The simple model just described does not explain how improvements in technology come about. They are just assumed to happen exogenously, so that this model is said to have exogenous technological change. More recent models attempt to endogenize technological change, explaining technological progress within the growth model as the outcome of decisions taken by firms and individuals. In endogenous growth models, the relationship between capital and output can be written in the form Y=AK. Capital, K, is defined more broadly than in the neoclassical model. It is a composite of manufactured and knowledge-based capital. Endogenous growth theorists have been able to show that, under reasonable assumptions, the A term in the preceding expression is a constant, and so growth can continue indefinitely as capital is accumulated.
The key point is that technological knowledge can be thought of as a form of capital. It is accumulated through research and development (R&D) and other knowledge-creating processes. Technological knowledge has two special properties. First, it is a public good: the stock of this form of capital is not depleted with use. This is important because it implies that the knowledge stock can be stored over time, even when it is being used. Second, it generates positive externalities in production: although the firm doing R&D obtains benefits from the knowledge acquired, others benefit too—the benefits that the firm accrues when it learns and innovates are only partly appropriated by itself. There are beneficial spillovers to the economy from the R&D process so that the social benefits of innovation exceed the private benefits to the original innovator. These externalities create momentum in the growth process. As firms install new capital, this tends to be associated with process and product innovations. The incentive to devote resources to innovation comes from the prospect of temporary monopoly profits for successful innovations. The growth of K thus means the growth of a composite stock of capital and disembodied technological knowledge. Therefore, output is able to rise as a constant proportion (A) of the composite capital stock, and is not subject to the diminishing returns shown in Fig. 1.
So, in an endogenous growth model, the economy can sustain a constant growth rate in which the diminishing returns to manufactured capital are exactly offset by the technological growth external effect just described. The growth rate is permanently influenced by the savings rate; a higher savings rate increases the economy’s growth rate, not merely its equilibrium level of income.