A rivalrous good is a type of good that can be used only by one person or firm. Consumption of a rivalrous good by one person or firm necessarily entails that it cannot be consumed by another person. An example is a can of coke. If one person consumes it, it is no longer able to be consumed by any one else.
A good is excludable when the owner of the good can prevent others from using it. To extend the coke analogy, a can would also be excludable as the owners are able to prevent consumption of the good until a consumer has paid for it.
Romer suggests that technological advances (in the case of his model, this is composed of the production of discrete ‘designs’ for producer durables) are essential. He also flags capital accumulation as a source of growth, and suggests that capital tends to be accumulated as technology increases. Designs are produced by employing human capital, and the rate at which human capital produces these is modified by some proportion of the existing stock of designs. The relevant goods here are the designs (A), human capital (H), and capital (K).
Designs are considered to be nonrival (all can use them for research), but excludable (they can only be directly used by patent holders). Human capital is considered to be rivalrous (as it is possessed by particular individuals), and excludable (as those individuals can choose how it is deployed). Capital is both rivalrous and excludable.
Human capital is rivalrous, as the individual providing it can only provide a fixed quantity, and if it is consumed by a particular firm then no others will be able to access it.
Romer (1990, p. 74-75) uses the example of the “ability to add” as a piece of human capital which is rivalrous, as it is tied to a physical object (a human body) and as such can only be used to solve a single problem at a time.
The replication argument used to justify homogeneity of degree one does not apply because it is not necessary to replicate nonrival inputs. The replication argument implies that, in a production function \(F(A, X)\) where A represents nonrival inputs and X rival inputs, \(F(A, λX) = λF(A, X)\). This argument assumes that X is an exhaustive list of the rival inputs. But it neglects integer problems relevant for small market that can get stuck between \(n\) and \(n+1\) plants.
If a nonrival input has productive value, that means that \(F (λA, λX) > λF (A, X)\). A firm with these kinds of production possibilities cannot survive as a price taker because if goods are sold for their marginal cost, annual revenue for the firm would just equal interest payments on the capital and wage payments to workers, so the firm would suffer losses.
Knowledge in an economy has two functions; it forms the basis for the production of new intermediate outputs; and increases the total stock of knowledge. As designs are non rivalrous, they are able to be used by other economic agents without restricting the ability of the owner to do so. The property of partial excludability is dervied as the owner of the design has property rights over its use in the production of a new producer durable but is unable to prevent other researchers from using it as a source of knowledge. Competitors are free to spend time studying the patent application and as the owner is unable to prevent this the competitors are able to learn and benefit from the design.
No, they do not. The knowledge spillover effects (the non-rivalrous knowledge component arising from a design) cannot be charged to the purchaser of the design, as they will be unwilling to pay for benefits generated by the design that do not accrue to them. The designs would need to be fully rivalrous and fully excludable for the designer to recoup the full marginal value (as then all that value would accrue to their customer, and could be charged for).
The value of patents (ideas) is determined by the present discounted value of the profits recieved by producing the durable goods. Potential investors can put their money in the bank and earn \(r\), or invest in a patent with the intention of earning the stream of profits and the value the patent upon selling in the future.
Given that \(P_A = \frac{\pi}{r-n}\), we can expect a decrease in the interest rates to increase the value of patents. This occurs as profit maximizing agents seek the highest returns possible. If the returns on bank deposits were to decrease the relative value of other investments, including investments in research, would increase. This dynamic would increase the value of patents.
The returns to research will be greater with an increase in population. A larger population will drive up demand for final goods due to the increased size of the consumer market. Production in the final goods sector will increase to meet the demand and an equivalent increase will take place in the intermediate goods sector. The increase in revenues accruing to the firms in the intermediate goods sector will lead them to demand new designs to bring to the larger market. This increased demand for designs will increase the returns to firms in the research sector.
The opportunity cost of human capital is the wage income that can be earned instantaneously in the manufacturing sector. The return to investing human capital in research is a stream of net revenue that a design generates in the future. If the interest rate is larger, the present discounted value of the stream of net revenue will be lower. Less human capital will be allocated to research, and the rate of growth will be lower
Romer (1990, p.98) states that the model “suggests that what is important for growth is integration not into an economy with a large number of people but rather into one with a large amount of human capital”.
If we take national education systems as an indicator of the level of human capital which is available to an economy, it is suggested that Singapore (ranked 3rd globally) would have a higher level of human capital than Malaysia (ranked 52nd) (BBC 2015). In addition, given that their similar GDP is distributed among populations of very different sizes, we observe that Singapore’s GDP per capita is much greater than Malaysia’s.
In light of these observations, Savageland would experience greater returns to reasearch by trading with Singapore. Through a trade relationship with Singapore, Savageland opens its economy to the influx of new ideas likely generated by the human capital rich state.
Too little because research has positive external effects, so an additional design raises the productivity of all future individuals who do research. But because this benefit is nonexcludable, it is not reflected at all in the market price for designs. Another reason is that research produces an input that is purchased by a sector that engages in monopoly pricing. The markup of price over marginal cost forces a wedge between the marginal social product of an input used in this sector and its market compensation.
Romer, P 1990, ‘Endogenous Technological Change’, Journal of Political Economy, vol. 98, no.5, pp. 71-102
BBC 2015, Asia tops biggest global school rankings, BBC, viewed 15eptember 2015, http://www.bbc.co.uk/news/business-32608772