Solow Growth Model: Concept and Formula

What’s it: Solow growth model is a long-term model of economic growth by looking at three main factors, namely capital accumulation, labor growth, and multifactor productivity. For the latter, economists refer to technological progress, which affects the other two variables, labor, and capital.

The Solow growth model presents a framework for identifying long-term economic growth and its determinants. This model adopts the Cobb-Douglass production function to explain the economy’s potential GDP and uses capital and labor as predictors. It also describes the residual effects that contribute to the productivity of labor and capital.

Solow growth model formula

The Solow economic growth model adopts the Cobb-Douglas production function to explain the economy’s long-run determinants of output (potential GDP). Its functions are as follows:

Y = A K^α L^β … (Equation 1)

Where:

• Y = Aggregate output
• L = Number of labor 
• K = Amount of capital
• A = Multifactor productivity or total factor productivity
• α = Output elasticity of capital 
• β = Output elasticity of labor

As a note to you:

α and β are constant and determined by the available technology. Both are worth less than 1, indicating that both labor and capital face diminishing marginal returns.

α plus β is equal to 1, which indicates a constant scale of return. Thus, if the quantity of labor and capital simultaneously doubles (assuming constant total factor productivity), the output will double.

Total factor productivity is the residual factor. It represents any factor that increases economic output beyond labor and capital. Economists argue it refers to technological advances.

Technological advances allow an economy to produce more output using the same number of inputs. Furthermore, technology also affects the productivity of labor and capital in the economy.

The model shows that the growth of GDP potential comes from three sources:

• Increase in the number of labor (L).
• Increase in capital stock (K)
• Increased productivity (A).

Let’s rewrite Equation 1 as output per worker (labor productivity) =

Y/L = A K^α L/L = A K^α L^β L^-1 = A K^α L^β-1 = A K^α/L^1-β = A K^α/L^α = A (K/L)^α … (Equation 2)

Note that a + β = 1. From Equation 2, output per worker (labor productivity) increases due to advanced technology or increased capital per worker.

Capital per worker faces diminishing returns to scale. Thus, investment to increase capital per worker (K ​​/ L) will slowly result in a smaller contribution to output per worker, depending on the current K / L ratio. For this reason, economists believe that capital investment is not a significant contributor to sustaining economic growth in the long run.

When the capital per worker ratio is high, the investment to increase capital per worker has a relatively small effect. That is the case in developed countries.

On the other side, for developing countries, where capital per worker ratio is low, increased capital investment will contribute more significantly to output than in developed countries.

For this reason, developed countries should not rely on capital investment but encourage technological progress. Advances in technology resulted in an outward shift in the production function. That enables them to produce greater output with the same amount of labor and capital.

Contribution of capital accumulation to economic growth

This model shows you how important physical capital investment and technology is to a country’s long-term economic growth.

Economic growth is high when the country starts to accumulate capital. Growth will slow down as the accumulation process continues (due to diminishing returns). Thus, capital accumulation will have a more significant impact when the ratio of capital per worker is lower, as in developing countries.

Developing countries should enjoy higher economic growth than in developed countries. That leads to economic convergence. When developing countries accumulate capital, their per capita output and living standard will catch up with developed countries. Thus, all countries will finally have the same standard of living and achieve stable conditions.

However, in reality, such predictions do not happen. Developing countries like China, Brazil, and India cannot catch up with developed countries.

Does the Solow model predict incorrectly? From Equation 2, you can see that per capita output increases due to a combination of increased capital per labor and multifactor productivity (technological progress). So, as long as developed countries encourage technological progress, economic convergence will not be achieved.