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

Solow Growth Model
  • What is the Solow growth model?

The solow growth model describes an exogenic model of economic growth that shows a change in economic growth over time which occurs as a consequence of the following:

  1. Changes in the population growth rate, known to be as solow model population growth
  2. The savings rate, and
  3. The rate of technological progress.

The solow growth model was developed by the economist Robert Solow, which was also the first solow neoclassical growth model, built upon the Keynesian Harrod-Domar model. And it is the basis for the modern theory of economic growth. So, the economist Robert Solow got the Nobel Prize for the solow neoclassical growth model.

  • Solow growth model formula:

The formula depicting the solow growth model equation is as:

  • Equation 1: Y = A Kα Lβ

Where in the above equation 1. We see

  1. Y = Aggregate output
  2. L = Number of labor 
  3. K = Amount of capital
  4. A = Multifactor productivity or total factor productivity
  5. α = Output elasticity of capital 
  6. β = Output elasticity of labor
  • Equation 2: Y/L = A Kα L/L = A Kα Lβ L-1 = A Kα Lβ-1 = A Kα/L1-β = A Kα/Lα = A (K/L)α

Where in the above equation 2. We see

  1. L refers to the increase in the number of labor 
  2. K refers to the Increase in capital stock 
  3. A refers to the Increased productivity
  • Assumptions of the Solow growth model:

1. The production in the Solow model of economic growth grows at a constant rate g. Likewise, the current population in the Solow growth model with population growth is represented by N, and also the future population is represented by N’ which gives the equation as follows:

> N’ = N(1+g)

So, suppose the existing population is 100 and the population growth rate is 3 %, then the future population will be calculated by the flowing equation as N’ = N(1+g) and will be 103.

2. A constant proportion, ‘s’ is saved by all the consumers in the economy and the rest is all consumed. So, here we represent the consumption by C and output is represented by Y and link both consumption and output by the equation as follows:

> C= (1-s)Y

So, suppose a consumer gets 100 units of output as his income and the savings rate is 30 %, then the consumer consumes 70 units and saves 30 units in all, which we can calculate using the C= (1-s) Y equation.

3. Output is created in a company or a firm by using the same production technology which grows at an exponential rate, where the labour level is depicted as L and the capital level is represented by K. So, here we represent the labour by L and capital is represented by K and link both labour and capital by the equation as follows:

> Y = aF (K, L).

4. Further, we also show the present capital stock which is represented by K, the future capital stock is represented by K’, and also the rate of capital depreciation is represented by d, and we have the level of capital investment denoted by I. So, here we represent the capital accumulation equation as follows:

K’= K(1-d) + I.

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  • Solow growth model example:

We use the Cobb-Douglas production function as:

# Y = A X K 1/3 X L 2/3

Where we see that,

  1. Y is the total output
  2. A is total factor productivity

Where, this the production function can be written in per-worker terms as:

= Y/ L

= A X K 1/3 X L 2/3  /  L

= A X K 1/3 X L 2/3 -1

= A X K 1/3 X L -1/3 

= A X ( K / L ) 1/3

By, this we know that the output per worker is dependent on the capital per worker. And the 1/3 as exponent power tells us that there is one unit increase in capital.

Now, let us assume that irrigation canals depreciate at a rate of δ each period, which tells us that that the stock of irrigation canals per worker when we decrease by a factor of δ × K/L, will be expressed as:

k = K / L, this k = K / L can also be written as:

And giving the equation as: 

δ k = δ X k 

So, the deterioration of their capital tells us that we should new canals but, it also depends upon investment capability per worker as well as on income per worker Y/L and savings rate s. So, we have the equation as:

i = s X y

And now, the net change in the capital (∆k) can be shown as follows:

∆k = I – δ k = sy – δ k

Steady State

To reach the point when the net change in the capital is zero, both Output per worker y grows less and less when there is an increase in capital per worker k. So, therefore in the Solow growth model, the steady-state occurs when the state of zero net change in capital and zero growth in output per worker occurs.

Let’s take an example as:

  1. Opening stock of canals is taken to be 200 miles 
  2. the number of workers is taken to be 1,000 which remains constant.
  3. The depreciation rate is taken to be 10 % i.e. 10 % of canals must be reconstructed in each period.
  4. The savings rate is taken to be 40 %

Thus, by this information we can create a relationship between capital, and output, investment, and depreciation:

Period k y i = s × y δk
1 0.20 0.58 0.23 0.02
2 0.41 0.75 0.30 0.04
3 0.67 0.88 0.35 0.07
4 0.95 0.98 0.39 0.10
5 1.25 1.08 0.43 0.13
75 7.93 1.99 0.80 0.79
76 7.94 1.99 0.80 0.79
77 7.94 1.99 0.80 0.79
78 7.94 2.00 0.80 0.79
79 7.95 2.00 0.80 0.79
80 7.95 2.00 0.80 0.80

So, this process will keep on continuing up to the point when new investment and depreciation are equal and also where there is no increase in capital seen. Thus, by now we know in the solow growth model, the steady-state occurs when the state of zero net change in capital and zero growth in output per worker occurs. 

  • Solow growth model graph:

solow diagram

Here, the graphical figure of the solow growth model describes, the solow growth model variables where on the x-axis we have capital per worker as well as on the y-axis we have shown output, investment, and depreciation. Wherewith the help of technological progress, sustained economic growth is possible.

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  • What are the factors of production in the Solow model of economic growth?

The factors of production in the Solow model of economic growth are labor, capital, and technology. Although, there exist limited resources in the economy with respect to labor, capital, and technology.

  • Merits of the Model:

Some of the merits of the model areas:

  1. The solow growth model explained in a simple way. 
  2. Solow growth model has contributed to economic growth theory.
  3. This solow growth model is an improvement over the Harrod-Domar model. 
  4. Some of the main features of the Harrod-Domar model are retained in this model. 
  5. According to the Solow growth model, with high population growth rates, we can see that this model offers a more realistic touch.
  6. The steady-state growth paths are also shown by the prof. Solow in this model. 

Conclusion:

The solow growth model summary tells us that the solow growth model is based on the assumption of the neoclassical growth model and describes an exogenic model of economic growth. Further, shows the change in economic growth over time which occurs as a consequence of changes in the population growth rate, known to be as solow model population growth, the savings rate, and the rate of technological progress.

Frequently Asked Questions:

  • What are the key assumptions of the Solow growth model?

  1. The key assumptions of the Solow growth model areas:
  2. The production in the Solow model of economic growth grows at a constant rate g. 
  3. A constant proportion, ‘s’ is saved by all the consumers in the economy and the rest is all consumed. 
  4. Output is created in a company or a firm by using the same production technology which grows at an exponential rate, where the labor level is depicted as L and the capital level is represented by K. 
  5. The present capital stock is represented by K, the future capital stock is represented by K’, and also the rate of capital depreciation is represented by d, and we have the level of capital investment denoted by I.
  • What does the Solow growth model explain about a steady state?

The steady-state growth paths are also shown by Prof. Solow in this model. In the solow growth model, the steady state occurs when a state of zero net change in capital and zero growth in output per worker occurs. 

  • What are the factors of production in the Solow model of economic growth?

The factors of production in the Solow model of economic growth are labor, capital, and technology. Although, there exist limited resources in the economy with respect to labor, capital, and technology.

  • What does the Solow growth model explain about a steady state?

As we study the solow growth model we can see that the equilibrium growth path is a steady-state where the K and Y as level variables have a constant rate of growth. 

 

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