Solow Growth Model

Solow Growth Model refers to an exogenous neoclassical model of economic growth representing enhanced capital accumulation, technological progress, and increased labor used to achieve short-term equilibrium. It shows that the economies of every nation will reach a steady state or converge at the same level of savings, labor, depreciation, and production growth.

The Solow model is the foundation of the latest theories on economic growth. This model has made it possible to explain the faster economic growth of developing nations. It had also successfully predicted the fast economic growth of China as compared to western nations and the speedier economic recovery of war-hit Japan and Germany.

• Solow Growth Model is an exogenous neoclassical model of economic growth representing the changes in output level due to changes in labor, capital accumulation change, and technological progress. 
• The most commonly used Solow growth model equation is Y = Af (K, L) 
• A few Solow growth model assumptions are- the manufacture of a single blended product, deduction of depreciation, variable costs, sufficient & endless labor employment, sufficiently employed capital, homogenous technical progress, and unchanged saving ratio.
• Economist Robert M. Solow won the Nobel Prize for economics in 1987 for this model.

Robert Solow's Growth Model represents the economic model that economists use to explain the direct relationship between economic growth that capital accumulation leads. Professor of economics, Robert. M Solow forwarded the Solow neoclassical growth model or Solow swan economic growth model. In 1956, he did it to produce an alternative to the Keynesian Harro-Domar model in the absence of the assumed fixed ratio in productions. Robert M. Solow received the Economic Nobel Prize in 1987 for this pathbreaking growth model in macroeconomics.

This neoclassical growth model assumes that the output of goods producers produce utilizes the labor and capital at a scale of constant returns. It means that the output produced is either stored or completely used up. Moreover, the capital stock accumulated during the production is determined by subtracting the depreciation from the total accumulated savings related to the past periods. Here, the producers assume a fixed labor supply and deem the saving to be a fixed output ratio. 

The model assumes that initially, the economy is in a position of minimal capital stock. Hence, in every specified period, the capital stock will increase with the help of saving until it reaches a steady state where the depreciation equals the savings. During the path to a steady state of capital stock, there will also be an increase in consumption per capita, leading to the economy's growth.

Furthermore, as soon as it achieves the steady-state, the consumption per capita also becomes saturated. As a result, economic growth stops. Therefore, if the economy has to witness any more growth, then the exogenous factors have to change, like the improvement in the technology for enhancing the quantity of output vis-a-vis the inputs for production.

Here is a Solow growth model graph to understand the concept better.

The graph represents the output-per-effective-worker, on the Y-axis, for an economy over a specific period. For simplicity, it assumes the absence of the government sector, zero population growth, and constant labor productivity.

The graph represents a steady-state at the point where the line (n+d)k intersects with the sY curve. The economy will always end up in a steady state. Steady-state is the key to understanding the Solow model.

The depreciation curve, i.e., the straight line, is proportional to the amount of capital. With the capital increase, depreciation also increases. Capital and labor also observe proportional growth. Prof. Solow assumes constant returns to scale, so real output grows at the same rate (n), and output per head of worker remains constant.

Extra investment increases the output. So, the output per worker increases with an increase in capital per worker. However, the production function line, i.e., Y = f(K), shows that output per worker increases at a diminishing rate as K (capital) increases due to the law of diminishing returns.

The saving rates (assumed fixed) are equal to actual investment, i.e., sY. So firms multiply their investments by savings.

So one can observe that initially, Investment > Depreciation, i.e., capital grows.

In the next phase, Investment < Depreciation. It means the capital shrinks.

At the steady-state, Investment = Depreciation. At this point, all the investment is used to maintain the depreciation.

Here is the Solow growth model equation-

For the sake of simplicity, analysts and economic researchers assume that the economy is a closed economy without any external trade influence or government role. The most common equation used in this growth model is-

Y = Af (K, L) 

where Y= real GDP

• A = Measure of productivity
• K= Capita Share (measured in physical units or in $ value)
• L= Labor 

For other equations of the Solow neoclassical growth model formula, one will be using the following terminologies:

• G_w = Per worker GDP (Gross Domestic Product) and is also the capital’s square root
• K_w = Per worker capital
• R_d = Depreciation rate
• R_s = Rate of saving

For isolated economy, per worker GDP, G = C_w + I_w where C_w = per worker consumption & I_w = investment per worker

Applying the above terminologies, the major equations of the Solow growth model steady state are:

1. Production function, G_w = function (per worker capital, K) = f(kW)
2. Investment, I= saving rate (per worker capital, Y) = R_s (G_w)
3. Consumption, C= (1-R_s) G_w
4. Variation in capita concerning labor ratio, V_cl = I_w-d K_w
5. If the V_cl becomes zero for an economy, it has achieved the steady-state. As a result, the per worker investment gets equal to that of the product of the depreciation rate and per worker capital. So, I_w = R_d* K_w

Solow hypothesized that the constant production function could link the outputs to labor and interchangeable capital inputs. To prove his theory, he assumed the following for his model:

1. Manufacturing single blended product.
2. One can consider output only after capital deducting depreciation from the net output.
3. The function of production is congruent to the first degree.
4. Production grows at a constant rate.
5. One compensates labor and capital as per the insignificant tangible efficiency.
6. Costs and compensation are variable.
7. Labor employment is always sufficient and endless.
8. The stock of capital is also fully sufficiently employed.
9. Capital is interchangeable with labor, and vice versa is also true.
10. The technical progress is homogenous across the production of the goods.
11. The ratio of savings is always unchanged. Savings = Investment.

Moreover, the Solow model assumptions also give rise to some prime equations to determine the growth of the economy, as shown below: 

1. At constant population growth (g), P’= future population, P= current population (1+rate of growth of population). So the population growth equation is P’= P(1+g).
2. Consumption, C= output (1-saving). So the consumption equation is C= (1-s)Y, at a constant rate of saving (s).
3. Output, Y= function (labor, capital). One can write the production function symbolically as Y = aF(K, L) with the same production techniques.
4. Production function gives CRS, i.e., constant-returns-to-scale.
5. One can write the capital accumulation equation as K’= K (1-d) + I.

Here K’= Future capital stock

          K= Present capital stock

          d= Rate of capital depreciation

           I= Capital investment

This has been a guide to what is Solow Growth Model. We discuss assumptions, graph, equation of solow growth model along with detail explanation. You can learn more about it from the following articles – 

• Centrally Planned Economy
• Traditional Economy
• Market Economy