Economic growth is welcome for everyone. After all, it means that the satisfaction of an increasing number of needs is provided. There are numerous opportunities to predict what will happen and how. An example is the Solow-Swan model. In order to have an idea of what is happening and how, certain mathematical apparatuses are created. An example is the numerous neoclassical models of economic growth.
general information
Directly, Solow’s economic growth models brought her developer the Nobel Prize. And this is not surprising - because now we will talk about the fundamental work that has been developed over two decades (in 1950-1969). Why is it needed? Due to the fact that we have Solow’s economic growth models, we can evaluate different options for the state’s economic policy, as well as how it affects the living standards of the population. This can be used to predict what part of the created product people will use now, which will be saved for the future. This is very important, because savings are investments. The size of capital that the economy will have in the future depends on them. Solow's economic growth models show how output is affected by rising labor, capital stocks, and technology improvements. And the increase in time of national income already depends on this. To better understand the topic and present complex knowledge, several more interesting aspects will be considered in parallel, such as the Harrod-Domar model.
Capital accumulation
The Solow Model of Economic Growth pays considerable attention to this aspect. It is built from the classic premise of creating a market equilibrium, in which there is a demand for created goods from consumers and investors. In other words, the created products are used and invested. Now let's use the formulas and the mathematical apparatus a little. So, the consumption function has such a simple formula: (1-NS) * D. Here, NS is the rate of savings, D is income. The formula itself means how much is consumed and shows the percentage value of stocks. And potentially it is an investment and means of support. Part of the amount received, which is saved, in the future will support the subject in difficult times. Mathematically, this can be explained (and expanded at the same time) through national accounts (US). Then our formula will look like: (1-NS) * D + NaS. If we make a small transformation, then we will have NS * D. It’s not clear how it happened. It doesn’t matter, now we’ll figure it out. The point is this: investments - they, like consumption, are proportional to income. In cases where they are equal to the amount of savings, their rate indicates the amount of production that was directed to capital investments.
Change the view
Now consider the Solow model as a function of production and consumption. From this position, one can analytically understand how capital accumulation contributes to the country's economic growth. Its total value in the economic sector of countries varies for two reasons:
- Investing is carried out and its volume is growing.
- Partially, capital fails or is depreciated, which negatively affects its size.
When dealing with how the volume of capital is changing, care should be taken to identify the factors on which the size of investments and depreciation depend. To find the size of the indicator per employee, we slightly modify our formula by introducing a production function that shows the size of investments per employee based on the size of capital-labor ratio: NS * PF. What does this formula tell us? The higher the capital-labor ratio, the greater the volume of production and investment. Other Keynesian models of economic growth also speak of this. Moreover, in this case, the capital productivity ratio is of great importance. After all, one could use industrial equipment of the middle of the last century, but ... It is not effective enough for successful activities.
Depreciation
We bring the available data closer to reality. And for this we need to consider depreciation. Assume that the average life of capital is 25 years and the rate of disposal (IO) is five percent per year. Since the size of the losses is known, care must be taken that they are compensated on time as they are disposed of. As a result, the formula is as follows: IZK = I - HB. What is the last meaning, we already know. IZK - a change in capital stocks, and I - investment. Easy, right? If you focus on what we have already done, then this formula can be modified as follows: IZK = NS * D - HB.
The consequences
The greater the capital-labor ratio, the higher and more significant is the volume of investments and production per employee. At the same time, the size of the retirement is also growing. Optimal for a stable situation is a precisely balanced point of contact. If the subject of the economy develops, then there is more investment, with stagnation, retirement is observed. Over time, any economy occupies a stable position, regardless of the size of the initial capital. For the Solow economic growth model, the ability to evaluate the chosen development path is characteristic.
Application example
Let's pay attention to the past of the global economy. The objects for us are Germany and Japan. In 1945, they were in ruins, approximately 60% of their fixed assets were destroyed. Now they are considered one of the most highly developed countries. At some points , their economic growth rates exceeded several times the global average. Neoclassical models of economic growth, including Solow, considered their position as a disturbed stable state. The level of production fell significantly, but due to the high rate of savings in the share of GNP (which has been preserved from previous years), these economies were able to demonstrate amazing growth rates. And since with a low capital-to-labor ratio, investments significantly exceed the existing disposal rate, there was a high growth. After all, at first the output volume decreased, and after that the investment boom began. This is the effect 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 the Solow model, then this was quite expected. Something similar happened on the territory of the countries of the former USSR after its collapse. True, it cannot be said that our savings and investments had exactly the same effect.
And what in modern developed countries?
Suppose we have a national economy that is in a steady state. It begins to develop at the rate of savings HC1 and capital reserves K1. Then HC1 grows to HC2. Because of this, there is a general shift in the economy. And he will compensate for the ever-increasing retirement. Capital will gradually increase until the K2 state, balancing the economy, is reached. And it will work in a stable mode until HC2 grows to HC3. The Solow model indicates that the savings rate is a key determinant of a steady increase in capital-labor ratio. All other things being equal, it provides a significant advantage when operating in global markets. Indeed, thanks to the savings rate, the volume of investments is growing, followed by the level of production - and profit (read - satisfaction of needs). Because of this, countries that have significant per capita income and a high NA indicator have high economic growth rates. And this continues until a steady state is reached.
Population growth
Agree - Keynesian models of economic growth are enough interests, and Robert Solow was able to create a very high-quality business card. But that's not all. After all, there is constant economic growth, which we can observe in all countries of the world. To do this, we should include another indicator - population growth. How does it affect him? Let's remember: investment increases capital, retirement decreases. Population growth leads to a reduction in the capital-labor ratio of each employee. After all, it is one thing - when a person has a car, and quite another - when it is one in ten employees. Thanks to this, one can give an indirect explanation of why poor countries are at the same time such that they are developing fastest (in this case, the states of Africa, Asia and South America are meant). And while the population is growing, new scientific discoveries are being made, continuous economic growth is fate.
Other models
Remember, earlier there was a promise to consider other mathematical apparatuses? And now we will consider the Harrod-Domar model. Its feature is that for the first time animation and acceleration were 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 for the growth of the economy, only work with the standard of maintenance is enough. Within the framework of the Harrod-Domar model, formulas were derived that made it possible to calculate the so-called guaranteed rates of economic growth. In the event of any deviations, it was believed that the cumulative reasons were to blame for them. Subsequently, under the pressure of criticism and due to the emergence of a more perfect model of Solow, she was discarded due to her imperfection.
Conclusion
So we examined what this model is. Thanks to the theoretical basis, one can understand where one should move in order for the economy to benefit - it is necessary to stimulate the growth of savings.