The analysis of why some countries have achieved a high and rising standard of living, while others have been left behind, is one of the major challenges of economics in general, and macroeconomics in particular.

In this chapter we begin to investigate the determinants of long-run economic growth. We focus primarily on the relationship between savings, investment, physical capital accumulation and economic growth.

The starting point for the analysis of this process is the model of Solow (1956). This model is based on a neoclassical production function and the assumption of a constant savings rate. Given that in a closed economy savings are equal to investment, the process of capital accumulation depends on the savings rate which determines the investment rate.

In this model, capital accumulation per worker continues until savings per employee are equated with depreciation and the additional investment required to maintain a constant ratio of capital to labour.

In the case where technological progress raises labour productivity continuously, then capital accumulation per efficiency unit of labour continues until savings per efficiency unit of labour are equated to depreciation plus the additional investment required to provide for population growth and the rate of technological progress.

In the long-run equilibrium of this model, economic growth is exogenous and equal to the rate of population growth plus the rate of technical progress, which raises the efficiency of labour. Essentially, in the long-run equilibrium, commonly referred to as the balanced growth path, per capita output increases at the exogenous rate of technical progress.

An economy that has a low initial capital stock, during the adjustment process to the balanced growth path, has a growth rate which is higher than the long-run growth rate. Capital accumulates at a rate that exceeds the sum of the rate of growth of population and the rate of technical progress. For an economy that has a high initial capital stock, the growth rate is below the long-run growth rate, as capital accumulates at a rate that falls short of the sum of the rate of growth of population and the rate of technical progress. .

This model predicts that economies converge to a balanced growth path. A “poor” economy, it terms of its initial capital stock, and a “rich” economy, again in terms of its initial capital stock, converge to the same balanced growth path, provided that they are characterized by the same savings rate and the same technological and demographic parameters.

However, if two economies have different savings rates, different total factor productivity, different initial work efficiency, different rates of population growth or a different depreciation rate of capital, they will converge to different balanced growth paths. Convergence in this model is conditional, and the conditions are related to the structural characteristics of different economies, such as the rate of savings and investment, total factor productivity, the rate of population growth and technological progress.

This model predicts that the higher the savings (and investment) rate, the higher will capital and output per worker be along the balanced growth path. Furthermore, it predicts a positive impact on capital and output per worker from higher total factor productivity and initial work efficiency, and a negative impact from the rate of population growth, the rate of technological progress and the depreciation rate of capital.

The Solow model is a key model and a reference point in the theory of economic growth. Although its roots lie in older models, and although it has a number of theoretical and empirical weaknesses, this model provides a very useful, simple and flexible framework for the analysis of the growth process.

However, accumulation of physical capital, which is the main engine of economic growth in the Solow model, cannot fully explain either the long-term growth of output per worker and per capita income that has been observed in developed economies, or the large differences in labour productivity and living standards per head between developed and less developed economies.

Only a small part of these differences can be explained by the accumulation of physical capital. Most is accounted for by differences in total factor productivity and technical progress, which in the Solow model are considered exogenous parameters. In this sense, the Solow model, like all the models that rely on similar assumptions about technology and technical progress, shows us how to overcome its weaknesses and to try to explain technical progress endogenously.

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