A purely rivalrous good has the property that it’s use by one firm or consumer prevents its use by anyone else. Rivalry is a purely technological attribute. An example of a rival good could be a bike or hammer.
Excludability is a function of both the technology and the legal system. A good is excludable if the owner can prevent others from using it. An example of an excludable good would be the copyright protection schemes utilised in online text books.
Most conventional goods are both rivalrous and excludable. Goods that are both non-rival and non-excludable are called public goods.
Investment in physical capital can only be effective when coupled with investment in research and reduced interest rates lead to endogenous growth.
Human capital is mostly rivalrous as ideas and innovation are considered to only have productive value in how the individual chooses to use them. Romer however discusses that knowledge is shared once produced but the skills to do so are rivalrous and measurable on a per capita basis.
The replication argument says that total output can be calculated as the marginal product of rival inputs (the derivative) times the total amount of rival inputs. But if a non-rival input has productive value then output cannot have constant-returns-to-scale function of all inputs together. The replication argument implies that long-run cost curves are horizontal.
This replication argument assumes that X is an exhaustive list of rival inputs. If A is productive as well, it follows that production cannot be a concave function because F(hA, hX) > hF(A, X), implying increasing returns to scale.
A design is not fully excludable because while designers have the sole right to produce that particular input by means of a patent, there are no laws to prevent researchers from studying the original design and applying that knowledge to develop something similar. If a widget is developed and produced, someone also manufacturing widgets can simply buy one to examine and build upon the design.
If a product sold for marginal cost, annual revenue for the firm would equal interest payments on the capital and wage payments to workers. That is, if all inputs were paid there marginal value, the firm would suffer losses when accounting for sunk costs. The only way designers recoup the losses incurred through R&D is to operate as a price-setter.
The model proposes some relationships should hold:
The opportunity cost of studying is the income that could be earned immediately in the manufacturing sector. Therefore by reducing the interest rate, income forgone today will have appreciate to a lower value in the future. This implies that the lower the interest rate is, the more human capital will be allocated to research. The benefits of research tend to present themselves in the future while the cost, the interest rate, is incurred immediately.
The correct inference from this model is that increasing the size of population leads to a larger labour force, meaning more workers in the R&D sector creating a larger pool of ideas, ultimately leading to an increase in return to research.
By increasing the stock of human capital, the returms to reasearch also increases. This increases the demand for human capital and technology further, implying increasing returns to scale. Figure 2 illustrates the rate of growth and amount of human capital used in research is a function of total human capital.
Singapore would seem to be the obvious choice if the decision is made today, given its highly developed, trade oriented market economy. It has high levels of human capital in place and is at the forefront of technological change, which offers opportunities to learn through replication.
Free international trade can act to speed up growth, therefore with a long term view Malaysia may be a better trade relationship. Once Malaysia’s levels of effective human capital per worker reaches that of Singapore, given its 25m extra population it’s larger total stock of human capital will experience faster growth in the future.
Too little research is getting done in the Romer model. This is clear because research is still presenting positive external effects and because research tends to produce an input that is purchased by a firm that will then use mark-up methods to achieve monopoly profit. This creates a wedge between social marginal product of the input and its market compensation.