Background
Solow Growth Model is one of the basic Macroeconomic model in the neoclassical era. It was first introduced by Robert Solow in 1956 (Verner, 1995). The model tries to explain the long term economic growth of an economy. The dependent variable of the Solow Model is long term rate of economic growth (output) and independent variables are capital accumulation, labor (also expressed in terms of population growth) and increase in productivity (technological innovation) (Verner, 1995).
Figure: Solow Equation: Y- Output, A- Productivity, And K – Capital Accumulation and L – Labor Growth (Boianovsky and Hoover, 2009)
The main assumption of Solow model is diminishing return of capital accumulation. This means that the output generated from the last accumulated capital will always be lower than the output generated from the accumulated capital before that. With this assumption, without labor or technological growth, at steady state the economy seizes to grow (Boianovsky and Hoover, 2009). For example, when the first road is built in a city, it is of very high value and lot of people uses that. The second road built in a city is also valuable but is not as valuable as the first one. Similarly, as the number of roads in the city goes up the marginal utility of the road goes down. Finally, a day will come when a new road will be built that will not be used by anyone (Okada, 2006). This is an example of diminishing return.
Figure: Capital Accumulation and Depreciation in long run reach a steady state (Boianovsky and Hoover, 2009)
Additionally, because of depreciation, the value of the capital decreases over time which also is another factor for diminishing return. Depreciation helps achieve a steady state point in the Solow Growth equation. For example, a company will continue to buy machines till the time it has enough labor to increase output (equilibrium going upwards). However, when the number of machines will exceed worker capacity then the company will lose money (more depreciation than output increase). In such case, the company will stop investing in machinery (downward movement of the temporary equilibrium point). Eventually a steady state point will be reached (Okada, 2006).
Also, the model assumes that technological improvement is necessary for long term constant growth. Without technological growth in steady state the growth tends to zero. Solow also assumed that the production function does not change as more variables are added in the economy and only labor, technology and capital affects output/growth rate (Boianovsky and Hoover, 2009).
As per the model assumptions, economies which have more saving should grow at a faster rate other factors (labor and productivity). China and India which has more than 35% savings rate are growing at a rate more than 8% year on year (The World Bank, 2016). Whereas countries such as UK and USA with an 18% savings rate is growing only at a rate of 2% Year on year (The World Bank, 2016). This GDP growth rate (Output) follows the model of Solow. However, this is not always the case as Kenya has 50% savings rate but it is growing at a much slower rate than China or India (The World Bank, 2016).
Population Growth and Growth Rate of Capital per Worker
Population growth automatically increases the availability of labor in the economy. All other factors (Capital accumulation and technological progress) remaining constant population growth means that the growth of capital per worker decreases. Population growth will change the capital stock per worker as below
Δk = i – (δ+n)k (Boianovsky and Hoover, 2009)
This shows that the population growth will have a negative impact on capital accumulation. (δ+n)k can be thought of as break-even investment which is required to bring back the capital per worker at the same level. Therefore, at level where capital accumulation and technological growth is constant, long term steady state growth rate due to increased population is zero. For example, if the population of a countries grows, then initially it will help in increasing the output. However, as the population increases further, as per the diminishing return assumption the overall rate of out will come down. At steady state, the output will not grow even if the population grows at the same rate (Boianovsky and Hoover, 2009).
Suppose, population growth changes from n1 to n2. Then the line representing depreciation and growth will shift upward. A new steady state will be reached (as shown in the above figure) at a point where the output per worker is lower (Okada, 2006). Therefore, we can say that higher rates of population growth will have lower levels of capital per worker and lower levels of income. For example, India which has a population of 1 billion (growth rate of 1.2% annually) has a GDP per capita of $5350 whereas United States which has a population of 330 million (growth rate of 0.7%) and a per capita income of $53, 750 (The World Bank, 2016).
Decline in Labor Participation and Growth Rate of Capital per Worker
Solow equation has no factor for labor participation rate. Therefore, as per Solow Model labor participation rate has no impact on the growth rate of labor force. As the model is only dependent on growth rate of labor force and not the labor participation rate, there is no direct impact on the steady state capital (Boianovsky and Hoover, 2009). The economy will take more time to reach the steady state point but will eventually reach the same steady state point.
However, lower labor participation means that a smaller fraction of the population is working. Smaller fraction of the population working leads to less consumption per person (Okada, 2006). This may lead to less savings per worker. Less savings per worker means less capital accumulation rate and less output rate. This will slower the growth rate of the economy but as stated previously, the final steady state point will not change.
Effects of Positive Technology Growth and Growth Rate of Capital per Worker
Positive technological growth means that the labor productivity will go up. If the output equation is expressed as Y= F(K,L*E) where “E” is the labor efficiency. L*E is a measure of number of efficient workers. If we assume the growth rate of technology (productivity) be “g”, then the productivity equation becomes y=Y/(L*E) and k=K/L*E) (Okada, 2006). Now suppose the additional capital required to replace depreciating is δk, nk is the capital required for the new workers and gk is the capital required for effective workers. Then the steady state equation becomes
Δk = s*f(k) – (δ+n+g)k (Okada, 2006)
At steady state Δk=-0. Therefore, s*f(k) = (δ+n+g)k. Therefore, like depreciation and population growth technological progress (productivity) also causes the capital per worker to shrink.
At steady state additional capital required to replace depreciation is zero. Additionally, capital required for new worker is also zero. Therefore, the above equation reduces to
s*f(k) = gk (at steady state). Therefore, we see that at steady state, output per worker growth rate is equivalent to g. However, this implies that economies with higher rates of worker efficiency growth will have lower levels of capital per worker and lower levels of income.
References
The World Bank. (2016). GDP Per Capita (Current $$$). Retrieved on 25 Jan 2016 from <http://data.worldbank.org/indicator/NY.GDP.PCAP.CD>
Verner, D. (1995). Can the variables in an extended Solow Model be treated as exogenous?. Florence: European University Institute, Economics Dept.
Boianovsky, M., & Hoover, K. (2009). Robert Solow and the development of growth economics. Durham: Duke University Press.
Okada, T. (2006). What Does the Solow Model Tell Us about Economic Growth?. Contributions In Macroeconomics, 6(1), 1-30. http://dx.doi.org/10.2202/1534-6005.1228
