Economic growth is welcome for all.After all, it means that more and more needs are met. There are numerous opportunities to predict what will happen and how. An example is the Solow-Swann model. To have an idea of what happens and how it happens, certain mathematical devices are created. As an example, there are numerous neoclassical models of economic growth.

## general information

Directly models of Solow's economic growthbrought her developer a Nobel Prize. And this is not surprising - because now we will talk about the fundamental work, which was developed over two decades (in 1950-1969). Why is it needed? Due to the fact that we have models of Solow's economic growth, we can evaluate different options for the state's economic policy, as well as how it affects the standard of living of the population. This can be used to predict what part of the created product people are using now, which will be saved for the future. This is very important, because savings are investments. The size of the capital, which the economy will have in the future, depends on them. Solow's economic growth models show how the volume of production is affected by the growth in the number of labor, capital stocks and technology improvements. And from this already depends the increase in time of the national income. To better understand the topic and present complex knowledge, several interesting aspects will be considered in parallel, such as the Harrod-Domar model.

## Accumulation of capital

In the Solow economic growth model, this aspectpaid considerable attention. It is built from the classical premise of creating a market equilibrium, in which the demand for created goods is available from consumers and investors. In other words, the products created are used for consumption and investment. And now let's use formulas and mathematical apparatus a little. So, the consumption function has such a simple formula: (1-HC) * D. Here NS is the norm of savings, D - income. The formula itself means how much is consumed, and shows the percentage value of the stock. And potentially - this is investment and support. Part of the amount received, which is preserved, in the future will support the subject in difficult times. Mathematically this can be explained (and at the same time expanded) through national accounts (NA). Then our formula will have the form: (1-HC) * A + Ha. If we make a small transformation, then we will have NS * D. It's unclear how it happened? No problem, now we'll figure it out. The point here is this: investments - they are like consumption, proportional to income. In cases where they are equal to the amount of savings, their rate indicates the amount of output produced, which was directed to capital investments.

## We change the representation

And now consider the Solow model asfunction of production and consumption. From this position, one can analyze analytically how the accumulation of capital contributes to the economic growth of the country. Its total size in the economic sector of countries varies for two reasons:

- Investments are carried out and its volume is growing.
- In part, capital is out of order or is being depreciated, which negatively affects its value.

Understanding how the volume of capital varies,care must be taken to identify the factors on which the amount of investment and depreciation depends. In order to find the size of the indicator per employee, we slightly modify our formula by introducing a production function that shows the size of the investment per worker of the capital-labor ratio: NA * PF. What does this formula tell us? The higher the capital ratio, the greater the volume of production and investment. Other keynesian models of economic growth speak about this. And in this case, the capital-return ratio is also of great importance. After all, it would be possible to use industrial equipment of the middle of the last century, but ... It is not effective enough for successful activity.

## Depreciation

Approaching the available data to reality.And for this we need to consider depreciation. Suppose that the average life of capital is 25 years, and the retirement rate (HB) is five percent per year. Since the size of the losses is known, care must be taken that they are compensated in time as they are disposed of. As a result, the formula looks like this: ISK = I - NV. What is the last meaning, we already know. IZK is a change in the capital stock, and I is investment. It's easy, right? If we are guided by what we have already done, then this formula can be modified as follows: ISK = HC * D - NV.

## Consequences

The greater the capital-labor ratio, the higherthe volume of investments and production is more significant when calculating for one employee. At the same time, the amount of retirement grows at the same time. Optimum for a stable situation is precisely balanced point of their contact. If the subject of the economy develops, then the investment is greater, with stagnation there is a retirement. Over time, any economy has a stable position, regardless of the size of the initial capital. For Solow's economic growth model, it is characteristic to assess the chosen path of development.

## Application example

Let's pay attention to the past of the worldeconomy. The objects for us are Germany and Japan. In 1945, they were in ruins, about 60% of their fixed assets were destroyed. Now they are considered one of the most highly developed countries. At some points, the growth rates of their economies exceeded several times the average world. Neoclassical models of economic growth, including Solow, considered their position as a disturbed stable state. The level of production has fallen significantly, but because of the high saving rate in the share of GNP (which has been preserved since previous years), these economies were able to demonstrate surprising rates of increase. And since with a low capital investment, investments far exceed the existing size of retirement, then there was a high growth. After all, the output volume first decreased, and after that the investment boom began. This is the impact of savings and investment. Many people call what happened in Germany and Japan, an economic miracle. But if you look from the point of view of Solow's model, it was quite expected. Something similar was in the territory of the former Soviet Union after its collapse. True, we can not say that savings and investments have had exactly the same impact.

## And what about modern developed countries?

Suppose that we have a nationalan economy that is in a stable state. It begins to develop at the rate of savings НС1 and the stock of capital К1. Then HC1 grows to HC2. Because of this, there is a general shift in the economy. And he will compensate for the increasing dropout. Capital will gradually increase until the state of K2 balancing the economy is reached. And it will work in a stable mode, until there is an increase in HC2 to HC3. The Solow model indicates that the saving rate is the key determinant of the steady increase in the capital-labor ratio. Other things being equal, it provides a significant advantage when operating in world markets. After all, thanks to the rate of savings, the volume of investments is growing, behind them is the level of production - and profit (read - satisfaction of needs). Because of this, countries that have a significant per capita income and a high NA rate are experiencing high growth rates in the economy. And this continues until a steady state is achieved.

## Population growth

Agree - Keynesian models of economicgrowth is enough interests, and Robert Solow was able to create a very high-quality business card. But that is not all. After all, there is a constant economic growth, which we can observe in all countries of the world. To do this, we need to include another indicator - population growth. How does it affect him? Let's remember: the investment increases capital, retirement - reduces. The growth of the population leads to a reduction in the capital-labor ratio of each employee. After all, it's one thing - when a person has a car, and quite another - when she is alone for a dozen employees. This can provide an indirect explanation and why the poor countries are at the same time that they are developing the fastest (in this case, the states of Africa, Asia and South America are meant). And while the population is increasing, new scientific discoveries are made, continuous economic growth is destiny.

## Other Models

Remember, earlier there was a promise to consider and othersmathematical apparatus? And we now consider the Harrod-Domar model. Its feature is that for the first time animation and acceleration was introduced. It served as a platform on the basis of which the Solow model was subsequently developed. Its feature is that it is one-factor. So, it was believed that only the work with the standard of content is sufficient for the growth of the economy. Within the framework of the Harrod-Domar model formulas were derived that allowed to calculate the so-called guaranteed growth rates of the economy. In the event of any deviation, it was believed that they were to blame for the cumulative causes. Subsequently, under the pressure of criticism and because of the appearance of a more perfect model of Solow, it was discarded because of its imperfection.

## Conclusion

So we looked at what thismodel. Thanks to the theoretical basis, one can understand where to move, so that the economy will benefit - it is necessary to stimulate the growth of savings.