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 the product per worker (marginal labor productivity) grows, but to a lesser extent.

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". AT general view The golden rule of accumulation can be formulated as follows: the level of capital accumulation that ensures the highest consumption of society and the 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 the original model in 3 ways:

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 one with no access to foreign loans, the only way to increase investment is through increased 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 the 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 achieved the best way if the marginal productivity of capital (MPC) is equal to the time preference discount 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 us 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 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. Gold and foreign exchange reserve assets 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 separating 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 a particular city have apartments that they have earned by their long work 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 accumulation is maximum level per capita consumption can be achieved with 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 solving the question 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 determining the optimal rate of 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 for the safety of 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 shares, is associated with a non-zero level of risk of bankruptcy of the issuer of the 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 restoration method is the growth of production, the elimination of state budget deficits mainly by increasing 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). During 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 its cost equal to the amount of metal used in its 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 items. 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

Well economic theory Ed5 (2006) - [ c.25 ]

Managers are not born, managers are made

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

Target this model is 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:

1. Unlike neo-Keynesian models, the factors of production in the Solow model based on the Cobb-Douglas production function are interchangeable.
2. 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.
3. 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.
4. It is assumed that the growth rate of labor resources (labor supply, L) is equal to the population growth rate n.
5. 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).
6. 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 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 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 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 low-income countries saved between 10% and 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, a stable state of the economy can correspond to different norms savings. 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-labor ratio, 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*.

Macroeconomic theory deals with different types technological progress, 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 technical 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 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 a 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

The fundamental merits of Phelps include, firstly, the contribution to the creation of the neoclassical theory of economic growth, and, secondly, the answer to the question of the relationship between inflation and unemployment. The Nobel Prize was awarded to the latter, but it is still worth saying a few words about Phelps' contribution to growth theory. In the early 60s, he formulated the so-called "golden rule" of capital accumulation. The question was at what rate of accumulation the economy reaches the optimal mode of consumption in the long run. According to the golden rule, the return on capital should be equal to the cost of its reproduction. Only then is the optimal level of household consumption ensured; the excess of returns over costs indicates a lack of investment and vice versa. Such, at first glance, a simple principle of equality of costs and results, is universal in the economy. The merit of Phelps is that he formulated and substantiated it in a dynamic context. All modern models of economic growth use the same principle as a key condition for optimality.

The golden rule proved to be important for economic policy. First, in the post-war period, the question of the optimal rate of capital accumulation was topical in many countries. What share of GDP should have been invested to ensure optimal consumption over the long term? Phelps gave a clear answer, which made it possible to judge the effectiveness of this or that growth regimen. From the golden rule, for example, it followed that Soviet Union, which by the beginning of the 1960s had good dynamics, actually provided it due to the excess rate of accumulation. The additional costs significantly outweighed the return on capital, indicating the inefficiency of growth in the "golden era" of socialism. Secondly, the application of the Phelps rule at the household level makes it possible to determine the optimal principles of taxation. For example, a consumption tax turns out to be neutral with respect to this rule, that is, it does not affect the savings rate. In this respect, such a tax (and its practical embodiment is the retail sales tax) is much preferable to taxes on income, especially on capital.

CONCLUSIONS:

1. Macroeconomics studies aggregate, or aggregated, values: aggregate demand, aggregate supply, employment, general price level, inflation, balance of payments, etc.

2. Methods of macroeconomics are both positive and normative analysis, as well as:

· aggregation;

the principle of "ceteris paribus";

a balanced approach

The difference between stocks and flows.

3. The main subjects of the market studied by macroeconomics:

households;

· state;

Abroad (in an open economy).

4. The circulation of income and expenses in the economy shows the relationship between all market entities in the process of their spending and receiving income.

5. Injections in the circulation of income and expenditure are investments, government spending and exports. Leaks are savings, taxes and imports.

6. The main competing schools in macroeconomics are represented by Keynesianism and the neoclassical trend.

7. GDP is the main macroeconomic indicator that measures business activity over a certain period of time. The calculation of GDP is carried out by three methods: production, summation of expenses and summation of income. As a result, all three methods give the same final result of calculating GDP.

8. The main national accounts identity is: Y = FROM +I+G+NX.

9. GDP expressed in current prices is called nominal, and in prices of the base year - real. The GDP deflator is the quotient of nominal GDP divided by real GDP and shows the change in the price level over a certain period.

10. The price index with a constant set of goods and services (consumer basket) is called the Laspeyres index; a price index with a changing set of goods and services - the Paasche index, or the GDP deflator.

11. Potential GDP is the GDP calculated for the level of full employment of all the resources of society.

12. The System of National Accounts (SNA) reflects the relationship of the most important macroeconomic indicators: GDP, net domestic product (NDP), national income (NI), personal income (DI), disposable income (DI).

13. Economic growth is expressed in real GDP growth. The measure of economic growth is the annual growth rate of real GDP.

14. GDP is not an ideal measure of the economic activity of the population and its economic well-being, since GDP does not reflect the non-observed economy - shadow production, illegal production, informal sector production, household production for own final use, as well as activities that affect economic well-being, but without a market value. This shortcoming is proposed to be eliminated by the introduction of indicators of net economic well-being (NEW) and true savings.

15. Extensive economic growth is carried out due to the quantitative growth of its factors - labor, capital, land resources, intensive - due to the growth of labor productivity. The most important components of labor productivity growth are technological progress, education (human capital), the cost of physical capital, economies of scale in production, and improved allocation of resources.

16. Models of economic growth fall into two main groups.

One of them is a neoclassical direction and is reflected, in particular, in the models of Cobb-Douglas, R. Solow. The second group includes models based on Keynesian theory. The most famous of these is the Harrod-Domar model. The main difference between neoclassical and Keynesian models of economic growth is that the former take into account several factors of economic growth, while the latter take into account one factor.

17. According to the golden rule, the return on capital should be equal to the cost of its reproduction. Only then is the optimal level of household consumption ensured: the excess of returns over costs indicates a lack of investment and vice versa.

BASIC CONCEPTS:

macroeconomics

circular flow of incomes and expenditures

injections

leakages

stocks

flow

neoclassics neoclassics

new classics new classics

monetarists

Keynesians

neokeynesians neokeynesiaps

new Keynesians new Keynesians

gross domestic product gross dostic product (GDP);

- nominal - potipal;

Real - real;

gross national product gross domestic product (GNP);

gross national income gross patiopal ipcote (GNI);

added value value added;

GDP deflator GDP-deflator;

Laspeyres index Laspeyres ipdex;

Paasche index Paacshe ipdex;

system of national accounts patiopal associate system;

personal consumption spending persopal copsutptiop expepditures;

disposable income disposabIe ipcote;

gross domestic investment gross dotestic ipvestment;

depreciation depreciation;

net export pet export;

non-observed economy pop-observipg esopot;

net economic wealth (NEW) pet ecopotic welfare;

the economic growth economic growth;

extensive economic growth extensive economic growth;

intensive economic growth intensive economic growth;

human capital human capital;

true savings genuine savings.

1.Agapova T.A., Seregina S.F. Macroeconomics. Tests. Topic 1, 10

Galperin V.M., Grebennikov P.I., Leussky A.I., Tarasevich L.S. Macroeconomics. Ch. 1,2,14

2.Dolan E. Macroeconomics. Ch. 2, 3.

3. Dornbusch R., Fisher S. Macroeconomics. Ch. 1, § 1, ch. 19

4. Linwood T. Geiger. Macroeconomic theory and transition economy. Chapter 4, § 1.

5. McConnell K., Bru S. Economics. Ch. 9.

6. Mankiw N.G. Macroeconomics. Ch. 1, 2,3,4

7. Linwood T. Geiger. Macroeconomic theory and transition economy. Chapter 4, § 1.

8. System of National Accounts - a tool for macroeconomic analysis: Textbook / Ed. Yu.N. Ivanova - M

9. Fisher S., Dornbusch R., Schmalenzi R. Economics. Ch. 24, 35.

10. Heine P. Economic way of thinking. Ch. 16.

Consider the impact of a change in the savings rate on the level of consumption.

It follows from the analysis of Figure 4.1 that the volume of consumption at the static point η = η*, which is determined by the distance between the production function schedule and the savings curve, is simultaneously equal to the distance between the production function schedule and direct investment at this point. But this distance, when the static point is displaced in the same direction, can both increase and decrease.

If the initial savings rate is small ( s 1 ), the static point is close to the origin. Then, when the static point shifts to the right (that is, when the savings rate increases), the specified distance will increase - consumption will grow.

This is clearly shown in Figure 4.2 (segment A 1 B 1).

Figure 4.2 - Influence of the savings rate on the level of consumption

This means that an increase in investment in the development of production in this case will bring such a high return that the result will allow more funds to be allocated to consumption.

In the case of a high initial savings rate ( s 2) its further increase will already lead to a decrease in consumption (segment A 2 B 2). Such savings (and investments) are not profitable, because an increase in investment in this case gives a low return.

From all this we can conclude that there should be such a savings rate s m , at which the level of consumption will be the highest. Investments in this case also have maximum efficiency. Let's define this rule.

We have established that the amount of consumption is equal to the difference between income and savings (investment). Taking into account (4.21), we write:

where c is consumption per worker.

To calculate the maximum value With you need to calculate the derivative of With at the rate of savings s and equate it to zero, i.e.

Differentiation (4.22) is carried out taking into account the fact that in the problem posed by us, the quantity η * is itself a function of the savings rate s :

In this way, . In order for such an expression to be equal to zero, it is necessary that the first factor (content in square brackets ) or the second factor would be equal to zero. However, as we have already shown, with an increase in the savings rate s, the capital-labor ratio η also increases, therefore the derivative cannot be equal to zero.

Thus, to calculate it is necessary to equate the content in square brackets to zero

. (4.24)

This condition is called the golden rule of capital accumulation. It corresponds to the capital-labor ratio η g , which determines the maximum possible consumption per capita. The savings rate corresponding to the golden rule is determined from (4.21)

, (4.25)

and the value maximum consumption- from ():



The solution of equation (4.21) can be obtained analytically, if the expression of the production function is known, or graphically. Condition (4.21) means that at the point η g the slope of the tangent to the graph of the production function f(η ) coincides with the slope of the direct required investment. Having attached to the graph a ruler directed parallel to direct investment and shifting it up or down, it is necessary to find its position in which the ruler will touch the production schedule.

functions at a single point. This point will determine the capital-labor ratio corresponding to the golden rule. If the system is in a static state, which corresponds to the golden rule, then the level of consumption per worker, being the maximum possible for this system, will remain the same in the future, because. population growth will be offset by a corresponding increase in output.

If the savings rate exceeds s g , then the investment is economically inefficient. It makes sense to reduce this rate to s g . However, immediately after the decrease t 0 consumption will increase sharply (jump) to a value significantly exceeding s g and then gradually

decrease towards this value. The dynamics of changes in the level of consumption for this case is shown in Figure 4.3, a.

In any case, after a change in the savings rate, consumption

of all subsequent generations will be higher than it was before this change.

Figure 4.3 - Dynamics of changes in consumption after changing the norm

saving:

a) the initial savings rate is higher s g; b) the initial savings rate is lower s g

If the savings rate is lower s g , it should be raised to s g . However, immediately after the change t 0 consumption drops sharply and then starts to rise. For some time after the change in the savings rate, consumption will be lower than before the change, although in the long term it will still become higher and tend to the maximum level. with g . Thus, we can conclude that immediately after the reform, the standard of living of the population will decrease. It is necessary to go through difficult times in order to subsequently achieve a higher standard of living than before the reform.

Example 4.1. The economic system is described by a production function

.

Depreciation rate δ and growth rate of labor resources n are equal to 0.1. It is necessary to determine the value of the savings rate, the volume of consumption and investment per capita corresponding to the maximum level of consumption.

Solution

.

,

,

,

 ,

3. Labor productivity

4. The savings rate corresponding to the maximum level of consumption (the golden rule of capital accumulation)

5. Volume of savings (investments) per capita

6. Consumption per capita

The value of per capita consumption can also be obtained as follows

Example 4.2. Show how to change the values ​​of the calculated values, if the depreciation rate δ and the growth rate of labor resources n take the same - 0.1 each, and change the parameters of the production function

.

Solution

1. Labor productivity (reduced production function) is described by the expression

.

2. Capital-labor ratio is calculated by solving the equation

,

,

,

For the economy of the USSR for 1960 - 1985, according to the results of the analysis of economic indicators, the production function had the form

Y = 1.022 K 0.5382 L 0.4618 ,

while for the US economy

Y = 2.1005 K 0.7986 L 0.2014 .

It follows from a comparison of production functions that the volume of production in the USSR depended to a greater extent on the number of workers (labor costs) than in the United States. This, in turn, indicates a large proportion of unskilled labor in the USSR.

From the analysis of the calculations, we can conclude that in order to increase the volume of production and the standard of living of the population, it is necessary to change the structure of the production function, increasing the dependence of the volume of production on capital investments - i.e., increasing the exponent at the value K .

This can be realized by increasing the automation of production and reducing the share of unskilled manual labor, i.e. improvement of scientific and technological progress.

Accounting for scientific and technological progress in the production function leads to the appearance of a factor of the form e λt in it, where t is time, and λ is a positive coefficient.

"Golden Rule of Savings"

In the simplest model of accumulation, three sectors are distinguished: enterprises, the state and the population. For each sector, money accumulation is expressed as the difference between income and investment spending.

For industrial enterprises, the main sources of capital accumulation are cash in the form of temporary free capital. For the process of production, the accumulation of money is necessary to ensure continuity, expand production, limit it from various fluctuations in supply and demand. As a rule, enterprises account for up to 20% of all monetary accumulation.

State funds are state reserves and act as the difference between tax revenues and expenditures of the central government and local governments. The main prerequisites for such an accumulation are: the state of the state budget, investment costs, which require the preliminary accumulation of funds.

The public sector also includes the accumulation of money capital through state pension insurance funds. Although the source of funds in these funds is mainly the income of the population, the state manages the capital. The share of the state in the total volume of capital accumulation accounts for about 10%.

3. Savings of the population represent that part of wages that is not used for current needs and is set aside for unforeseen cases or provision in old age, for the purchase of durable items, expensive goods. In the economic literature, four motives for such accumulation are distinguished: income-related, commercial motive, precautionary motive, speculative (P. Samuelson and M. Friedman).

The growth of household savings as the main source of accumulation is a characteristic process for all countries. The indicator of this growth is both the absolute value and the savings rate.

An increase in the savings rate can be described by a function called "golden rule of accumulation":

SY=PCR+YR+DU+RR+GPP,

where SY- share of savings in income;

PCR- the rate of change in consumer prices;

YR- the rate of change in real income;

DU- differences in the level of unemployment;

RR- real interest rate;

GPP- the rate of change in government consumption.

The accumulation process is influenced by the following factors:

With income growth the consumption of durable goods is increasing, which requires preliminary cash savings;

changes in the structure of consumption of the population;

3) influence tax system and social insurance.

The higher the taxes on income, the lower the disposable income, and hence the savings. The role of the social insurance system is twofold. On the one hand, it reduces income and savings, and on the other hand, it makes it possible to increase national economic accumulation;

inflation, the meaning of which is also ambiguous. According to one theory, money depreciates, so it moves to other assets (real estate, gold), but in fact, people, having even small amounts, begin to save more for a rainy day. The second point of view relates the change in savings to inflationary expectations, which leads to an increase in savings, since the precautionary motive plays a role in this;

cyclical development of the economy, during which, during the boom, there is a decrease in savings, since the favorable environment weakens the precautionary motive and the speculative motive (interest rates fall). During a crisis, both of these motives appear quite clearly, which leads to an increase in savings.

non-cash payment of wages, which leads to some savings (reducing the cost of going to the bank) and the ability of the bank to use the balance of accounts in the form of loan capital.

In general, there are three main forms of accumulation: deposits in the credit system, purchase of securities, deposits in insurance companies. Nevertheless, different actors prefer certain forms of accumulation.

In economic science, there are two main directions of theories of economic growth: neo-Keynesian and neoclassical, and, accordingly, two types of models that characterize it.

Keynesianism

The central problem of macroeconomics for Keynesian theory - the factors that determine the level and dynamics of national income, as well as its distribution to consumption and savings (it is then transformed into capital accumulation, i.e. investment). It was the shift in consumption and accumulation that Keynes linked the volume and dynamics of national income, the problem of its implementation and the achievement of full employment.

The more investments, the smaller the amount of consumption today and the more significant the conditions and prerequisites for its increase in the future. Looking for a reasonable relationship between saving and consumption- one of the permanent contradictions of economic growth and at the same time a condition for improving production, multiplying the national product.

If savings exceed investment, then the potential economic growth of the country is not fully realized. If investment demand outstrips the size of savings, then this leads to an "overheating" of the economy, spurring inflationary price increases and borrowing abroad.

All models of the Keynesian direction are characterized by a common relationship between saving and investment. Growth rates Neo-Keynesianism

Among the neo-Keynesian models in economics, the most famous are the models of economic growth created by the English economist Roy Harrod (1900-1978) and the American economist of Russian origin Yevsey Domar (1914-1997). The models they proposed are very similar; they analyze a long period of sustainable economic growth, one of the main conditions of which is the equality of savings and investment (). However, in the long run, there is a difference between today's savings and tomorrow's investment. For a number of reasons, not all savings turn into investments. The level and dynamics of savings and investments depend on the action of various factors. If savings are determined mainly by income growth, then investments depend on many variables: the state of the economy, the level of interest rates, the amount of taxation, the expected return on investment.

national income depend on the rate of accumulation and the efficiency of investment.

R. Harrod's complete model of economic growth analyzes the relationship between three quantities: actual (), natural () and guaranteed () growth rates.

The initial equation is the actual growth rate:

A sustainable rate of production growth, which is provided by all population growth (this is one factor of economic growth) and all opportunities for increasing labor productivity (this is the second factor of growth), Harrod calls the natural growth rate, i.e. the kind that would take place if there were no chronic unemployment, underutilization of capacities and economic crises. The third growth factor Harrod considers is the amount of accumulated capital and the capital intensity ratio.

The greater the amount of savings, the greater the size of investment and the higher the rate of economic growth. The relationship between the capital intensity ratio and economic growth rates is inverse. The natural growth rate represents (according to Harrod) the maximum possible growth rate of an economy given population growth and technological capabilities.

Neoclassical direction

At the center of the neoclassical direction is the idea of ​​equilibrium based on an optimal market system, considered as a perfect self-regulating mechanism that allows the best use of all production factors not only for an individual economic entity, but also for the economy as a whole.

In the real economic life of society, this balance is disturbed. However, equilibrium modeling makes it possible to find the deviation of real processes from the ideal.

A significant contribution to the development of the theory of economic growth was made by the American Nobel Prize winner Robert Solow (b. 1924), who modified the Cobb-Douglas production function by introducing one more factor - the level of technology development. At the same time, he proceeded from the fact that a change in technology leads to the same increase in and:

where is the output; - main capital; - invested labor (in the form of wages); - level of technology development; is the Cobb-Douglas production function.

If the share of capital in output is measured by such indicators as capital-labor ratio (or capital investment) per worker, and capital productivity (quantity of output per one monetary unit of production assets); the share of labor - based on labor productivity, then the contribution of technological progress is presented as the remainder after subtracting from the increase in output the share received from the increase in labor and capital. This is the so-called Solow residual, which expresses the proportion of economic growth due to technological progress, or "progress in knowledge."

Technological progress in the Solow model is the only condition for a continuous increase in the standard of living, since only if it is present, there is a steady increase in capital-labor ratio and output per employee, i.e. return on assets. In the Solow model, output is determined by investment and consumption. It is assumed that the economy is closed from the world market in nature and domestic investment is equal to national savings, or the volume of gross savings, i.e. .

THE GOLDEN RULE OF ACCUMULATION

The condition under which the maximum level of consumption is reached, the American economist E. Phelps in his work "Fable for those who are engaged in growth" (1961) called the golden rule of accumulation.

In accordance with this rule, the level of consumption becomes high when the largest difference between the volume of output and the volume of disposal is reached under conditions of a stable level of capital-labor ratio.

The consumption according to the golden rule is called the sustainable level of consumption. The stock of capital that provides a steady state with such consumption is called the golden level of capital accumulation.

Thus, the maximum level of consumption can only be reached at the golden level of capital accumulation. Such a level of capital accumulation is possible only if the marginal productivity of capital is equal to the rate of capital withdrawal. This is the golden rule.

Indeed, if the existing stable stock of capital exceeds the gold level, then with a further increase in capital, its marginal product will be less than the rate of disposal, which will reduce the level of consumption. Otherwise, the growth of capital will cause an increase in consumption, since the marginal productivity of capital will exceed the rate of disposal. Therefore,

the golden rule is a condition for achieving the maximum level of consumption at a given rate of economic growth.

To maintain maximum consumption, it is necessary that the marginal product of capital remaining after depreciation should be equal to the rate of increase in production.

With a stable increase in labor costs, there is a direct relationship between the rate of accumulation and the capital stock, referred to the annual product.

The outflow of capital cannot be greater than the marginal product created by the operation of capital. The golden rule clearly shows the level of capital-labor ratio.

Undoubtedly, population growth affects the capital-labor ratio in the same way as the retirement rate, that is, it reduces the stock of capital.

That is why, in order to achieve the maximum level of consumption, it is necessary that the net marginal product of capital be equal to the population growth rate.

From this we can conclude that according to the R. Solow model, a country with a rapidly growing population will have a lower stable level of capital-labor ratio and a lower per capita income