Because technological change is assumed to be outside the economy, the Solow growth model exhibits constant returns to scale and diminishing marginal returns to capital. An increase in the savings rate in the Solow model results in a short term increase in growth during the transitional period, however, because of the diminishing returns to capital, the per capita growth in the economy occurs only until the capital stock reaches a steady state. Once that state is achieved, there is equilibrium and intensive growth becomes zero.
To experience per capita growth again, either an exogenous technological change needs to occur or savings rate needs to increase or population growth rate should fall. But the effect of all these factors on growth is only transitory.
Endogenous Growth Model However, some later growth economists - Frankel, Romer [] and Lucas []- found it difficult to accept that the rapid improvements in technology that were witnessed in the twentieth century, as emanating solely from outside economic activity. This was because any activity, including innovation and technical improvement, is pursued continuously only if people are rewarded for it. It was unlikely that a production process would be continuously bettered by people who will not reap the benefits for their efforts — which would be the case if the innovators were outside the economy.
So the producers of goods were more motivated to introduce new products or find ways to improve their productivity to increase profitability.
Therefore the new growth economists were of the view that technological change was generated by the day to day economic activity and so endogenous, to the model of growth. According to the endogenous growth theory, a firm that accumulates physical capital to produce goods will also gather knowledge specific to that production process.
Thus technological knowledge was itself a kind of capital as it was changing the productivity of capital. Knowledge once created can be reused with zero cost and almost no depreciation as old knowledge builds new knowledge. So the new growth economists introduced technology to impact capital instead of labour as Solow had presented in his model.
By assuming that technology augmented capital, the new growth economists changed the productivity of capital from one of diminishing marginal returns in the Solow model to one of either constant or even increasing marginal returns on capital. There is no steady state in an endogenous growth model, which means an increase in savings rate will result in a permanent long run increase in output per capita unlike in the Solow growth model where an increase in savings rate has only a short term impact on increasing the growth rate.
The endogenous growth economists therefore see a role for governments in propelling growth in their countries by encouraging innovation and research, raising the savings rate, investing in infrastructure, building institutions, improving the quality of human capital through education and training and facilitating international trade among other things.
Since the exogenous growth economists treat technology as a factor outside economic activity, government policies help in driving transitional growth towards the new steady state but have little impact on the long run growth. References: 1. Principles of Macroeconomics Authors: Mankiw, N. Durlauf and Lawrence E. Blume 6. The Growth of Nations Author s : N. Gregory Mankiw, Edmund S. Phelps, Paul M. The earlier growth models of Harrod and Domar were interpreted by Solow , p.
However, Swan , p. Although the models of Solow and Swan are fundamentally the same, there are some significant differences, including differences in the diagrams that illustrate the model.
The Solow diagram highlights the substitutability of labour for capital by measuring the 1 Harrod's "warranted" rate of growth arising from savings and investment behaviour is represented by the rate of growth of capital in the Solow and Swan models. In the absence of technical progress, Harrod's "natural" rate of growth is the rate of growth of the labour supply. The levels of output and investment per head are shown on the vertical axis. This focus on rates of growth is particularly useful for illustrating the effects of changes in the rate of technical progress see Dixon, Swan also considers effects on growth arising from a fixed supply of a third factor, land, which creates diminishing returns.
We present the Swan diagram in Section 1 because we believe it provides an easier introduction to the model. Section 3 contains a brief history of the development of the Solow-Swan model. Output, denoted Y, is produced under constant returns to scale by labour, L, and capital, K. All labour is fully employed. The model suggests the surprising result that an increase in capital formation through a rise in the willingness to save, s, is not a route to increased long-run growth.
An increase in s would increase the slope of the capital growth line causing both it and the growth line for output to swing upwards. Initially capital grows faster and there is a rise in the rate of growth of output per head since y is above n , but in equilibrium, the growth rates for capital and output must return to their original level equal to the growth rate of labour which is unchanged at n.
However, equilibrium involves a higher output per head since the increase in investment raises the marginal productivity of labour. By contrast, an increase in the rate of technical progress raises long-run growth. As shown by the dotted line, 0A, in Figure 2, an increase in k increases output per head at a decreasing rate.
As shown by Swan , Harrod neutral labour saving technical change is required for the existence of steady state growth, but Hicks neutral and Harrod neutral coincide for a Cobb-Douglas production function. The vertical distance between lines 0A and 0B represents consumption per head.
As illustrated in figure 2, nk is straight line from the origin with slope n. If k is initially to the left of kE, then capital is growing faster than labour, which leads k to rise. Similarly, if k is to the right of kE, then k falls. Output per head increases from the movement to the right along 0A , but consumption per head, represented by the vertical distance between lines 0A and 0B, falls. Technical progress causes both an upward shift in 0A and a movement along OA due to the rise in the capital to labour ratio.
A constant rate of technical progress would cause 0A to continuously swing upwards. The seminal contribution of Solow was to address how technical progress represented by upwards shifts in OA could be estimated separately from movements along OA.
Solow points out the possibility of multiple equilibria. For example, if there is a region in which investment per head increases at an increasing rate with k, it is possible that the line OB representing investment per head cuts the line nr in three places.
There are then two stable equilibria, one at a low value of k and one at a high value of k, with an unstable equilibrium between the two stable equilibria. Solow and Samuelson
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