Solow model
Robert Solow's model was built on the neoclassical premise of the dominance of perfect competition in factor markets, ensuring full employment of resources. The scientist proceeded from the fact that a necessary condition is the equality of aggregate demand and aggregate supply. Moreover, the aggregate supply in his model was determined on the basis of the Cobb-Douglas production function, which expresses the relationship of functional dependence between the volume of production, on the one hand, and the factors used and their mutual combination, on the other.
The purpose of the Solow model is to answer the questions: what are the factors of balanced economic growth, what growth rate can the economy afford given the given parameters of the economic system, and how are household incomes and consumption volumes maximized?
In general, the volume of national output Y is a function of 3 factors of production: labor L, capital K, land N:
Y = f (L, K, N)
The land factor in the Solow model was omitted due to low efficiency in economic systems characterized by a high technological level, and therefore the volume of output depends on labor and production factors Y = f (L, K).
In expanded form, this formula looks like:
Y = DY / DL) * L + (DY / DK) * K(3.31)
where DY / DL is the marginal product of labor MPL, DY / DK – marginal product of capital MPK.
This means that the total product is equal to the sum of the products of the expended amount of labor and capital by their marginal products, i.e. on the increase in products DY from an increase in labor costs DL and capital costs DK. In simplified form y= Y/L , Where y– labor productivity; k = K/ L , Where k- capital-labor ratio. Then the production function has the form y=f (k), Where f (k) = F (k,1).
The graphical representation of this function is shown in Fig. 3.1. The figure shows that the capital-labor ratio k determines the size of output per worker: y = f (k).
Rice. 3.1. Graph of the production function in the Solow model
Wherein tga = MPK: If k increases by one unit, then y increases by MRC units. As the capital-to-labor ratio increases, its productivity increases, but at a decreasing rate, because RTO decreases.
Aggregate demand in the Solow model is determined by investment and consumer demand. The equation for output per worker is:
g = c + i (3.32)
Where With And i– consumption and investment.
Income is divided between consumption and savings according to the savings rate, so consumption can be represented as
With= (1 - s) y, (3.33)
Where s- rate of savings (accumulation)
Then y = c + i =(1-s)y+i, where i = sy. In equilibrium, investment is equal to saving and proportional to income.
As a result, the condition of equality of supply and demand can be represented as:
f(k)= c + i or f(k)= i/s.
The production function determines supply in the goods market, and capital accumulation determines the demand for industrial products. The volume of capital changes under the influence of disposal investments. Investment per worker is part of the income per worker ( i = sy) or
i = s * f(k).(3.34)
It follows from this that the higher the level of capital-labor ratio k, the higher the level of production f(k) and more investment i.
In R. Solow's model, the savings rate is a key factor that determines the level of sustainability of the capital-labor ratio. A higher savings rate results in a larger capital stock and a higher level of output.
Another factor for continued economic growth in a sustainable economy is population growth. For economic sustainability it is necessary that investments sf(k) must compensate for the consequences of capital disposal and capital growth ( d+n) k, point on the graph E(Fig. 3.2). However, if population growth is not accompanied by an increase in investment, then this leads to a decrease in the stock of capital per worker.
Thus, if countries with higher population growth rates have lower capital-labor ratios, this means lower incomes.
Rice. 3.2. Investments sf(k) and capital growth ( d+n) k
The third source of economic growth, after investment and population growth, is technological progress. In neoclassical theory, technical progress is qualitative changes in production (increasing the education of workers, improving the organization of labor, increasing the scale of production).
Including technological progress in the model will change the original production function: Y = f(K, L e, e), Where e- labor efficiency of one employee (depends on health, education, qualifications), L e– the number of effective labor force units.
Technological progress leads to increased efficiency e at a constant pace g. If g= 5%, then the return on each unit of labor will increase by 5% per year, and this is equivalent to the fact that the volume of production increases as if the labor force increased by 5% per year. It is a labor-saving form of technological progress.
If the number of employees L growing at a rate n, and efficiency e growing at a rate g, That L e will increase at a rate n+g. Capital per unit of labor with constant efficiency will be k 1 + [K /(L e)], and the volume of production per unit of labor with constant efficiency y 1 = Y / (L e). A state of stable equilibrium is achieved under the condition s x f(k 1) = (d+n+g)x k 1 where d- depreciation rate.
From the above equality it follows that there is only one level of capital-to-weight ratio k 1, in which capital and output per unit of labor with constant efficiency are constant (Fig. 3.3).
Rice. 3.3. The condition of constant capital and output per unit of labor with constant efficiency
Steady state k 1 in the presence of technical progress, the total amount of capital TO and release Y will grow at a rate n+g. Capital-labor ratio per employee k/L and release Y/L will grow at a rate g. Thus, technological progress in the Solow model is the only condition for continuous economic development.
R. Solow's model of economic growth is a neoclassical model of economic growth that reveals the mechanism of influence of savings, growth of labor resources and scientific and technological progress on the standard of living of the population and its dynamics.
R. Solow's model was developed in 1956 and is intended to study equilibrium trajectories of economic growth; it shows the relationship between savings and capital accumulation.
This is a simple continuous single-sector model of economic dynamics where only households and firms are represented.
R. Solow showed that the instability of dynamic equilibrium in the models of E. Domar and R. Harrod is a consequence of the non-interchangeability of production factors.
Prerequisites for R. Solow's model:
- a necessary condition for equilibrium of the economic system is the equality of AD and AS;
- AS is determined based on Cobb-Douglas production function, expressing the relationship of functional dependence between the volume of production, on the one hand, and the factors used and their mutual combination, on the other;
· perfect competition in the factor market and full employment;
· price flexibility in the goods market;
· constant returns to scale;
· decreasing productivity of capital;
· constant rate of capital retirement.
R. Solow's model consists of the following equations characterizing economic dynamics.
1. The volume of supply in the goods market is described by a production function with constant returns to scale:
Y s = f(L, K).
In expanded form, this function will take the form:
Y = (Δ Y/ Δ L)L + (Δ Y/ Δ K)K ,
where ΔY/ ΔL is the marginal product of labor MPL;
ΔY/ ΔK - marginal product of capital of RTOs
This means that the total product (output) is equal to the sum of the products of the expended amount of labor L and capital K and their marginal products, i.e., the increase in products ΔY from an increase in labor input ΔL and capital input ΔK.
To simplify the function, we denote:
where y is output per worker, or labor productivity;
where k is the capital-labor ratio (capital-labor ratio).
Then the production function can be written:
Thus, the volume of production per worker is a function of its capital-labor ratio (Fig. 3.3).
The graph shows that the capital-labor ratio k determines the size of output per worker: y = f(k). The tangent of the tangent h is equal to the marginal productivity of capital: if k increases by one unit, then y increases by MRC units. At the same time, we see that as the capital-labor ratio increases, its productivity increases, but at a decreasing rate, since the marginal productivity of capital decreases.
2. The volume of demand for goods and services presented by consumers and investors,
i.e. by the private sector without government orders and net exports:
In terms of one employee: i t = I t /L t– investments per employee;
with t = C t /L t– consumption per worker.
3. The equilibrium condition is the equality of I and S .
Since the volume of investment is the share of savings in income:
In equilibrium, investment is equal to savings and proportional to income.
Capital stocks in the economy depend on the volume of investment (i t) and disposal (depreciation) of capital (dk t),hence:
The capital stock at which investment (i t) is equal to capital depreciation (dk t), and Δk t = 0, is called the sustainable level of capital-labor ratio (k*).
In a stable (stationary) state, a constant ratio of K t /L t and output per worker Y t /L t is established. At a capital-labor level corresponding to k* , the economy is in a state of long-term stable (stationary) equilibrium, to which it will always return.
The functioning of the Solow model can be illustrated graphically (Fig. 3.4.).
If capital reserves are equal to k 1, then investments are greater than depreciation, the capital-to-work ratio increases and will continue to grow until it approaches the level k*.
If capital reserves correspond to k 2 , then investment is less than depreciation, which means capital reserves will decline, approaching the level k*.
The equilibrium level of capital-labor ratio is influenced by the rate of accumulation (savings). Its growth from s 1 to s 2 shifts the investment curve from s 1 f(k) to s 2 f(k), and the economy moves to a new equilibrium state with a higher capital-labor ratio (k* 2) and higher labor productivity (Fig. 3 -5).
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Thus, R. Solow’s model shows that the rate of savings (accumulation) is a key factor determining the level of sustainable capital-labor ratio. A higher saving rate ensures a larger capital stock and a higher level of output.
4. The country's population growth is increasing at a constant rate. Thanks to the flexibility of prices in the factor market, full employment is constantly maintained, i.e., the number of employees grows at the same rate as the population in the country.
In this case, capital reserves may change because:
♦ investments lead to an increase in capital reserves;
♦ part of the capital is depreciated, which leads to a decrease in capital reserves;
♦ part of the capital goes to newly recruited workers.
Capital accumulation will therefore be:
where k t is the change in capital reserves per employee;
i – investments per employee;
dk t – depreciation per employee;
nk t is capital growth due to population growth and employment in the economy.
The product nk t shows the need for additional capital per worker so that the capital-labor ratio remains constant.
Since y =f(k), then the condition for stable equilibrium in the economy with constant capital-labor ratio:
In order for the capital-labor ratio to remain constant as population grows, it is necessary that capital increases at the same rate as the population. In addition, output and population should grow at the same rate:
Let's consider the economic consequences of increasing population growth rates and their slowdown for the country's economy.
5. The population growth rate increased from n to n" at the same rate of accumulation (Fig. 3.6).
The initial steady state of the economy corresponds to point E. As population growth rates increase, capital per worker will decrease until the economy reaches a new steady state at point E 1 with a lower capital-labor ratio. A lower level of capital-labor ratio corresponds to lower labor productivity. Thus, R. Solow’s model explains that countries with higher rates of population growth have lower capital-labor ratios, and therefore lower incomes. Accordingly, if countries with lower population growth rates have higher incomes
6. The key idea in R. Solow’s model is that economic growth should be achieved through scientific and technological progress, and not through an increase in capital-to-labor ratio.
So, including technical progress in the model changes the original production function:
Y = f(K, L, e),
where e is the labor efficiency of one employee (depends on the health, education and qualifications of the workforce);
L – number of effective labor force units.
If we assume that labor efficiency per employee grows at a constant rate of g = 0.03, then the return on each unit increases by 3%.
Since labor grows at a rate of n and output grows at a rate of g, output in a steady state of equilibrium grows at a rate of n + g.
In a steady state k* 1 in the presence of technical progress, the total amount of capital K and output Y will grow at a rate of n + g. Per employee, capital-labor ratio K/L and output Y/L will grow at a rate of g. This suggests that technical progress in R. Solow’s model is the only condition for continuous growth in living standards.
Thus, R. Solow’s model allows us to reveal the relationship between three sources of economic growth - investment, labor force and technical progress. The influence of the state on economic growth is possible through its influence on the rate of saving (accumulation) and on the speed of technical progress.
7. The "golden rule" of savings.
What should the savings rate be? Equilibrium economic growth is compatible with different savings rates, so the optimal rate will be the one that ensures economic growth with the maximum level of consumption. This norm corresponds to the “golden rule”.
The “golden rule” of accumulation was formulated by the American economist E. Phelps in 1961. According to this rule, per capita consumption in a growing economy reaches its maximum at the moment when the marginal product of capital becomes equal to the rate of economic growth.
At the optimal rate of capital accumulation (k**), corresponding to the “golden rule”, the condition must be met: the marginal product of capital is equal to depreciation (capital retirement), i.e.
and if we take into account the rate of population growth and technological progress, then
MRC = d + n+g.
Now let’s assume that the economy is in a state of equilibrium, but does not correspond to the “golden rule” and the government has to determine a growth policy and develop a program for achieving maximum per capita consumption.
In this case, two options for the state of the economy are possible.
1. The economy has a greater stock of capital than is necessary to comply with the “golden rule”.
2. The capital stock does not reach the “golden rule” level.
Determining the capital stock that corresponds to the “golden rule” means solving the problem of choosing the optimal rate of accumulation.
Let's consider first option economic development.
A decrease in the saving rate leads to an increase in consumption and a decrease in investment. At the same time, the economy goes out of equilibrium. The new equilibrium will correspond to the "golden rule" with a higher level of consumption, since the initial stock of capital is excessively high, with a reduction in income and the level of investment.
Second option economic development requires a responsible choice of politicians, since the decisions they make affect the vital interests of different generations. An increase in the saving rate leads to a decrease in consumption and an increase in investment. As capital accumulates, production, consumption and investment begin to increase until a new steady state with a higher level of consumption is reached. But a high level of consumption will be preceded by a transition period with a decrease in consumption. This period can span the life of an entire generation, providing the benefits of economic growth to subsequent generations.
R. Solow's model identifies technological progress as the only basis for sustainable growth of well-being and allows us to find the optimal growth option that ensures maximum consumption. However, it considers technical progress as an external (exogenous) factor, and therefore does not explain it. Some scientists believe that the determinants of technological progress are not clear enough today. However, public policy can stimulate technological progress through a variety of tools, including encouraging research and development. For example, by improving patent legislation, some developed countries (USA, Japan, Germany) granted a monopoly to inventors for the right to produce a new product for a long time. Tax laws in many countries provide significant benefits to research organizations. Specially created national science funds subsidize basic scientific research. It is no less important, and in modern conditions it becomes paramount, to invest in human capital, whose role in technical progress is key.
R. Solow's model of economic growth is a neoclassical model of economic growth that reveals the mechanism of influence of savings, growth of labor resources and scientific and technological progress on the standard of living of the population and its dynamics.
R. Solow's model was developed in 1956 and is intended to study equilibrium trajectories of economic growth; shows the relationship between savings and capital accumulation.
This is a simple continuous single-sector model of economic dynamics where only households and firms are represented.
R. Solow showed that the instability of dynamic equilibrium in the models of E. Domar and R. Harrod is a consequence of the lack of interchangeability of production factors. Instead of V. Leontiev's production function, he uses the Cobb-Douglas production function, where labor and capital are substitutes, and the sum of their elasticity coefficients for production factors is equal to one. In addition, the model is built on the following premises of the neoclassical school:
♦ perfect competition in the factor market and full employment;
♦ price flexibility in the goods market;
♦ constant returns to scale;
♦ diminishing productivity of capital;
♦ constant rate of capital retirement.
R. Solow's model consists of the following equations characterizing economic dynamics.
1. The volume of supply in the goods market is described by a production function with constant returns to scale:
For any positive Z the following is true:
where Y/L is the average labor productivity per employee (y); K t /L t capital-labor ratio (capital-labor ratio) of labor per employee (k t). Therefore we can write:
Thus, the volume of production per worker is a function of its capital ratio (Fig. 30.2).
Rice. 30.2. Graph of the production function per worker
2. The volume of demand for goods and services presented by consumers and investors, i.e., by the private sector without government orders and net exports: 
Then - investment per employee; - consumption per
one employee.
The equilibrium condition is the equality of I and S. Since the volume of investment is the share of savings in income:
In equilibrium, investment is equal to savings and proportional to income.
Capital stocks in the economy depend on the volume of investment (it) and capital outflow (dkt), therefore:
The capital stock at which investment (i t) is equal to capital outflow (dk t), and Ak t = 0, is called the sustainable level of capital-labor ratio (k*).
In a stable (stationary) state, a constant ratio of K/L and output per worker Y t /L t is established. At a capital-labor level corresponding to k*, the economy is in a state of long-term stable (stationary) equilibrium, to which it will always return.
The functioning of the Solow model can be illustrated graphically (Figure 30.3).
Rice. 30.3. Sustainable level of capital ratio
If the initial value k 4 is lower than k*, then sf(k) > dk.
If k 2 > k* - investment is less than depreciation. If the system deviates from the trajectory of equilibrium development, the economy, under the influence of endogenous mechanisms, will return to the equilibrium trajectory.
An increase in the savings rate from Sy 1 to Sy 2 shifts the investment curve upward. Now at the previous steady state point, investment exceeds disposal. The economy will strive to achieve a new steady state with greater capital and labor productivity (Figure 30.4).
From the foregoing, the following conclusions can be drawn:
♦ an increase in the savings rate in the short term leads to an acceleration of the growth rate of national income (from k 4 * to k 2 *);
♦ in the long run, a new long-term equilibrium state is established, while the level of capital and labor productivity per worker increases.
3. The country's population growth is increasing at a constant rate. Thanks to the flexibility of prices in the factor market, full employment is constantly maintained, i.e., the number of people employed is growing at the same rate as the population in the country.
In this case, capital reserves may change because:
♦ investments lead to an increase in capital reserves;
♦ part of the capital is depreciated, which leads to a decrease in capital reserves;
♦ part of the capital goes to newly recruited workers.
Capital accumulation will therefore be:
Rice. 30.4. Increase in savings rate
where k t is the change in capital reserves per employee; i t - investments per employee; dk t - depreciation per employee; nk t is capital growth due to population growth and employment in the economy.
The product nk t shows the need for additional capital per worker so that the capital-labor ratio remains constant.
Since yt = f(k), then the condition for stable equilibrium in the economy with constant capital-labor ratio:
In order for the capital-labor ratio to remain constant with population growth, it is necessary to increase capital at the same rate as the population. In addition, output and population should grow at the same rate:
Let's consider the economic consequences of increasing population growth rates and their slowdown for the country's economy.
1. The population growth rate increased from n to n" at the same rate of accumulation (Fig. 30.5).
In Fig. Figure 30.5 shows that an increase in the population growth rate shifts the line (d + n)k up and to the left.
The initial steady state of the economy corresponds to point c. As the population growth rate increases, capital per worker will decrease until the economy reaches a new steady state at point C with a lower capital-labor ratio. A lower level of capital-labor ratio corresponds to lower labor productivity (from point y 0 * to point y 1 **). At the same time, the equilibrium growth rate of national income increases.
2. Slowdown in population growth rates from n to n" at the same rate of accumulation (Fig. 30.6).
From Fig. 30.6 it follows that the slowdown in population growth shifts the line (d + n)k down and to the right, from point k* the capital-labor ratio per worker begins to grow until the economy reaches the desired steady state at point C with a higher capital-labor ratio and, accordingly labor productivity.
At the same time, the equilibrium rate of economic growth slows down. In the first case, rapid population growth at a given level of savings determines a low level of per capita income. The level of savings of the population is insufficient for the growth of capital-labor ratio. In the second case, the level of per capita income increases.
Solow model
The model proposed by the American economist, Nobel Prize winner R. Solow, makes it possible to more accurately describe some of the features of macroeconomics onomic processes due to a number of features. This model is based on the Cobb-Douglas production function, in which the contribution of various factors of production was calculated. The Cobb-Douglas function states that a 1% increase in capital input increases output by?, and a 1% increase in labor input increases output by?.
Other prerequisites for economic growth in the Solow model:
1. Labor (L) and capital (K) are completely interchangeable;
2. Positive diminishing returns to factors of production;
3. Savings (S) are fully invested.
So the Solow model looks like this:
Y = F (K, L).(10)
Let's divide everything by L:
Let where be labor productivity. Then, where is the capital-labor ratio. Income is a function of one factor - capital-labor ratio, i.e.
Note that (c + i) is the consumption of goods and investments per worker.
C = (1 - S) y,
then y = (1 - S) · (y + i). Divide both sides of the equation by y, then 1 = (1 - S) + i/y, or i/y = s, therefore,
That is, investments are proportional to income. Substitute y = f(K):
I = s f(K).(14)
The greater the capital-to-labor ratio, the greater the volume of production and the higher the amount of investment.
Thus, a high level of savings leads to faster economic growth.
The Solow model was used by economists to answer what optimal economic growth should be. In the 1960s American economist Phelps, considering the economic problems of his invented kingdom of Solovia (named Solow), formulated the so-called “golden rule” of capital accumulation.
"Golden Rule" of Saving by E. Phelps
Equilibrium economic growth is compatible with different savings rates tion, but only the one that ensures economic growth with the maximum level of consumption will be optimal. The optimal rate of accumulation corresponds to the “golden rule”, which entered economic science thanks to the American economist Edmund Phelps.
E. Phelps asked the question of how much capital a society on a trajectory of balanced growth would want to have. If it is large enough, this will guarantee a high level of production, but most of it will go not for consumption, but for accumulation - society will not be able to enjoy the fruits of growth. If the volume of capital is too small, then it will be possible to consume almost everything that is produced, but very little will be produced. Somewhere in the middle between the two extremes, obviously, there is an optimal point for society, at which the maximum volume of consumption is achieved.
Let k** be the level of capital-labor ratio corresponding to the rate of accumulation according to the Golden Rule, and c** be the level of consumption.
All produced products are spent on consumption (c) and investment (i):
y = c + i => c = y - i.(15)
Substituting the values of each of the parameters that they took in a steady state, we obtain:
c* = f(k*) - dk*.(16)
From here, a stable level of capital-labor ratio (k**) is determined, at which the volume of consumption (c**) is maximized and corresponds to the “golden rule” (Figure 2). At point E, the production function f(k*) and the line dk* have the same slope and consumption reaches its maximum level.
Figure 2 - “Golden rule” of savings
At the capital-labor level k**, the condition MPK = d is satisfied (an increase in the stock of capital by one unit gives an increase in output equal to the marginal product of capital and increases the disposal of capital by the amount d), and taking into account population growth and technical progress, the following condition is satisfied:
MPK = d + n + g.(17)
R. Solow's model and the “golden rule of accumulation” allow us to formulate some practical recommendations.
1) Increase or decrease the savings rate. If an economy develops with a capital stock greater than it would have under the “golden rule,” then it is necessary to implement policies aimed at reducing the savings rate. In turn, this will lead to an increase in consumption and a corresponding decrease in investment and, therefore, a decrease in the sustainable level of the capital stock.
If the economy develops with a lower capital-labor ratio than in a steady state according to the “golden rule,” then it is necessary to stimulate the growth of the savings rate in society. This will lead to a decrease in consumption and an increase in investment, which will ultimately lead to an increase in consumption again.
2) Increasing returns from the labor factor, increasing the efficiency of the labor factor. Based on the assumptions, population growth in the Solow model is assumed to be an increase in the working-age population (an increase in the number of effective labor units). At the same time, it is obvious that the presence of a working-age population can be ensured either through an increase in the birth rate or through the influx of migrants into the country.
3) Stimulating technical progress. As follows from R. Solow's model, a faster rate of population growth will have an impact on accelerating economic growth, but per capita output will decline in a steady state. Another factor, an increase in the saving rate, will lead to higher per capita income and increase the capital-to-labor ratio, but will not affect the steady-state growth rate. Therefore, technological progress is the only factor that ensures economic growth in a steady state, that is, an increase in per capita income. However, how it is achieved is not described in the Solow model; it is something like manna from heaven.
In conclusion, we note that in the Solow model, whether a country’s economy is on an equilibrium growth trajectory is determined primarily by exogenously given values of s, n and g??. The exogenous nature of these determinants of economic growth led to criticism of the Solow model and indicated the vector of development of modern theories of economic growth in the direction of endogenizing indicators of the population growth rate, the level of technical progress and the savings rate. A significant part of modern so-called theories of endogenous growth is devoted to the consideration of these aspects of the problem and has been one of the most promising areas of economic science since the emergence of the Solow model.
6.3.1 Models of economic growth R. Solow
R. Solow (b. 1924), winner of the Nobel Prize in Economics in 1987, developed two models: a factor analysis model of the sources of economic growth and a model showing the influence of savings, labor force growth and scientific and technical progress on the standard of living of the population and its dynamics.
The basis of the first model was the Cob-ba-Douglas production function, modified by introducing another factor - the level of technology development:
Solow concluded that a change in technology will lead to an equal increase in the marginal product K and L, i.e. Q = Tf(K, L).
Thus, the increase in output depends proportionally on the increase in technology, the increase in fixed capital and the increase in invested labor.
If the shares of labor and capital in output are measured on the basis of labor productivity, capital-labor ratio per worker and capital productivity, then the contribution of technical progress is presented as the remainder after subtracting from the increase in output the share obtained due to the increase in labor and capital. This is the so-called Solow residual, which expresses the share of economic growth due to technological progress, or “advancement in knowledge.”
Another Solow model shows the relationship between saving, capital accumulation and economic growth. If we denote the production per employee q, the amount of capital per employee k (capital or capital-labor ratio), then the production function will take the form: q = Tf(k).
As the capital-labor ratio increases, q increases, but to a lesser extent, since the marginal productivity of capital (capital productivity) falls.
In the Solow model, output is determined by investment (I) and consumption (C). It is assumed that the economy is closed from the world market and domestic investments (I) are equal to national savings, or the volume of gross accumulation (S).
The dynamics of output volume in this case depends on the capital ratio, which changes under the influence of the disposal of fixed capital or investment.
In turn, investments depend on the rate of gross accumulation, which is a relative value and is calculated as the ratio of gross accumulation to the created product. The savings rate determines the division of the product into investment, savings and consumption. With an increase in the rate of accumulation (savings), investments increase, exceeding disposal. At the same time, production assets increase. In the short term, the acceleration of economic growth depends on the rate of accumulation.
Subsequently, developing his model, Solow introduced new factors that, along with investment and disposal, affect the capital-labor ratio: labor force growth and technological progress. It is believed that technological changes are labor-saving, promoting advanced training, development of professional skills, and raising the educational level of workers.
(Materials are based on: E.A. Maryganova, S.A. Shapiro. Macroeconomics. Express course: textbook. - M.: KNORUS, 2010. ISBN 978-5-406-00716-7)