNP that can be produced if:

- available technology;

- the maximum possible use of workers;

- efficient use of the means of production.

Real economic growth is actually achieved.

The main indicators for measuring economic growth are:

- growth factor - the ratio of the indicator of the study period to the indicator of the base period;

- growth rate - growth factor multiplied by 100%;

- growth rate - growth rate minus 100%.

1.2 Extensive and intensive types of economic growth

There are two types of economic growth: extensive and intensive.

The first type of economic growth is extensive (lat. Extensivus - expanding). In this case, the increase in production volumes occurs due to the increase in three factors:

- fixed capital (funds);

- work force;

- material costs (natural raw materials, materials, energy carriers).

The extensive development of the economy implies the presence in the country of a sufficient amount of labor and natural resources, due to which the scale of the economy can increase.

However, this inevitably worsens the conditions of reproduction. Thus, the equipment at operating enterprises is becoming more and more old. Due to the growing depletion of non-renewable natural resources, more and more labor and means of production have to be spent to extract every ton of raw materials and fuel. As a result, economic growth is increasingly becoming costly.

A long-term orientation towards a predominantly extensive path of output growth leads to the fact that deadlocks arise in the national economy associated with a shortage of certain resources.

A way out of such difficulties can give the second type of economic growth - intensive (fr. Intensive - tension). Its main difference from extensive growth is that the increase in the scale of production in this type of growth is achieved by increasing the efficiency of the factors of production used. As a rule, the focus is on:

- the use of more advanced technology, advanced technologies;

- use of more economical materials, energy carriers;

- advanced training of personnel, that is, the qualitative improvement of all factors of production.

At the same time, the qualitative transformation of factors based on the achievements of scientific and technological progress is accompanied by a quantitative reduction in traditional factors during the period of technical re-equipment of production.

There are three main types of economic growth intensification:

Labor-saving intensification - new technology displaces labor force from production. That is, the entire increase in production is achieved partially or completely by increasing labor productivity. The efficiency of the use of labor resources is determined by the ratio of output to the cost of living labor. And its inverse indicator - characterizes the complexity of products. This type of intensification is most characteristic of the initial period of development of industrial production.

Capital and material-saving intensification is carried out through the use of more advanced machines and equipment, more efficient use of materials, energy carriers, etc.

At the same time, the rate of return on capital characterizes the efficiency of the use of productive capital. It is determined by the ratio of the volume of output to the value of the cost of purchasing fixed assets. And its inverse indicator - characterizes the capital intensity of production. The indicator of material and resource productivity characterizes the efficiency of the use of material, natural resources. It is determined by the ratio of output to the cost of material, natural resources - raw materials, energy, etc. Its inverse indicator characterizes the material and resource intensity of products.

Capital and material-saving intensification are widely used in the conditions of industrial, post-industrial development.

The process of modern intensification in the conditions of limited raw materials, investment, human resources leads to the transformation into entrepreneurial ability, the scientific potential of society to solve urgent problems of economic development. Today it is impossible to do without the creation of new materials, fundamentally new sources of energy.

The latest scientific and technological orientation of the beginning of the XXI century. - on the development of nanotechnologies that provide the possibility of a "breakthrough", allowing the creation of hitherto unknown structural materials, the latest technologies using processes occurring at the atomic level. It is important to note that today Russia is one of the leaders, along with the United States and Japan, of work in this direction, which seems to be extremely promising.

1.3 Drivers of economic growth

In real economic practice, there is no purely extensive and purely intensive type of economic growth, since they are intertwined. Therefore, they speak of predominantly extensive and predominantly intensive types of economic growth, depending on the share of certain factors that caused this growth.

The process of economic growth includes the interaction of its factors. In macroeconomics, there are three groups of economic growth factors that determine the sources of economic growth, i.e. factors that make economic growth physically possible. These include:

- supply factors (availability of human resources, natural resources, fixed capital, level of technology);

- demand factors (price level, consumer spending, investment spending, government spending, net exports);

- distribution factors (rationality and completeness of the involvement of resources in the production process, the efficiency of the use of resources involved in the economic turnover).

It is obvious that large reserves of various natural resources, the presence of fertile lands, favorable climatic and weather conditions, and significant reserves of mineral resources make a significant contribution to the country's economic growth.

However, the availability of abundant natural resources is not always a self-sufficient factor in economic growth. For example, some countries in Africa and South America have significant reserves of natural resources, but are still on the list of backward countries. This means that only the efficient use of resources leads to economic growth.

Technology level. This factor is closely related to supply, since the accumulation of a sum of knowledge leads to the accumulation of capital. Usually, two types of development of scientific and technical knowledge are distinguished: inventions and innovations.

Inventions lead to serious, revolutionary, qualitative changes in production, and innovations improve existing knowledge. Inventions and innovations are embodied in capital and play a decisive role in its growth. Scientific and technological progress, as a factor of economic growth, is becoming increasingly important in modern conditions.

The volume of fixed capital. One of the most important factors in economic growth is the accumulation of capital (equipment, buildings and stocks of industrial goods used in the production process).

Aggregate demand factors. All factors affecting aggregate demand ultimately have an impact on economic growth. Insufficiently efficient aggregate demand does not stimulate proper economic growth. This factor is especially important for Keynes and his followers.

The implementation of the increased national product depends on the factors of aggregate demand, that is, all elements of aggregate demand must provide full employment of all increasing resources. In addition, factors related to aggregate demand include the efficient allocation of resources.

Factors holding back economic growth include:

- the degree of completeness and efficiency of the use of natural, industrial and labor resources. Efficient use of economic resources requires their most optimal distribution between spheres and sectors of the economy;

- efficient and fair distribution of the growing volume of resources and the growing volume of real production. Since aggregate demand is determined by aggregate costs, they must be increased in order to ensure the full use of the increased volume of resources;

- institutional factors constraining or stimulating economic growth. These include: legal norms (labor protection, environmental protection, crime control, etc.), morality and traditions, labor conflicts, discrimination, etc.

2. The essence and basic concepts of the "Golden Rule of Accumulation" by E. Phelps

2.1 Neoclassical growth model

The neoclassical model is also the fact that it demonstrates the sustainability of economic growth, that is, the ability of the economic system to return to the trajectory of balanced development with the help of internal market self-regulation mechanisms.

Figure 1 - Neoclassical model

Dividing the two-factor production function Y = f(K, L) by the amount of labor L, we get the production function for one worker: y = f(k), where k = K/L is the capital-labor ratio of a unit of labor, or one worker Income (y = Y/L) appears as a function of only one factor - the capital-labor ratio (k).

Such a unit production function, reflecting the average level of labor productivity, is shown in Fig. 1. Note that the steepness of its slope, determined by the value of the marginal productivity of RTO capital, changes. As the amount of capital per worker increases, the marginal productivity of this factor decreases (in accordance with the theory of marginal factor productivity), which causes a slowdown in the growth of the income function.

Part of the income Y is used for consumption, and the other part is saved. In the Solow model, where all macroeconomic indicators are calculated per worker, savings will also be a part of unit income sy or sf(k), where s is the savings rate that determines how much of the income is saved.

The condition for macroeconomic equilibrium is the equality of aggregate demand (AD) and aggregate supply (AS), which automatically leads us to macroeconomic equality I = S (investment is equal to savings). All savings in the economy are fully invested, and this allows us to equate the function of actual investment per worker (i) to the unit savings function: i = sy = sf(k). Keeping in mind the macroeconomic equality Y = C + I (income equals the sum of consumption and savings), output per worker can be written as y = c + i, where y = Y/L, c = C/L, i = I /L, and represent the consumption function as

c = y - i = f(k) - sf(k).

Graphically, the size of consumption and investment at each level of capital-labor ratio is shown in Fig. 1. The curve sf(k) denotes the graph of actually made investments, which, according to the model condition, are equal to savings. Since savings make up a certain percentage of output, the actual investment per capita is represented by the graph below the graph. production function y = f(k) in Figure 1.

The distance between the graphs of the functions f(k) and sf(k) determines the volume of consumption (c). Thus, the consumption function is described by the formula:

c = f(k) - sf(k).

To determine the stationary state of the economy in the Solow model, it is also necessary to consider the problem of capital accumulation. Obviously, in order for the capital-labor ratio to remain unchanged under the condition of population growth, it is necessary that capital K increase at the same rate n as population growth L. Thus, the required investment per worker ir (superscript r for the investment symbol i - from the English word required - required) can be written as the following equality: ir = nk. Moreover, if the population growth rate and the rate of capital accumulation are equal, then per capita output y remains unchanged.

Let's not forget that in order to describe the net capital gain, we need to take into account the departure of capital, or depreciation. The growing capital must be sufficient not only to equip the additional labor force with new capital goods, but also to replenish the retiring capital. Let's denote the retirement rate (depreciation rate) by the symbol d. Thus, the required investment per employee will be written as the equation ir = (n + d)k. Taking into account a constant population growth rate and a constant retirement rate, it is possible to write down the conditions for capital accumulation in a formalized form:

Дk = sf(k) - (n+д)k.

In the course of production, capital reserves are annually replenished, regardless of the amount of capital with which the economy begins to develop. However, the growth of actual investments, displayed by the sf(k) graph, is at a fading rate (Fig. 2). This is explained by the decrease in the marginal productivity of RTO capital, already discussed above, which occurs as the capital-labor ratio of one worker increases. But the increase in capital-labor ratio also increases the volume of required investments, shown in Fig. 2 by a straight line (n+d)k. The angle of inclination of this line is equal to the value (n + q). With the growth of production, the difference between the savings (actually made investments) sf(k) and the required investments (n + q)k will decrease until these values are aligned with each other. When Dk = 0, then production, savings and required investments reach a certain stable level, i.e. the economy reaches a state of equilibrium. The level of capital-labor ratio, at which Dk = 0, is called the stable level of capital-labor ratio (k *) and characterizes the equilibrium state of the economy. In the equilibrium state, output does not change, and savings and required investment are equal:

sf(k*) - (n+q)k* = 0 or sf(k*) = (n+q)k*.

Figure 2 - Determination of a sustainable level of capital-labor ratio

Thus, in fig. 2 the intersection of the schedule of savings sf(k) and the schedule of required investments (n+d)k will show the state of equilibrium, determining the value of the stable level of capital-labor ratio k*.

2.2 E. Phelps' golden rule of accumulation

Consider graphic image golden rule of accumulation. In accordance with the golden rule, the highest level of consumption is achieved at such a stable level of capital-labour, which, as can be seen in Fig. 4 corresponds to the largest gap between the volume of output f(k*) and the volume of required investments (n+d)k *. It is in this case that at point E, the amount of required investment (n + q)k * coincides with the amount of savings sf(k*). Distance AE and shows the largest amount of consumption. Therefore, the level of consumption c** in accordance with the golden rule is called the sustainable level of consumption:

c** = f(k) - (n+d)k

Figure 3 - The golden rule of accumulation

The slope of the production function y = f(k) is measured by the marginal productivity of capital, MPK, and the slope of the required investment is measured by the population growth rate and the rate of capital withdrawal (n+d). At point A, corresponding to a stable capital-labor ratio k**, the slope of the production function is equal to the slope of the required investment and consumption is at its maximum

The stock of capital that provides a steady state at maximum consumption is called the golden level of capital accumulation (k**). It is at the level k** that the slope of the graph of the production function y = f(k), measured by the slope of the tangent at point A, is equal to the slope of the graph of the required investment sf(k). In other words, the marginal productivity of capital MRK should be equal to the rate of economic growth (n + q). This is the very golden rule of accumulation: MRK = (n + q).

Figure 4 - Impact of technological progress on sustainable capital-labor ratio and output per capita

In Figure 4, along with a shift in the graph of the production function from position y1 = f(k) to position y2 = f(k), the savings (actual investment) graph also shifts from position s1f(k) to position s2f(k).

Technological progress leads to the fact that a stable level of capital-labor ratio moves from the point k1* to the point k2. The equilibrium level of required investments and savings moves from point E1 to point E2. Accordingly, the sustainable level of output per capita rises from y1 to y2*.

The reason for this is that the type of technical progress in question seems to increase the number of employed at the same rate as capital grows. The impact of this type of technical progress on economic growth is associated with an increase in the efficiency of labor A, going at a constant rate g. Actually, the indicator g appears as the rate of technical progress. Then the total amount of effective labor will be AL and, taking into account the growth rate of population and the growth rate of labor efficiency, will grow at a rate of n + g. We emphasize once again that the AL indicator is an expression of certain conventional units of labor, and not of people physically employed in production. It is possible to explain the idea of labor-saving technical progress in a slightly different way. Since efficiency and labor productivity are the same concept, we can talk not about conventional units of labor, but that AL means an increase in output with the same amount of labor, which is what labor saving is all about. The quantity of labor remains the same at higher output, and therefore the stable level of capital-labor ratio does not change.

Let us explain the idea of the considered type of technical progress on a conditional digital example. Thus, suppose that in some initial state t0 1000 people are employed in the economy. If the growth of effective labor A goes at a rate equal to the rate of technical progress of 3%, then the same 1000 employees will produce in the next period t1 as much production as 1030 employees would have produced.

Note that the growth rate of capital stocks now, taking into account technical progress, will be n + q + g, i.e. it is these values that measure the slope of the required investment per unit of effective labor.

Figure 5 - Model of growth taking into account technological progress

Let us denote by the symbol ke = K/(AL) the amount of capital per effective unit of labor, and by the symbol уe = Y/(AL) the volume of output per effective unit of labor. The stable capital-labor ratio ke*, as seen in Fig. 6 will be achieved only when the required investments can fully compensate for the decrease in ke due to the retiring of capital at a rate of e, population growth at a rate of n and technological progress at a rate of g: sf(ke) = (n + q + g)ke.

Taking into account the new variables, the maximum sustainable level of consumption will be:

ce = f(ke) - (n + q + g)ke .

Figure 6 - The golden rule of accumulation, taking into account technical progress

So, the maximum sustainable level of consumption ce (the distance between points A and E) is guaranteed by such a volume of accumulation ke, which is achieved when the golden rule is followed, taking into account population growth and technical progress:

RTO = n + q + g.

Conclusion

Economic growth calculated in comparable prices reflects real economic growth, and calculated in current prices reflects nominal economic growth.

Extensive production growth is the simplest and historically the first way to increase the volume of goods. He has his own merits. With its help, the development of natural resources is accelerated, and it is also possible to reduce or eliminate unemployment relatively quickly, and ensure greater employment of the labor force.

This way of increasing production also has serious drawbacks. It is characterized by technical stagnation, in which a quantitative increase in output is not accompanied by a technical and economic process.

Thus, intensification opens up wide opportunities not only for improving production, but also for the formation of new directions for its development, radically transforming the entire system of social development.

Labor resources. Of decisive importance is the working-age population, as well as the problem of overpopulation, characteristic of many economically backward countries of the third world, widespread unemployment and underutilization of the labor force. The main indicator of the efficiency of the use of labor resources is labor productivity, and the ways of full use and increase in efficiency - the growth of education, the improvement of health, the improvement of labor organization - in the broad sense of investment in human capital.

Natural resources. This factor has highest value for potential economic growth. Lack of natural resources can severely limit growth opportunities. At the same time, we can name countries that have very limited natural resources, but have achieved high growth rates. An important factor in economic growth is land, or rather, the quantity and quality of natural resources.

The growing volume of real production allows, to some extent, to solve the problem that any economic system faces: limited resources while limitless human needs.

Economic growth can be assessed using a system of interrelated indicators that reflect the change in the result of production and its factors.

The supply of capital exceeds the demand for it, i.e. the amount of capital at point k1 is excess. Under conditions of flexible prices, the process of making this factor of production cheaper compared to labor will begin, and thus the transition to more capital-intensive technologies will begin. The dynamic equilibrium turns out to be stable, since a change in the relative prices of factors of production will “push” the economy towards a state of stable capital-labor ratio k*.

In the case when the capital-labor ratio corresponds to the point k2, investments exceed savings. The resulting shortage of capital under a flexible price mechanism will lead to higher prices for this production factor, and the transition to less capital-intensive technologies up to the level of k * will begin.

The rise of needs, the depletion of traditional resources, the increase in the population determine the solution of a two-pronged task: economic growth and economic efficiency. Economic growth is an increase in the volume of created utilities, and consequently, there is an increase in the living standards of the population. The combination of these two factors - the relative limitlessness of human needs and the growth in the number of inhabitants in most countries of the world - forces humanity to constantly increase the scale of production of goods and services. This process is called economic growth.

The ability to maintain the level of consumption at the highest possible level is a kind of "elixir of political longevity" of the authorities. Achieving a high level of consumption is in the interests of any electorate. However, as can be seen from the graph in Fig. 3c, different savings rates may correspond to a stable state of the economy.

The condition under which this level of consumption is reached was deduced by the American economist Edmund Phelps and called it the golden rule of accumulation in his work "Fable for those who are engaged in growth."

Until now, we have abstracted from the factor of technological progress. Now we must see how the conditions for stationary growth change with the introduction of this variable. The term "technical progress" in economic growth models is understood in a very broad sense, namely, in the sense of all factors that, given the amount of labor L and capital K, allow increasing national income, or output Y.

The main thing we should pay attention to is the shift of the production function Y = f(K,L), which turns into a function depending on the variable t, i.e. on time: Y = f(K, L, t). As a result of technological progress, there is a shift in the production function per employee from position y1 = f(k) to position y2 = f(k) (Fig. 5). A shift in the production function can occur under the influence of a variety of factors: improving the quality of physical capital, the quality of the labor force (increase in the qualifications of workers), improving the structure of production, improving management, etc.

In macroeconomic theory, various types of technical progress are considered, characterized by a stable level of capital-labor ratio.

In the post-crisis period, economic growth is a factor in overcoming the crisis and the progressive development of the economy.

Each economic system seeks to maximize economic growth, focusing on the growth of the gross national product as a whole and per capita, strengthening the country's position in the international arena, thus the topic of the course work is relevant for its consideration.

Economic growth is the exit of the economy beyond the limits of pre-existing production possibilities, its transition to a new, higher level. Economic growth is a component of cyclical economic development.

Existing market economy dictates to the enterprises entering into it, to use various tools for an estimation of results of activity. The "golden rule of the economy" most fully reflects the important condition, observing which it is possible to ensure expanded reproduction, a stable position in the market, and thereby lay the foundation for the successful development of a commercial organization.

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3. Neoclassical Solow model

There are basic fairly simple models that explain the essence and the possibility of using macroeconomic production functions.

In addition to this or that combination of factors of production, the flexibility of the production function is provided by special coefficients. They are called coefficients of elasticity. These are power coefficients of factors of production, showing how the volume of output will increase if the factor of production increases by one unit. The coefficient of elasticity is found empirically by solving for this a special system of equations obtained from the original model of the production function.

The literature distinguishes between production functions with both constant and variable elasticity coefficients. Constant coefficients mean that the product grows in the same proportion as the factors of production.

The simplest model is two-factor: capital K and labor L.

If the coefficients of elasticity are constant, then the function is written as follows:

where Y- national product;

L - labor (man-hours or number of employees);

K - the capital of the whole society (machine-hours or the amount of equipment);

— coefficient of elasticity;

A is a constant coefficient (found by calculation).

When analyzing the model of aggregate demand and aggregate supply (AD-AS), it was assumed that the only variable factor of production is labor, and capital and technology were considered unchanged. These assumptions cannot be considered adequate for long-term analysis, since in the long term there is both a change in the capital stock and the presence of technical progress. Thus, with a change in capital and technology, the level of full employment will also change, which means that the aggregate supply curve will shift, which will inevitably affect the equilibrium output. However, an increase in output does not mean that the country's population has become richer, since the population changes along with output. Economic growth is usually understood as the growth of real GDP per capita.

N. Kaldor (in 1961), studying economic growth in developed countries, came to the conclusion that there are certain patterns in the change in output, capital and their ratios in the long term. The first empirical fact is that the growth rate of employment is less than the growth rate of capital and output, or, in other words, the capital-to-employment ratio (capital-labor ratio) and the output-to-employment ratio (labor productivity) are rising. On the other hand, the ratio of output to capital showed no significant trend, that is, output and capital changed at about the same pace.

Kaldor also considered the dynamics of returns to factors of production. It was noted that real wages show a steady upward trend, while the real interest rate does not have a definite trend, although it is subject to continuous fluctuations. Empirical studies also show that labor productivity growth rates vary significantly across countries.

The question of what factors influence economic growth remains one of the central questions of macroeconomics, and the debate over the sources of economic growth continues to this day. However, most economists, following the classic work of Robert Solow in 1957, identify the following key factors of economic growth: technological progress, capital accumulation and labor force growth.

To describe the contribution of each of these factors to economic growth, consider the output Y as a function of the capital stock ( K) used manpower ( L):

The volume of production depends on the stock of capital and the labor used. The production function has the property of constant returns to scale.

For simplicity, we correlate all values with the number of employees (L):

This equation shows that output per worker is a function of capital per worker.

y \u003d Y / L - output per 1 employee (labor productivity, output);

k = K/ L is the capital-labor ratio.

This function, according to neoclassical ideas, should illustrate the following: if the amount of social capital used per worker increases, then it increases, but in lesser degree, product per worker (marginal productivity of labor).

Graphically, this means that the function f(K) has a first derivative that is greater than zero f (K)>0. The second derivative of the function - f (K)

Rice. 12.2 Neoclassical production function

Capital and labor are rewarded on the basis of their respective marginal factors of production. The remuneration of capital is determined by the tangent of the slope to the curve f(K) at point P, the marginal productivity of capital. Then, WN is the share of capital in the total product; OW is the share of wages in the product; OW is the whole product.

In the Solow model, the demand for goods and services is presented by consumers and investors. Those. The output produced by each worker is divided between consumption per worker and investment per worker:

The model assumes that the consumption function takes a simple form:

where the savings rate s takes the values 0 – 1.

This function means that consumption is proportional to income.

Let's replace the value – c – with the value (1 – s)* y:

After transformation we will receive: i = s*y.

This equation shows that investment (like consumption) is proportional to income. If investment equals savings, then the savings rate (s) also shows how much of the product produced is directed to capital investment.

Capital stocks can change for 2 reasons:

- investments lead to an increase in reserves;

- part of the capital wears out, i.e. depreciated, which reduces inventory.

change in capital stock = investment - disposal,

σ is the retirement rate; ∆k is the change in capital stock per employee per year.

If there is a single level of capital-labor ratio at which investment equals depreciation, then the economy will reach a level that will not change over time. This is a situation of stable capital-labor ratio.

The level of capital accumulation that provides a steady state with the highest level of consumption is called the Golden level of capital accumulation.

In 1961 American economist E. Phelps deduced the rule of accumulation, called "golden". In general terms, the golden rule of accumulation can be formulated as follows: the level of capital accumulation that ensures the highest consumption of society and a stable state of the economy is called the golden level of capital accumulation, i.e. the optimal equilibrium level of the economy will be reached under the condition of full investment of income from capital.

The golden rule of accumulation - the hypothetical trajectory of balanced economic growth proposed by Phelps, according to which each generation saves for future generations the same part of the national income that the previous generation leaves it.

The golden rule of accumulation of E. Phelps is fulfilled when the marginal product minus the rate of disposal is zero:

If the economy starts to develop from capital stock greater than the Golden Rule, it is necessary to pursue a policy aimed at lowering the savings rate in order to reduce the sustainable level of the capital stock.

This will cause an increase in the level of consumption and a decrease in the level of investment. The capital investment will be less than the outflow of capital. The economy is coming out of a stable state. Gradually, as the stock of capital decreases, output, consumption, and investment will also decline to a new steady state. The level of consumption will be higher than before. And vice versa.

Capital accumulation alone cannot explain continued economic growth. A high level of saving temporarily boosts growth, but the economy eventually approaches a steady state in which capital stocks and output are constant.

The model includes population growth. We assume that the population in the economy under consideration is equal to labor resources and grows at a constant rate n. Population growth complements original model in 3 directions:

1. Allows you to get closer to explaining the causes of economic growth. In a steady state of the economy with a growing population, capital and output per worker remain unchanged. But since the number of workers grows at a rate of n, capital and output also grow at a rate of n.

Population growth explains the growth in gross output.

2. Population growth provides an additional explanation for why some countries are rich and others are poor. An increase in the population growth rate reduces the capital-labor ratio, and productivity also decreases. Countries with higher population growth rates will have lower GNP per capita.

3. Population growth affects the level of capital accumulation in terms of wages.

where E is the labor efficiency of 1 worker.

It depends on health, education and qualifications. The L*E component is the labor force measured in units of labor at constant efficiency.

The volume of production depends on the number of units of capital and on the number of effective units of labor. Labor efficiency depends on the health, education and qualifications of the workforce.

Technological progress causes an increase in labor efficiency at a constant rate g. This form of technological progress is called labor-saving. Because the labor force grows at a rate of n and the return on each unit of labor grows at a rate of g, the total number of effective units of labor L*E grows at a rate of (n+g).

The Solow model shows that only technological progress can explain the ever-increasing standard of living. This also changes the Golden Rule:

The state should encourage scientific research, protect copyright, give tax breaks.

The golden rule of capital accumulation defines

Golden Rule of Accumulation 110

Consider a graphic representation of the golden rule of accumulation.

The stock of capital that provides a steady state at maximum consumption is called the golden level of capital accumulation (k). It is at the level k that the slope of the graph of the production function y = f(k), measured by the slope of the tangent at point A, is equal to the slope of the graph of the required investment sf(k). In other words, the marginal productivity of capital MPk must be equal to the economic growth rate n + 5. This is the golden rule of accumulation itself.

The golden rule of accumulation

The golden rule of capital accumulation.

Solow model. Capital accumulation, population growth, technological progress. The level of capital-labor ratio and the "golden rule" of accumulation. Savings, growth and economic policy. Growth and taxation.

Harrod-Domar Models of Economic Growth, Solow. The "golden rule" of savings.

THE GOLDEN ACCUMULATION RULE

Golden Accumulation Rule 487

Condition 15, which determines a stationary level k that maximizes stationary consumption c, is called the golden rule of capital accumulation. The interpretation of the golden rule is that if we maintain the same level of consumption for all living now and for all future generations, that is, if we treat future generations as we would like them to do with us, then s=f(k )-(n+8)k is the maximum consumption level that we can provide.

In a closed economy, or an economy with no access to foreign loans The only way to increase investment is by increasing savings. In this case, a choice has to be made, since additional growth through accelerated capital accumulation implies a decrease in today's consumption. Of course, the government should not seek to maximize the level of savings at any cost, as this may be too severe a punishment for the current consumer. There is an optimal share of savings, which, admittedly, is difficult to measure. It is determined by public preferences in time, i.e. the value society assigns to future consumption compared to present consumption. If a investment project will bring such a large income that it seems reasonable to sacrifice some of the current consumption, then it should be accepted. According to the theory of the optimal level of savings, the balance between the present and the future is best achieved if the marginal productivity of capital (MRC) is equal to the discount of preferences over time plus the population growth rate. This famous ratio is known as the "modified golden rule" 44.

As a rule, the amount of gold coins needed for trade transactions was constantly in circulation. When buyers and sellers had an excess amount of money, it turned into the category of treasures. If the money was again required for the purchase and sale of goods, then they were taken from the places of accumulation and sent into circulation.

Let's pay attention to the fact that the position Reserve assets, in the case of their debit balance, means the accumulation of these assets and is a positive factor for macroeconomic development trends. When a credit balance arises, this indicates the inefficient inclusion of the state in international economic relations, the consumption of gold and foreign exchange reserves with the threat of financial bankruptcy of the country. The gold and foreign exchange reserve assets of the Russian Federation were formed mainly at the expense of monetary gold, special drawing rights (SDRs), a reserve position in the IMF and other foreign exchange assets.

CURRENCY FUNDS - formed in the capitalist. countries, funds in gold, national and foreign currencies used to influence exchange rates. They began to be created by bourgeois states since the world economic crisis of 1929-1933, accompanied by an acute currency crisis. In Sept. In 1931, the gold standard was abolished in England and the pound sterling began to fall, which put English exporters in an advantageous position in their struggle for foreign markets. In the spring of 1932, the influx of foreign capital into England caused the appreciation of the pound sterling. Since the First World War, the British Treasury has retained the so-called. An equalizing currency fund, to-ry was a reserve to pay for his obligations to the United States. In 1932, under pressure from the monopoly. associations, the Treasury was given the right to increase this fund by 150 million pounds. Art., in 1933 - by 200 million, and in 1937 - by another 200 million pounds. Art. To accumulate foreign exchange reserves, the Treasury issued short-term bills on the London market and bought foreign currency with the proceeds. The offer of pounds and the purchase of foreign currency contributed to the depreciation of the pound sterling and the appreciation of other currencies. In 1933, after the depreciation of the dollar, the Treasury began to carry out through V. f. policy of further depreciation of the pound. Between the USA and England there was a currency war (see). With the outbreak of World War II, the Bank of England, in exchange for Treasury bills, transferred all its gold reserves to the Monetary Equalization Fund for use

The government decree of October 11, 1922 stated that the right to issue was granted to the State Bank in order to increase the working capital of the State Bank for its commercial operations without further expanding the issue of banknotes and in the interests of regulating monetary circulation and based on the presence of real values accumulated by the State Bank in in the form of gold, other precious metals and hard foreign currency. .

The process of primitive accumulation, with certain historical features, took place later in other countries. In Russia, for example, the process of separation of producers from the means of production took place most intensively in connection with the abolition of serfdom. As a result of the reform of 1861, the landowners seized two-thirds of the land from the peasants. For a reduced plot of the worst land, the peasant was obliged to pay redemption payments and bear other duties in favor of the landowner. The size of redemption payments was calculated at inflated prices for land and amounted to about 2 billion rubles. gold. Describing the peasant reform of 1861, V. I. Lenin wrote that it was mass violence against the peasantry in the interests of the emerging capitalist class.

The trend towards the accumulation of gold by private owners has intensified in economically developed countries since the mid-1970s. This was facilitated by the transition to the Jamaican monetary system in 1976, which abolished the official price of gold, allowed the sale and purchase of gold at market prices, and stopped the exchange of dollars for gold for central banks and government bodies. Gold, like any other precious metal, is a commodity, just like currency and monetary resources are a commodity. Gold is sold on precious metal exchanges at market prices. Large sections of small proprietors are characterized by the predominant accumulation of gold in the form of coins, including "bullions", which have a convenient weight content - a troy ounce or its fractional parts. A troy ounce is 31.1034807 g. In bank calculations, the results are determined to the nearest 0.001 part of a troy ounce using the rounding rule.

At the same time, the mobility of the labor force should be provided, for example, in Russia infrastructurally and legally. The bottom line is that somewhere in Moscow, St. Petersburg, one or another specialist is needed, but they cannot invite him, as the institution of registration (in the past - registration) interferes. On the other hand, even if this institution is abolished, a serious barrier to labor mobility is the absence of a housing market. The essence of the problem lies in the fact that in places where the labor force is moving, people should be able to find and rent housing at an affordable price. Another serious obstacle to the mobility of the labor force in our country is the fact that workers in this or that city have apartments that they have earned by their long labor in the same place. In the absence of a developed housing market, a worker who is promised “mountains of gold” elsewhere cannot quickly and profitably sell his apartment (and often does not have the right to do so) and buy housing elsewhere. Therefore, he is ready to stay in the old place and get less, even in the prospect of becoming unemployed, but not to go to a new place. As a result, labor mobility in Russia is still very low, and, consequently, this area of human capital accumulation is underdeveloped.

Residents received the right to buy and sell foreign currency for rubles at the market rate within certain limits. For the transition to free convertibility of the ruble, stabilization of the economy, finance, money circulation, credit system, accumulation of gold and foreign exchange reserves and political stability in the country are necessary.

For this model, the golden rule of accumulation of E. Phelps is obvious, by virtue of which the elasticity of output with respect to capital must coincide with the rate of accumulation in fixed capital

As follows from the derivation of Phelps' golden accumulation rule , model (33)-(37) is an extreme case of model (33)-(37)

The third point of view was put forward by the French economist Maurice Allais, who believes that interest is a form of rewarding a person in the future for reducing consumption in the present. His famous "golden rule" of savings states that the maximum level of per capita consumption can be reached at zero bank interest. Denying himself the consumption of part of his income, a person gives his funds to accumulation, which ensures the growth of production. In this case, interest acts as a form of reward for reducing consumption in the present and for increasing production in the future. All three points of view have the right to exist, because each of them reflects the moment of truth, and together they provide an integrated approach to resolving the issue of the economic nature of interest.

Therefore, all statements made about the existence of the golden rule of accumulation, balanced growth, about the asymptomatic approach of the optimal growth trajectory to the highway, about the relationship between the growth rates of departments I and II, remain valid for the transformed time t, i.e., for any monotonically changing pace C1).

The Golden Rule, formulated by E. Phelps, is considered in some theories of economic growth as a kind of simplified approach to the definition optimal rate accumulation.

In terms of investment risk, traditional savings are much less risky than investments. The risks of the former include interest rate risk (when the inflation rate suddenly outstrips the deposit rate) and the risk of bank and interbank default. In the conditions of highly developed countries, when there is a system of guarantees of safety bank deposits, and inflation does not undergo sharp jumps, the risks of traditional savings are insignificant. Investment is another matter. Traditionally, high exchange rate risk, say, for stocks, is associated with a non-zero level of issuer bankruptcy risk security. However, high risk comes at the cost of high expected returns, and this so-called golden rule of investing applies at all times. As for speculation, the risk of these operations is comparable to the gambling risk in classic games of chance (toss, 21, etc.).

From the Marxist definition of value as materialized labor also follows the admiration for capital (and gold) as for accumulated labor. Capital is a purely religious concept. Capital is a right of power recognized by the rest, since the capitalist owns certain objects of idolatry.

CURRENCY RESTORATION (from lat. restau-ratio - restoration) - one of the methods of stabilizing currencies in the capitalist. countries was used mainly during the period of gold monometallism and was characterized by the resumption of the exchange of paper money for metal at face value with the restoration of the type of currency that existed in this country before the depreciation of money. Economical the basis for the stabilization of currencies by the method of restoration is the growth of production, the elimination of state budget deficits mainly due to an increase in the taxation of the working masses, the withdrawal of excess money supply from circulation by pursuing a policy of deflation (see), the accumulation of gold reserves, etc. A historical example R. v. is the restoration of the gold currency in England in 1821. this was preceded by a long period of circulation of fiat banknotes after the Restriction Act (see) 1797 R. century. was carried out in the interests of the English, the bourgeoisie, since the gold currency contributed to the growth of industry and trade and the strengthening of England's position in the world market. Special benefits from R. v. extracted by state creditors, who provided loans to the pr-vu in depreciated banknotes and received the return of these loans in full-fledged money. Another example of R. century. - restoration of the exchange of paper money (greenbacks) in the United States in 1879. As a rule, R. c. preceded by a gradual increase in the purchasing power of paper money to pre-inflationary levels. In this regard, in conditions of deep inflation, R. century. turns out to be usually impossible, and stabilization is carried out by other methods - by devaluation (see) or nullification (see). In the era of the general crisis of capitalism, a monetary reform close to R. v. in England. It was characterized by the resumption of the exchange of banknotes for gold, but without a return to the gold-coin standard, a gold bullion standard was introduced instead (see Gold Standard).

The first theoretical economists discovered a source of state enrichment in foreign trade. The state, in their opinion, had to constantly observe the following rule to sell goods to foreigners annually for a greater amount of money than it buys from them. In this case, the state received continuously increasing sums of money for goods sold to other countries. At that time, money was mainly in the form of gold coins. The accumulation of gold was seen as the only solid basis for the wealth of the nation.

On Wednesday. century, banking revived primarily in the North. Italy. In ancient Greek and lat. languages, the words for a banker came from the word table. In Italian. language, this word comes from ban o - a bench (shop) or desk, for which the money changer and the banker conducted their operations, then it passed into other modern. languages. By the 14th century banking got a mean scope in the cities of Italy, Germany and the Netherlands. Bankers lend in the main. kings and great feudal lords. In large trading centers (Amsterdam, Hamburg) there appeared a new type of B., the activity of which was already regulated by the bourgeoisie. mountains the authorities. Such banks (which were called girobanks) pursued the goal not so much of lending as of mediation in settlements and the establishment of hard money. units. The growth and evolution of B. in the 17th and 18th centuries. were closely connected with the development of capitalism in the West. Europe. Modern capitalist principles. banking was the earliest to develop in England, which became in the 17th century. the most advanced capitalist country. The first bankers in England were, as a rule, goldsmiths. Then the capital accumulated in trade began to be invested in banking.

The metal theory of money arose in England since the time of the primitive accumulation of capital, BXVI-XVII centuries. The main representative of this theory is W. Stafford / 1554-1 612). This theory organically follows from mercantilism, which identified the country's wealth with the accumulation of money supply, usually consisting of metal money. Accordingly, the metal theory of money assumes the identification of the wealth of the country with precious metals, to which all the functions of money are attributed, and only metal money, consisting of these metals proper, is recognized as the only monetary means possible in economic life. This theory said that only metallic money, containing in itself a cost equal to the amount of metal used in their production, can perform the functions of money. Accordingly, this school not only denied the possibility of abandoning the gold standard, but also generally did not welcome the creation of paper money.

The country was faced with the urgent need to move to the gold standard. From the autumn of 1894 in Russia began to accumulate gold in the State Bank. This was achieved not only with the help of an active foreign trade balance, but also with external loans. In addition, high indirect taxes (excises) were introduced on consumer goods - matches, kerosene, tobacco, sugar, vodka, cotton fabrics and others, due to which the state budget deficit was largely eliminated, and indirect taxes increased during the 1890s. gg. by 42.7%. In 1895, a wine monopoly was introduced in Russia, that is, the exclusive right of the state to trade in alcoholic beverages. All these measures, carried out by S. Yu. Witte, helped to overcome high inflation and stabilize the country's financial system.

TREASURES - accumulations of precious metals in the form of coins, ingots, jewelry and other items owned by the state or private individuals. Treasures partly represent a gold reserve, partly - artistic values and household jewelry, antiquities, antiques. Tesauramia, or tezavrying (from the Greek thesauros - treasure) - 1) the accumulation of money by the population by withdrawing it from circulation 2) the accumulation of gold by private individuals in the form of wealth, treasure 3) the creation of the country's gold reserves. Treasure - discovered hidden valuables, the owner of which cannot be established and, by virtue of the law, has lost the rights to them. Treasures belong to the state and the persons who discovered them.

See pages where the term is mentioned The golden rule of accumulation

Course of Economic Theory Vol.5 (2006) - [ c.25 ]

Managers are not born, managers are made

Solow's Neoclassical Growth Model and the Golden Rule of Accumulation

Target this model - to answer very important questions of economic theory and economic policy; what are the factors of balanced economic growth; what growth rate can an economy afford given the parameters of the economic system and how to maximize per capita income and consumption in the process; how the growth rate of the economy is affected by population growth, capital accumulation and technological progress. The Solow model shows not only the possibility of equilibrium economic growth with full employment and full utilization of production capacity. A feature of this neoclassical model is that it demonstrates the sustainability of economic growth, i.e. the ability of the economic system to return to the trajectory of balanced development with the help of internal market self-regulation mechanisms.

Rice. 1. Production function y = f(k). This function is built on the basis of one employee and is characterized by a decreasing marginal productivity of capital MR K

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Model background:

Unlike neo-Keynesian models, the factors of production in the Solow model based on the Cobb-Douglas production function are interchangeable.
capital-labor ratio k = K/L(where To- the amount of capital, L- the amount of labor) is not a constant ratio, as in neo-Keynesian models, but changing depending on the macroeconomic situation.
Prices in the Solow model are flexible; there is a premise of perfect competition in the markets for factors of production, which allows us to classify the model under consideration as neoclassical.
It is assumed that the growth rate of labor resources (labor supply, L) is equal to the population growth rate n.
Initially, when building the model, it is assumed that the population growth rate does not change, and there is no technical progress (in the future, these restrictions are removed).
Variables such as savings rate, depreciation rate, population growth, technological progress are exogenously given.

Model building

Dividing the two-factor production function Y = f(K, L) by the amount of labor L, we obtain the production function for one worker: y = f(k), where k = K/L is the capital-labor ratio of a unit of labor, or one worker Income (y = Y/L) appears as a function of only one factor - the capital-labor ratio ( k). Such a unit production function, reflecting the average level of labor productivity, is shown in Fig. 1. Note that the steepness of its slope, determined by the value of the marginal productivity of capital MR K, changes. As the amount of capital per worker increases, the marginal productivity of this factor decreases (in accordance with the theory of marginal factor productivity), which causes a slowdown in the growth of the income function.

Part of the income Y is used for consumption, and the other part is saved. In the Solow model, where all macroeconomic indicators are calculated per worker, savings will also be a part of unit income. sy or sf(k), where s The savings rate determines how much of income is saved.

The condition for macroeconomic equilibrium is the equality of aggregate demand (AD) and aggregate supply (AS), which automatically leads us to macroeconomic equality I=S(the amount of investment is equal to the amount of savings). All savings in the economy are fully invested, and this allows us to equate the function of actual investment per worker ( i) to the unit savings function: i = sy = sf(k). Keeping in mind the macroeconomic equality Y = C + I (income equals the sum of consumption and savings), output per employed person can be written as y = c + i, where y \u003d Y / L, c \u003d C/L, i = I/L, and represent the consumption function as c \u003d y - i \u003d f (k) - sf (k).

Graphically, the size of consumption and investment at each level of capital-labor ratio is shown in Fig. 1. Curve sf(k) the schedule of actually made investments is indicated, which, according to the model condition, are equal to savings. Since savings make up a certain percentage of output, the actual investment per capita is represented by a graph that lies below the graph of the production function y = f(k) in fig. 1. Distance between function graphs f(k) and sf(k) determines the volume of consumption ( c). Thus, the consumption function is described by the formula: c = f(k) – sf(k).

According to the Solow model, the economy is initially in a state of stable equilibrium. This means that the planned or required investment I are equal to the investments actually made, i.e. savings S. In the Solow model, it is described as a stable, or stationary state of the economy, in which the amount of capital per worker is constant. To determine the stationary state of the economy in the Solow model, it is also necessary to consider the problem of capital accumulation. Obviously, in order for the capital-labor ratio to remain unchanged under the condition of population growth, it is necessary that capital To increased at the same rate n, which is population growth L. Thus, the required investment per employee i r(superscript r at the investment symbol i- from the English word required - required) can be written as the following equality: i r = nk. Moreover, if the population growth rate and the rate of capital accumulation are equal, then output per capita at remains unchanged.

Let's not forget that in order to describe the net capital gain, we need to take into account the departure of capital, or depreciation. The growing capital must be sufficient not only to equip the additional labor force with new capital goods, but also to replenish the retiring capital. Let us denote the retirement rate (depreciation rate) by the symbol δ . Thus, the required investment per worker will be written in the form of equality i r = (n+δ) k. Taking into account a constant population growth rate and a constant retirement rate, it is possible to write down the conditions for capital accumulation in a formalized form: Δ k = sf(k) – (n+δ) k. So, we have all the necessary data in order to explain the mechanism of establishment of a stationary state in the Solow model.

In the course of production, capital reserves are annually replenished, regardless of the amount of capital with which the economy begins to develop. However, the increase in actual investment shown in the graph sf(k), goes at a fading rate (Fig. 2). This is explained by the decrease in the marginal productivity of capital MR K, already discussed above, which occurs as the capital-labor ratio of one worker increases. But the increase in capital-labor ratio also increases the volume of required investments, shown in Fig. 2 straight line (n+δ) k. The slope of this line is equal to the value (n+δ) . With the growth of production, the difference between the savings (actually made investments) sf(k) and required investments (n+δ) k will decrease until these values are equal to each other. When Δ k = 0, then production, savings and required investment reach a certain sustainable level, i.e. the economy reaches a state of equilibrium. The capital-labor ratio at which Δ k = 0, is called stable capital-labor ratio (k*) and characterizes the equilibrium state of the economy. In the equilibrium state, output does not change, and savings and required investment are equal: sf(k*) – (n+δ) k* = 0 or sf(k*) = (n+δ) k*.

Rice. 2. Determination of a sustainable level of capital-labor ratio

Thus, in fig. 2 intersection of the savings graph sf(k) and schedule of required investments (n+δ) k will show the state of equilibrium, determining the value of the stable level of capital-labor ratio k*.

What is the mechanism in the Solow model that ensures equilibrium growth? For this, let us turn again to Fig. 2. At the point k 1 savings exceed the required investment. The supply of capital exceeds the demand for it, i.e. the amount of capital at the point k 1 is redundant. Under conditions of flexible prices, the process of making this factor of production cheaper compared to labor will begin, and thus the transition to more capital-intensive technologies will begin. The dynamic equilibrium turns out to be stable, since a change in the relative prices of factors of production will “push” the economy towards a state of stable capital-labor ratio k*.

In the case where the level of capital-labor ratio corresponds to the point k2 investment exceeds savings. The resulting shortage of capital under a flexible price mechanism will lead to higher prices for this factor of production, and the transition to less capital-intensive technologies will begin, up to the level k*.

How will a change in the rate of disposal affect a stable level of capital-labor ratio and output per capita (δ), population growth rate (n) and savings rates (s)? On fig. 3 shows the consequences of the changes. To understand how the Solow model works, one must keep in mind that the fiscal and monetary policy of the state, as well as institutional and psychological factors, can affect the level of k* through the impact on the savings rate s or depreciation rate δ , on the value of which the rate of renewal of capital depends. For example, an accelerated depreciation policy (Fig. 3a) will result in a shift in the schedule (n+δ) k to level (n+δ1)k. At the same time, the stable level of capital-labor ratio will decrease c k* before k 1 * just as output per capita will decline with y* before y 1 *.

Rice. 3. Influence of model parameters on the stable level of capital-labor ratio; changes: (a) the rate of disposal (depreciation) δ ; (b) population growth rate n; (c) savings rate s

If the population growth rate increases to n 1(Fig. 3b), then the volume of accumulated capital will be distributed among a larger number of employees, and the level of sustainable capital-labor ratio will decrease to k 1 *. The required investment curve will shift from (n+δ) k into position (n 1 +δ) k. At the same time, output per capita will also decrease. This explains the low per capita income in many developing countries. The population growth rate in the world's poorest countries is much higher than in industrialized countries. The low savings rate characteristic of these countries does not compensate for the effects of high population growth on the capital-labor ratio. It is no coincidence that in such conditions, if moral assessments are left aside, a decrease in the birth rate seems to be almost the most important way to improve the well-being of the population.

An increase in the savings rate due to various reasons (an increase in the propensity to save under the influence of various factors of a psychological, institutional nature, as well as under the influence of indirect methods of state regulation) from the level s before s 1 as seen from fig. 3c, on the contrary, will lead to an increase in the equilibrium level of capital-labor ratio to k 1 * as a result of shifting the savings schedule to the level s 1 f(k). Thus, we can conclude that a higher saving rate, other things being equal, leads to more capital accumulation and to a higher level of output per capita. This is statistically confirmed by the studies of many economists. Thus, the countries with the highest annual income (in US dollars at the current exchange rate, for 2000) include the USA ($ 36,611), Great Britain ($ 23,868), Germany ($ 22,841), France ($ 22,006), Italy ( $18,645), Japan ($37,571). During the last three decades of the 20th century, this group of countries had the highest savings rate (about 23% of GDP on average) compared to countries with lower incomes. Middle-income countries saved between 20% and 22% of GDP, while those with low level income per capita - from 10% to 19% of GDP.

However, we must emphasize the important conclusion that Solow draws: an increase in the saving rate only in the short run increases the rate of output growth. In other words, during the transition from the curve sf(k) on a curve s 1f(k)(Fig. 3c) output growth rates are increasing compared to the previous stationary state of the economy. When moving from point E to point E 1, the stable level of capital-labor ratio increased from k* before k 1 * under the new steady state of the economy. For what reasons could this happen? The answer is quite simple: the capital-labor ratio can only increase if the stock of capital grows at a faster rate than the supply of labor and the outflow of capital. But an increase in the savings rate does not affect the long-term growth rate of output, but only increases the capital-labor ratio and per capita income in the long run.

This conclusion may seem unexpected and contradictory to the close relationship between investment and economic growth. The explanation for this seeming contradiction may be that the stationary state of the economy is not inherent in all countries. If the economy is not characterized by a state of equilibrium, then it is going through a process of development, and this process can be very long.

The Solow model is also interesting in that it helps to identify ways to maximize consumption at a given rate of economic growth. The ability to maintain the level of consumption at the highest possible level is a kind of “elixir of political longevity” of the authorities. Achieving a high level of consumption is in the interests of any electorate. However, as can be seen from the graph in Fig. 3c, different savings rates may correspond to a stable state of the economy. What is the rate of saving that maximizes consumption for a given rate of population growth and technology unchanged?

The condition under which this level of consumption is reached was derived by the American economist Edmund Phelps and called it the golden rule of savings in his work "Fable for those who are engaged in growth" (1961)

Consider a graphic representation of the golden rule of accumulation. In accordance with the golden rule, the highest level of consumption is achieved at such a stable level of capital-labour, which, as can be seen in Fig. 4 corresponds to the largest gap between the volume of output f(k*) and the volume of required investments (n+δ) k * . It is in this case at the point E investment required (n+δ) k * matches the amount of savings sf(k*). Distance AE and shows the largest amount of consumption. Therefore, the level of consumption with** according to the golden rule is called sustainable consumption: c** = f(k*) – (n+δ) k *

Rice. 4. The golden rule of accumulation. The slope of the production function y = f(k) is measured by the marginal productivity of capital, MR K , and the slope of the required investment schedule is measured by the population growth rate and the rate of capital retirement (n+δ) . At the point BUT, corresponding to a stable level of capital-labor ratio k**, the slope of the production function is equal to the slope of the required investment and consumption is at its maximum

The stock of capital that ensures a steady state at maximum consumption is called the golden level of capital accumulation ( k**). It is at the level k** the slope of the production function y= f(k), measured by the slope of the tangent at the point BUT, is equal to the slope of the schedule of required investments sf(k). In other words, the marginal productivity of capital MP K should be equal to the rate of economic growth (n+δ) . This is the golden rule of accumulation itself: MP K = (n+δ).

Until now, we have abstracted from the factor of technological progress. Now we must see how the conditions for stationary growth change with the introduction of this variable. The term "technical progress" in economic growth models is understood in a very broad sense, namely, in the sense of all factors that, given the volume of labor L and capital To allow for an increase in national income, or output At.

The main thing we need to pay attention to is the shift in the production function Y= f(K,L), which turns into a function depending on the variable t, i.e. from time: Y= f(K,Lt). As a result of technological progress, there is a shift in the production function per employee from the position y 1 = f(k) into position y 2 = f(k)(Fig. 5). A shift in the production function can occur under the influence of a variety of factors: improving the quality of physical capital, the quality of the labor force (increase in the qualifications of workers), improving the structure of production, improving management, etc.

Rice. 5. Impact of technological progress on sustainable capital-labor ratio and output per capita

On fig. 5 together with the shift of the graph of the production function from the position y 1 = f(k) into position y 2 = f(k) there is also a shift in the schedule of savings (actual investments) from the position s 1 f(k) into position s 2 f(k). Technological progress causes the stable level of capital-labor ratio to move from the point k 1 * exactly k2 *. The equilibrium level of required investment and savings moves from the point E 1 exactly E 2. Accordingly, the sustainable level of output per capita rises from the level u 1 * to level y 2*.

In macroeconomic theory, various types of technical progress are considered, characterized by a stable level of capital-labor ratio. In the study of the Solow model, we will proceed from the so-called neutral technical progress. This means that with an increase in the capital-labor ratio k the marginal productivity of capital MR K does not decrease, as it could happen in the absence of technical progress (see Fig. 1). The reason for this is that the type of technical progress in question seems to increase the number of employed at the same rate as capital grows. The impact of this type of technological progress on economic growth is associated with an increase in labor efficiency. BUT going at a constant pace g. Actually, the index g and appears as the rate of technical progress. Then the total amount of effective labor will be AL and, taking into account the rate of population growth and the rate of growth in labor efficiency, will grow at the rate n+ g. We emphasize once again that the AL is an expression of certain conventional units of labor, and not of people physically employed in production. It is possible to explain the idea of labor-saving technical progress in a slightly different way. Since the efficiency and productivity of labor are the same concept, we can talk not about conventional units of labor, but about the fact that AL means an increase in output with the same amount of labor, which is the saving of labor. The quantity of labor remains the same at higher output, and therefore the stable level of capital-labor ratio does not change.

Let us explain the idea of the considered type of technical progress on a conditional digital example. So, suppose that in some initial state t0 The economy employs 1,000 people. If the increase in effective labor BUT goes at a rate equal to the rate of technical progress of 3%, then the same 1000 employed will produce in the next period t1 production is as much as 1030 employees would produce. Now, taking into account the factor of technological progress, going at a pace g, we can present a modified Solow growth model (Fig. 6). Note that the growth rate of capital stocks now, taking into account technical progress, will be n+ δ + g, i.e. it is these values that measure the slope of the required investment per unit of effective labor.

Rice. 6. The Solow Growth Model Taking into Account Technological Progress

Denote by the symbol k e = K/(AL) the amount of capital per effective unit of labor, and the symbol at e= Y/(AL) is the output per effective unit of labor. Stable capital-labor ratio ke *, as seen in Fig. 6 will be achieved only when the required investment can fully compensate for the decrease in k e due to the retirement of capital, going at a rate δ , population growth with the rate n and technological progress with the pace g:
sf(k e) = (n+ δ + g)k e. Taking into account the new variables, the maximum sustainable level of consumption will be: with e**= f(k e **) – (n+ δ + g)k e(Fig. 7).

Rice. 7. The golden rule of accumulation, taking into account technological progress

So the maximum sustainable consumption level with e**(distance between points BUT and E) is guaranteed by such a volume of accumulation **, which is achieved when the golden rule is followed, taking into account population growth and technological progress: MR K = n+ δ + g.

We considered the impact of technological progress on a sustainable capital-labor ratio **(per unit of effective labor) and came to the following conclusion: output per unit of effective labor in the stationary state remains unchanged. Indeed, if the output of Y grows at a rate n+ g(2% + 3%), and AL grows at the same rate, then, using a conditional digital example, we get the following: in the period t0 issue of 10,000 den. units accounted for 1000 employed. Then the output per one employed was in the period t0 10000/1000 = 10 den. units But if output grows at a rate n+ g, i.e. increases by 5% (2% + 3%), then in the next period of time t1, it will be 10500 den. units Output per unit of effective labor ( at e) did not increase, because AL growing at the same rate n+ g, i.e. Now, as it were, 1,050 people are working. Based on one unit of effective labor, we get: 10,500 den. units/1050 = 10 den. units

What then is the impact of technological progress on improving the well-being of the population? How does economic growth accompanied by technological progress lead to an increase in per capita output and consumption? To answer these questions, one should not forget that physically in a period of time t1, worked (taking into account the population growth rate, equal in our example to 2%) 1020 people, so the output per capita ( at) increased: 10500/1020 = 10.29 den. units

For a better understanding of the impact of the population growth rate n and pace of technological progress g on the dynamics of macroeconomic variables, let us summarize our analysis of the Solow growth model in a table (Fig. 8). Disposal rate δ in this case we neglect, assuming that the service life of physical capital is a very significant value.

Rice. 8. Influence of population growth rate ( n) and technical progress ( g) on the dynamics of macroeconomic indicators; for simplicity, we assumed that the rate of disposal (depreciation) δ = 0

As can be seen from the table, the growth rate of output per unit of effective labor in a steady state does not change; the same conclusion can be drawn with respect to the capital-labor ratio per unit of effective labor in a steady state. The main indicator characterizing the increase in the well-being of the population, i.e. output per capita at growing at the same rate as technological progress.

Let me once again draw attention to the problem of stationary, or sustainable growth in the long run. When the economy is in stable equilibrium in the short run, in addition to the fact that all savings are fully invested, there is another equality associated with the coincidence of the required and actually made gross investment. Each variant of such an equilibrium corresponds to a stable level of capital-labor ratio k* and the equilibrium level of income y*. If we build a function options equilibrium income depending on all values k*, then we will face the trajectory of the development of the economy in the conditions of long-term dynamic equilibrium y* = f(k*), included in the economic literature under the name sustainability trajectory.

Since in the model of such an economy all levels of capital-labor ratio turn out to be stable, in the long-term dynamic equilibrium the functions of the required i r and actual investment sf(k) will always match. In other words, at any level of income in dynamic equilibrium and, accordingly, for all values k* equality will be maintained (n+ δ + g)k* = sf(k*).

So, the Solow model shows that in the long run, the growth of production depends on the rate of technological progress. It is this exogenous factor that can support the continuous growth of production, and hence the growth of the welfare of the population, expressed in the growth of output and consumption per capita.

The Cobb-Douglas function shows what share of the total product is rewarded by the factor of production involved in its creation: Y = A K α L β , where α varies from 0 to 1, and β = 1 – α. The Cobb-Douglas function contains two variable factors of production - labor (L) and capital (K). Parameter A is a coefficient reflecting the level of technological productivity, and it does not change in the short term. For more details, see Course of Economic Theory, ed. Chepurina, Kiseleva, chapter 25

Neo-Keynesian models (for example, the Domar model) consider investment growth as the only growth factor of aggregate demand and aggregate supply; see, for example, Neo-Keynesian Models of Economic Growth

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The "golden rule" of accumulation by E. Phelps. E. Phelps' golden rule of accumulation List of sources used

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Introduction

economic growth accumulation phelps

The purpose of the course work - is to consider the golden rule of accumulation E. Phelps.

In the course of this goal, it is necessary to solve the following tasks of the course work:

- consider the concept of economic growth;

- to define extensive and intensive types of economic growth;

- to study the factors of economic growth;

- consider the neoclassical model of economic growth;

- reveal the golden rule of accumulation of E. Phelps.

The object of the course work is the golden rule of accumulation.

The subject of the course work is macroeconomics.

The methodological and theoretical basis of the study are the works of leading domestic experts in the field of macroeconomics, namely Anisimov A.A., Anosova A.V., Anosova A.V., Antipina O.N., Antipina O.N., Balabanova A.V. ., Basovsky L.E., Blanchard O., Brodsky B.E. and etc.

1. Theoretical aspects of economic growth

1.1 The concept of economic growth

In the economic literature, the concept of economic growth is interpreted ambiguously.

Some economists understand economic growth as an increase in potential and real gross national product (GNP), an increase in the country's economic power.

Other economists characterize economic growth as:

- increase in production capacities;

- increase in the real volume of production (GNP);

- an increase in real output per capita.

In domestic economic literature, economic growth is understood as the quantitative and qualitative improvement of the social product and its factors of production.

Economic growth has:

- its content (social reproduction);

- movement mechanism (interaction of workers, means of production, nature, technology);

- economic growth cycle phase;

- quantitative and qualitative signs of this movement, reflected in the growth rate of the product;

- socio-economic result (national wealth);

- goal (public welfare).

Economic growth is measured in two ways:

- annual growth rates of the gross national product (GNP);

- annual growth rates of the net national product (NNP).

The second method is more preferred.

Distinguish between potential and actual economic growth. Potential economic growth refers to the total NNP that can be produced if:

- available technology;

- the maximum possible use of workers;

- efficient use of the means of production.

Real economic growth is actually achieved.

The main indicators for measuring economic growth are:

- growth factor - the ratio of the indicator of the study period to the indicator of the base period;

- growth rate - growth factor multiplied by 100%;

- growth rate - growth rate minus 100%.

1.2 Extensive and intensive types of economic growth

There are two types of economic growth: extensive and intensive.

The first type of economic growth is extensive (lat. Extensivus - expanding). In this case, the increase in production volumes occurs due to the increase in three factors:

- fixed capital (funds);

- work force;

- material costs (natural raw materials, materials, energy carriers).

The extensive development of the economy implies the presence in the country of a sufficient amount of labor and natural resources, due to which the scale of the economy can increase.

A long-term orientation towards a predominantly extensive path of output growth leads to the fact that deadlocks arise in the national economy associated with a shortage of certain resources.

- the use of more advanced technology, advanced technologies;

- use of more economical materials, energy carriers;

- advanced training of personnel, that is, the qualitative improvement of all factors of production.

At the same time, the qualitative transformation of factors based on the achievements of scientific and technological progress is accompanied by a quantitative reduction in traditional factors during the period of technical re-equipment of production.

There are three main types of economic growth intensification:

Capital and material-saving intensification is carried out through the use of more advanced machines and equipment, more efficient use of materials, energy carriers, etc.

Capital and material-saving intensification are widely used in the conditions of industrial, post-industrial development.

1.3 Drivers of economic growth

In real economic practice, there is no purely extensive and purely intensive type of economic growth, since they are intertwined. Therefore, they speak of predominantly extensive and predominantly intensive types of economic growth, depending on the share of certain factors that caused this growth.

The process of economic growth includes the interaction of its factors. In macroeconomics, there are three groups of economic growth factors that determine the sources of economic growth, i.e. factors that make economic growth physically possible. These include:

- supply factors (availability of human resources, natural resources, fixed capital, level of technology);

- demand factors (price level, consumer spending, investment spending, government spending, net exports);

- distribution factors (rationality and completeness of the involvement of resources in the production process, the efficiency of the use of resources involved in the economic turnover).

It is obvious that large reserves of various natural resources, the presence of fertile lands, favorable climatic and weather conditions, and significant reserves of mineral resources make a significant contribution to the country's economic growth.

Technology level. This factor is closely related to supply, since the accumulation of a sum of knowledge leads to the accumulation of capital. Usually, two types of development of scientific and technical knowledge are distinguished: inventions and innovations.

The volume of fixed capital. One of the most important factors in economic growth is the accumulation of capital (equipment, buildings and stocks of industrial goods used in the production process).

Aggregate demand factors. All factors affecting aggregate demand ultimately have an impact on economic growth. Insufficiently efficient aggregate demand does not stimulate proper economic growth. This factor is especially important for Keynes and his followers.

The implementation of the increased national product depends on the factors of aggregate demand, that is, all elements of aggregate demand must provide full employment of all increasing resources. In addition, factors related to aggregate demand include the efficient allocation of resources.

Factors holding back economic growth include:

- the degree of completeness and efficiency of the use of natural, industrial and labor resources. Efficient use of economic resources requires their most optimal distribution between spheres and sectors of the economy;

- efficient and fair distribution of the growing volume of resources and the growing volume of real production. Since aggregate demand is determined by aggregate costs, they must be increased in order to ensure the full use of the increased volume of resources;

- institutional factors constraining or stimulating economic growth. These include: legal norms (labor protection, environmental protection, crime control, etc.), morality and traditions, labor conflicts, discrimination, etc.

2. The essence and basic concepts of the "Golden Rule of Accumulation" by E. Phelps

2.1 Neoclassical growth model

The neoclassical model is also the fact that it demonstrates the sustainability of economic growth, that is, the ability of the economic system to return to the trajectory of balanced development with the help of internal market self-regulation mechanisms.

2.2 E. Phelps' golden rule of accumulation

c** = f(k*) - (n+d)k *

Figure 3 - The golden rule of accumulation

Figure 4 - Impact of technological progress on sustainable capital-labor ratio and output per capita

c** = f(k) - (n+d)k

Technological progress leads to the fact that a stable level of capital-labor ratio moves from the point k1* to the point k2. The equilibrium level of required investments and savings moves from point E1 to point E2. Accordingly, the sustainable level of output per capita rises from y1 to y2*.

Note that the growth rate of capital stocks now, taking into account technical progress, will be n + q + g, i.e. it is these values that measure the slope of the required investment per unit of effective labor.

ce = f(ke) - (n + q + g)ke .

So, the maximum sustainable level of consumption ce (the distance between points A and E) is guaranteed by such a volume of accumulation ke, which is achieved when the golden rule is followed, taking into account population growth and technical progress: