Solow Growth Model – Overview, Assumptions, and How to Solve

Solow Growth Model

Economics offers you a variety of economic development model models, analysis of transitions, etc. This blog provides all the information that is important, such as description, conclusions, methods of resolution, etc. This blog is hopeful that students will benefit when they complete their jobs using the Solow growth model graph.

Let us go through the Solow model of economic growth and the Solow growth model example in this article for a better understanding of financial economics. 

What Is The Solow Growth Model?

For the Solow growth model summary, let us start everything from the beginning. Professor Robert M. ensures continuous development without pitfalls over the long term. Prof. Solow believed that the Harrod-Domar model was based on such unreal assumptions, such as constant capital production ratios, fixed factor proportions.

Alongside his model for long-term development, Solow declined these assumptions. Prof. Solow shows that Harrod-Model Domar’s can be rationalized and uncertainty minimized to some degree by adding factors that affect economic development. He has shown the capital-labor ratio will change over time if technological output coefficients are believed to be variable.

The economic system reaches a knife-edge balance between growth balance in the long-term timeframe in Harrod-model Domar’s for steady growth. This balance is determined as a result of natural growth rates (Gn) and guaranteed growth (Gw) pulls and counter pulls depends on the saving and investment habits of households and firms.

But substitutionally between capital and labor is the central parameter of Solow’s model. In his model, Professor Solow shows that “this fundamental opposition to guaranteed and natural prices essentially flows from the crucial presumption that the output is carried out under fixed proportion conditions.” A slight change in the main parameters can destroy the knife-edge balance set under the Harrodian steady growth course.

Prof. Solow says that Gw and Gn’s delicate balance depends on the critical assumption of set output proportions. When this presumption is removed, the knife-edge balance between Gw and Gn will vanish. According to according to the solow growth model, high population growth rates has solved two problems of disparity between Gw and Gn and of capitalist system instability. 

Simply put, Professor Solow has attempted to create an economic growth model by eliminating the basic assumptions of a fixed Harrod-Domar model. The Harrodian road to constant growth can be free from uncertainty if this presumption is eliminated according to Prof. Solow. This model, therefore, recognizes the potential factor substance.

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Streamlining The Solow Growth Model

We have simplified the Solow growth model in the section given below:

1. Assumptions

  • There is a steady population increase g. 1. The current (represented by N) and potential (represented by N’) population are intertwined with N’=N(1+g) equation. The projected population is 102, with the present population at a rate of 100, and its growth rate is 2%.
  • Economically, all customers save their profits and spend the rest in a constant proportion, “s.’ The consumption (represented with C) and output (represented with Y) are associated by the equation of consumption C=(1-s)Y. Solow model population growth is used for streamlining the Solow growth model.
  • The level of output (represented by Y), capital level (represented by K), and labor level (represented by L) are therefore all related by the equation of the production function Y=aF (K, L).

If we double the capital stock level and double the labor force, we exactly double the level of production. under this assumption. The Solow model, therefore, concentrates on production per worker and capital per worker in a large part of the mathematical analysis.

  • The current equity (represented in K), the potential share capital (represented in K’), the depression rate (represented in d), and capital level (represented in I) are related to the equation K’= K(1-d) + I.

How To Solve Solow Growth Model

  • In our analysis, we take the following form for the output function: Y = aKbL1-b < 1 < 1 < 1. The production function is known as the production function Cobb-Douglas, the most common neo-classical function. By the assumption that companies are competitive, i.e. pricing companies, factor b is the capital share (the share of income that capital receives).
  • Therefore, worker output is given as follows: y = akb, where y = Y/L (worker output and k = K/L) (capital stock per worker).
  • We have the following as a result of the assumption of competitive balance: The identity of income and expenditure is a balance: 

Y + I = C

Budget restriction for the consumer: 

Y = C + S

So in balance: I = S = SY.

  • Equation of capital accumulation is: 

K’ = (1–d)K + sY

This equation provides the capital accumulation in per worker’s time:

(1 + g) (1 + g) (1-d) k = (2) (1 –d) k + sy=. * saf(k) =(1-d)k + k.

  • The definition of solution used is a stable state. The steady-state is a state that does not alter the amount of capital per employee.
  • By solving the following equation, the steady state is determined: k’= k=> (1 + g) = (1-d)k + bagpipes
  • The stable state value of the capital per employee and the stable state value of the output per employee is therefore as follows:

K* = (sa/ g+d) ^(1/1-b)

Explaining Solow’s Model Of Long-Run Growth

Solow’s model of long-run growth can be explained in two ways:

1. Non-Mathematical Explanation

To achieve long-term growth, let’s assume, according to Prof. Solow, that capital and labor increase but capital increases at a faster rate than labor, so that the share of capital-labor. 

Community savings are declining and investment and resources are also declining. The decline process continued until capital growth matched the growth rate of the workforce. 

Therefore, the share of capital-labor and production capital remains stable, a ratio generally referred to as “the ratio of equilibrium.” Professor Solow presumed that the technological output coefficients were variable to allow the labor ratio to adapt to the balance. If the labor ratio is higher than the balance of capital, the labor ratio will be less than the capital-and-output capital growth ratio. 

Prof. Solow, like other economies, assumes that an underdeveloped economy has a dual economy as the most important characteristic. The accumulation rate for capital is higher than the absorption rate of jobs in the manufacturing sector. In the solow growth model, the steady-state occurs when output is constant regardless of labors.

Many job opportunities can be generated using variable technological coefficients. Real wages and productivity per worker are poor in the agricultural sector. To achieve sustainable growth, the capital-labor ratio must be high. To achieve continuous growth, underdeveloped economies must obey Prof. Solow. Solow growth model variables changes according to the population.

In this model, several balancing positions can also be found. If the rate of growth is not equal to the share of labor capital, the position of unstable equilibrium will emerge. To conclude the debate, the high ratio of capital work or intensification of capital is very useful for the capitalist sector’s production and growth, and instead, the low ratio of capital-labor or labor-intense technology is beneficial to labor market development.

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2. Mathematical Explanation

This model assumes that the economy produces a single composite product. Its production rate is Y (t), which constitutes the community’s real income. The remainder is saved and spent. Half of the output is used up.

The percentage of the saved output is s. The savings rate will therefore be YS (t). The community’s capital stock is marked K). The capital stock increase rate is calculated by dk/dt and gives net investment. Solow neoclassical growth model is calculated by capital stock.

The respective time path of actual output can be determined from the production function if the time path of the stocks and labor is known. The time course of the actual rate of pay is then determined by a marginal equation of productivity.

Provided that the true return to factors changes to achieve maximum employment of labor and capital, the production function (2) can be used to find the current output rate. Solow growth model equation is given by mathematical explanation.

Then we can save as much as we can save and spend in net output. Therefore, during the current cycle, we know the net capital accumulation. This gives us the resources for the next cycle, adding the already accumulated stock and the whole process can be repeated.

Possible Growth Patterns For Solow Growth Model Formula

We must be mindful, otherwise, of the exact shape of the output function if we want to find out that there is always a way of accumulating capital in keeping with any growth rate of the labor.

The F(r, 1) function gives a worker production or is the total product curve since different quantities of capital are used for one labor unit. Equation (6) notes that, as the difference of 2 terms, “the rate at which the capital-labor ratio changes represents the increase of capital and the rate at which the labor is increased.”

The diagram of the above pattern of growth is as follows:

The line through the origin in diagram 1 is no. SF (r, 1) function has the overall productivity curve and that curve is upwards convex. The assumption is that production must also be positive, meaning a reduction in marginal capital efficiency to make the output positive. The crossing point i.e. nr = of (r, 1) and I’m = or when a = o then the capital-labor ratio is r*.

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Applications Of Solow Growth Model To Underdeveloped Countries

Also, the Solow growth model describes to the underdeveloped countries’ development dilemma, as is the case with the Harrodian model. Either pre-start or pre-start, many of the underdeveloped countries do not analyze a formulation to meet the problems of under-developed countries.

Line No is the balanced line of demand. If the guaranteed growth rate is equal to that of natural growth, steady growth will be achieved. The s1 to 1 (r, 1) curve gives both production and savings efficient systems. On the other hand, s2 of the second half (r, 1) provides an unproductive mechanism and will decrease per capita income and savings. The marginal productivity in both systems is poor.

The first system is the industry sector in underdeveloped countries that continues to expand with an ever-growing labor capital intake. The second scheme is in line with underdeveloped countries’ agriculture sector.

The rapid population growth leads to more labor supplies. Positive investment too. The bottleneck of skilled labor hinders the growth of the underdeveloped countries’ manufacturing sector. Restricted labor productivity is bound to decline and disguised unemployment will fall below real minimum wages.

When the real salary rate is set at a certain amount, jobs are such that the marginal output of labor will remain at this level. Once the population has increased initially and land has dropped sharply, real wages appear to be set at some level while marginal productivity decreases. The outcome is veiled joblessness.

In a nutshell, we can infer that there are some elements to analyze the issue of under-development that can be used gainfully. In Solow’s model, it is possible to better understand that the phenomenon of technological dualism widespread in these economies. Solow growth model shifts changes according to population.

The Solow model, although essentially implemented into a different context, still offers an elegant theoretical apparatus with the principle of technological co-efficient to solve underdevelopment problems. Solow growth model calculator is used for growth model.

Implications Of The Balanced Growth Path Solow Model

In the long term, there is no development in Solow growth model with population growth. If countries are equivalent to (population growth rate), s (savings rate), and d (capital depreciation rate), so they are in the same steady-state, so that they will converge. A poorer country is rising faster along this route of convergence.

Countries with various savings rates have different constant states, and they will not converge, i.e. the Solow Model does not forecast complete convergence. In countries with lower initial capital stock, growth is not necessarily higher if the savings rates are different. This article is all about Solow growth model explained

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