Solow Model of Economic Growth

The Solow Model of economic growth is a model that explains the growth of an economy and suggests that sustained growth in the economy is due to growth in technology and not really due to other factors such as increase in capital and labour. The reason for that is because capital offers diminishing returns in the long run in the economy. Through the model one can understand why certain countries grow faster whereas others seem to stabilize after years of growth.

Key Points in Solow Model

The Output in an economy is dependent on Population Growth Rate, Savings Rate, & Technological Progress.

All individuals save a constant proportion (of GDP).

All firms produce using the same Technology.

The Production Function, Y = a (K raised to b) (L raised to 1-b), has Constant Returns to Scale. b is proportional to the share of income that capital receives, and it has a value between 0 & 1. If Capital is doubled, so is Output. If Labour is doubled, so is Output. Labour + Capital have Constant Returns to Scale together, and Diminishing Returns to Scale individually.

Present Capital Stock, Future Capital Stock, Depreciation of Capital Stock and Investment can be represented by K’ = K(1-d) + I

Sustained increases in Capital Investment increase growth rates only temporarily. This is because the ratio of Capital to Labour goes up. As this happens, the Marginal Product of additional units of Capital decline due to diminishing returns. This, in turn, pushes the economy back to the equilibrium; with real GDP growing at the same rate as the growth of the workforce, plus a factor to reflect improvements in Productivity.

Output per Worker, y = Y/L = a (k raised to b), where k = K/L

Under conditions of equilibrium, Investment (I) = Savings (S)

The steady-state is one where the level of Capital per Worker does not change. In the steady-state, Output, Capital and Labour are all growing at the same rate. At the steady-state, the Savings Rate is just enough to offset the Capital Depreciation.

To increase the growth rate, an increase in Labour Supply + a higher level of Productivity of Labour & Capital are needed.

Output per Person depends on Capital per Person.

The differences in Technological change seems to explain much of the variation in Growth Rates that is observed around the world.

The implications of Solow’s Model are that countries with the same Population Growth Rate (g), Savings Rate (s) & Capital Depreciation Rate (d) will grow at the same rate. Countries with different savings rate will not converge.

Examples : Japan grew rapidly in 1960’s & 1970’s. Increased manufacturing activities, actively aided by Government Policies, helped Japan rapidly industrialize. Japan’s exports were robust during this period. This, in turn, helped Japanese companies earn enormous profits. However, over time, Japanese companies (eg, Automotive, Electronics) began facing increasing competition abroad, and their market shares declined substantially from their peak. Also, competitors began investing heavily in Technology, and the perceived superiority of Japanese companies began eroding (eg, Sony, Panasonic). As a result, Profits of Japanese companies began declining substantially from their peak; and eventually Japan’s growth rate started dropping from its peak.

This implies that Growth Rates decline as economies move towards steady-state.

Other examples include the rise of the Asian Tigers (Singapore, Malaysia, Taiwan and Hong Kong).

Examples that do not support Solow’s theory: the US Savings Rate has historically been lower than other countries. However, its enormous investments in Technology & Education have yielded enormous Productivity increases and provided it with a source of long-lasting competitive advantage, particularly in Hi-Tech industries. These fueled the US economy to unprecedented levels of prosperity.

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