1. Question 1
The Swan-Solow Growth Model posits that long term, sustained economic growth is only possible through technological progress and innovation which increases the efficiency of labour. Changes in the saving and/or investment rate only induces short term growth, in which diminishing returns to capital force the economy to return to a steady state level.
However, in endogenous growth theory, there is a vital assumption that human capital plays a vital role in economic growth. One way this is made possible is by defining human capital as being made up of knowledge and skills and then incorporating it into the Solow growth model. It is generally assumed that once accumulated; human capital does not exhibit the properties of diminishing returns since more of it does not “crowd out” other primary factors of capital, relative to other traditional forms of capital.(Roberts and Setterfield, 2005)
In addition, new knowledge begets further knowledge, which can be viewed as a positive externality, which also *might* have a virtuous cycle effect at best, and reduce knowledge depreciation at worst. Knowledge can also be viewed as a public good which benefits society as a whole. This makes it a more plausible description of long term economic growth. The diagram below illustrates this, where ke is “capital” combining physical and human capital (knowledge).
There are many other ways of introducing human capital to growth theories, such as incorporating human capital as a factor input by modifying or augmenting the Solow model,such as the Augmented Solow Model by Mankiw, Romer and Weil (1992), or Endogenous Growth models (Lucas 1988) as discussed previously.
Birdsall summarises the work of T.W Schultz, Hollis Chenery and the World Bank which points towards the contribution of skilled workers with increasing levels of human capital towards increased productivity and growth. The result is that sustaintable growth in these growth models is the result of positive externalities generated by education and training, at least in part. Hence new ideas, new technology and new know-how that a critical to high sustained growth are fundamentally reliant on high levels of human capital.
Neoclassical growth theory, or also known as the Solow growth theory or exogenous growth theory, is designed to show how growth in the capital stock, growth in the labor force, and advances in technology interact in an economy to affect total output of goods and services.
In the Solow Growth Model, it is required (and assumed) that the representative firm, which represents the aggregate behavior of the representative economy, has a production technology that exhibits constant returns to scale. This economy is also assumed to be of perfect competition, in order to allow one firm to be representative of the economy. We know that the representative firm’s technology takes the standard form of:
Y = f (L, K)
with Y being output, L being labour and K being capital. And constant returns to scale implies that a doubling of inputs would result in the doubling of output. Thus for any coefficient ?,
In the Swan-Solow model, we select the coefficient as 1/L to represent output and capital use on a per-worker basis, that is,
y = Y/L, k = K/L
and we have a production function expressed as a per-worker basis:
This production will normally take the Cobb-Douglas form in the Swan-Solow model, structured to ensure that constant returns to scale is retained. This will usually be of the form:
Y = AK?L1??, 0 < ? < 1
Where A is the “total factor productivity” factor (usually determined exogenously), ? is the elasticity of output to capital input (< 1) and 1-? is the elasticity of output to labour input.
So now we have an economy with perfect competition, where all firms share the same production technology which exhibits of scale. This result is critical towards developing the whole Swan-Solow model. However, in endogenous growth theory, it was firstly argued by Arrow (1962) that perfect competition might result in a market failure regarding allocating resources optimally with respect to invention and innovation, which constitutes technological progress. He wrote that “…. We expect a free enterprise economy to under invest in invention and research because it is risky, because the product can be appropriated only to a limited extent, and because of increasing returns in use.”
The basic argument then is that perfect competition does not copes well with the increasing returns to scale that should be present with respect to technological progress that is required for it(technological prices) to exist., since with free markets and no barriers to entry/exit, products prices would be at their marginal cost, and hence there would be no profits in the long run. The result is that innovators or inventors will not be able to recoup their initial investment in innovating or investing, and hence will have no incentive to produce or manufacture their inventions or innovations. Thus there will be no technological progress at all.
Hence an endogenous growth theory in which technological change is endogenous requires that there be an increasing rate of return instead of a constant return to scale, and hence would require a degree of imperfect competition, such as a model of limited monopoly or monopolistic competition that exhibits limited competition with increasing returns to scale. Such a model was first developed by Joseph Stiglitz and Avinash Dixit(Dixit and Stiglitz, 1977) in the 1970s and called the Dixit-Stiglitz order.
One of the key results of the endogenous growth model is that government policy decisions can permanently raise a country’s growth rate if they lead to more technological progress and innovation, hence making growth endogenous, as its name suggests. This also emphasize the role of private investment in research and development as the central source of technical progress and innovation, since most research and development is driven by a profit motive in order to capture a short term monopoly or patent, under which more profits can be made. This is embodied in the monopolistic competition model developed by Stigiliz and Dixit, with a limited number of agents competing in a market, each with a certain degree of market power.
This suggests that the protection of property rights and patents can increase the incentives for private organizations to engage in research and development. Since there are 3 main barriers to innovation and invention, namely:
· Risk – Invention and innovation is risky innately. There is no certainity of a pay-off, or even that the resulting pay-off is worth the risk and investment that is necessary for invention and innovation to begin.
· Inappropriability – Innovation and investment have huge positive externalities. For example, the innovation and investment of electricity generated a large amount of externalities to the whole world, but the inventor of electricity did not receive much of these generated externalities. Hence there is a great difference between the benefit society gains from an invention and the benefit gained by the inventor.
· Indivisibility – Invention and innovation requires a significant expenditure upfront for it to start, even before production of a single unit of this invention can be manufactured. However, after the first unit is produced, it is highly likely that each subsequent unit would cost drastically less to produce, since the initial cost was due to the creation of new technology. With the new technology in place, the marginal cost of production will dramatically fall. This results in a increasing returns to scale effect that is significantly large. However, in a perfectly competitive market, such an effect will not take reality, as other companies will quickly “free ride” on the new technology made available by the inventor to produce new units at low, marginal prices. Hence innovators would not be able to recover their significant upfront expenditure on the development of this new technology, and hence would lack the incentive to innovate.
Hence Governments can craft and implement policies that addresses these obstacles towards innovation, through implementing properties right and patents to address the issues of competiting organizations of “free riding” on the inventions of the innovator. This will introduce a degree of imperfect competition into the market, hence allowing innovators to sell their products above marginal cost, recoup their upfront expenditure and make a profit, hence providing an incentive for innovation and invention to occur. This potential of high profits would also make the risk of innovation and invention more worthwhile to undertake, as well as compensate innovators for the externalities generated by allowing them to keep some of these externalities for themselves for a period of time.
Other policies such as reducing the federal deficit to lower interest rates so that investment in capital and technological research will be simulated, as well as making it easier for people to invest in themselves through more education and training by diminishing the cost of student loans and increasing work pay are also strategies that can boost growth under endogenous growth theory. (DeLong, 1996) The main attraction of endogenous growth theory is that governments could easily find feasible and reasonably traditional policies that could influence the long term growth rate positively, which would be a huge achievement among the various standard goals of economic policy.
Technological progress, in particular that which increases the efficiency of labor, or labor-augmenting technological progress, leads to sustained growth in output per worker and hence sustained economic growth over time. This is achieved by increasing the efficiency of each worker (and their productivity), which also leads to an increase in income levels per worker and hence explains persistently rising living standards.
In the Swan-Solow Model, this technological progress is exogenously determined; that is, determined by factors outside the consideration of the model. The Swan-Solow model takes technological progress as it is, and does not explains how or why this is created. That is, in the Swan-Solow model, technological progress exogenous.
Critics of the Solow growth model say that this is an unrealistic assumption that does not reflect the underlying economic reality. Their answer to the Solow growth model of exogenous technological growth is a model of endogenous growth, in which technological progress is explained and determined by factors within the scope of the model. Proponents of the endogenous growth theory claims that it is a better and more accurate reflection of the real world, as well as being more relevant to the knowledge-driven economy we live in today, as it accounts for the non-diminishing and even cumulative effect of human capital and educational progress.
Attempts to explain the rate of technological progress has created a model of endogenous growth, in which constant returns to capital are the underlying assumption, compared to diminishing returns to capital in the Solow model (Mankiw, 2003). This is made possible by the broad assumption that human knowledge and skills are also a form of capital, and once accumulated; they do not exhibit the properties of diminishing returns since more of it does not “crowd out” other primary factors of capital, relative to other traditional forms of capital. In addition, as discussed in the answer to question 1, new knowledge begets further knowledge, which *might* have a virtuous cycle effect at best, and reduce knowledge depreciation at worst. Knowledge can also be viewed as a public good which benefits society as a whole. This makes it a more plausible description of long term economic growth.
The main implication of endogenous growth theory, as discussed in the answer to Question 3, is that governments could easily find feasible and reasonably traditional policies that could influence the long term growth rate positively, which would be a huge achievement among the various standard goals of economic policy. However, endogenous growth theory is not without its problems. One of the main failing of endogenous growth theory (theories) is their collective failure to explain non-convergence among rich and poor countries over the long term. In other words, it is unable to explain in sufficient detail why some countries are still much richer than others.
Delong, Brad, ‘Economic Theory and Faster Growth’, 1996
Dixit, A.K. and J.E. Stiglitz ‘Monopolistic competition and optimum product
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Lucas, R.E.,“On the mechanics of economic development,” Journal of
Monetary Economics, 1988, 22, 3-42
N. Gregory Mankiw, Macroeconomics, 5th edition, 1992, Worth Publishers, New York, 2003
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