Week Seven

Questions on the Romer Model

What is a rivalrous good; what is an excludable good?

A rival good is one where the use of the good by one party prevents the use of it by any other party. An excludable good is one where the owners of the good can prevent others from using it, such as a house.

What sort of goods does Romer suggest contribute to endogenous economic growth?

Romer suggests that the following goods contribute to endogenous economic growth. Capital (measured in units of consumption goods), Labor (Skills such as eye-hand coordination available from a healthy physical body, measured by counts of people), Human Capital (a measure of the cumulative effect of activities such as formal education and on-the-job training). and Technology (a count of number of designs).

Is human capital rivalrous?

Based on the text, human capital is referring to researcherd and the stock of knowledge. Generally these human capitals are not rivalrous as one use does not simply reduce the availability of the capital. In other word, anyone can access freely to the stock of knowledge. There is another case where we can consider human capital as rivalrous. Example if a person only can be in one place or do one job at same time.

What is the replication argument for constant returns to scale?

Constant returns to scale is an outcome where a percentage change in all inputs results in an equal percentage change in the output. The replication argument is that constant returns to scale can be achieved if both the rivalrous and non-rivalrous factors of production can be doubled. This would mean that if a firm doubles both its research (Non-rivalrous) and its other rivalrous costs (factories, workers etc.) then it should expect a doubling in output. This can be algebraically represented by \(F(A, \lambda X) = \lambda F(A, X)\). Romer’s paper disagrees with this assertion.

“If a nonrival input has productive value, then output cannot be a constant-returns-to-scale function of all its inputs taken together.” - What does Romer mean by this?

The point Romer is making here is that if a non-rival input with productive value is used, such as a design for a newer model of car engine, then output will have increasing returns to scale of all its inputs taken together. The reason being that the non-rival good with productive value provides the capacity to produce more of a good with any given level of capital - that is, the non-rival input has increasing returns to scale which causes the overall output to be an increasing returns to scale function of all its inputs taken together.

A design is partly excludable. Why is it not fully excludable in Romer’s model?

A design is not fully excludable in Romer’s model because even though a design can be patented or copyrighted, the technological understanding, structure and machinations of the design can still be eithe examined via patent documents or reverse engineered.

A good is excludable if the owner can prevent others from using it, a design can be made excludable by means of a legal system that prevents others from copying it. The owner of a design has property rights over its use in the production of a new producer durable but not over its use in research. If an inventor has a patented design for certain good, no one can make or sell that good without the agreement of the inventor. On the other hand, other inventors are free to spend time studying the patent application for that good and learn knowledge that helps in the design of a similar good. The inventor has no ability to stop other inventors from learning from their design . This means that the benefits from the first productive role for a design are completely excludable, whereas the benefits from the second are completely non- excludable. In an overall sense, this means that the non-rival design inputs are partially excludable because in theory there is always some ambiguity about what constitutes a design for a new and different good and what constitutes a copy of an existing design.

Do designers recoup the full marginal value of their designs?

Usually they do. They try to get an extra advantage by pattern their design. By that, they can differentiate themselves from other competitor. Whether they manufacture the good themselves or licences others to do so, it can extract some monopoly profit.

The model proposes some relationships should hold:

• What is the impact of a reduction in the interest rate on the value of ideas, and on research? Do you see this in the data?

If there is a reduction in interest rates, the Romer model predicts that the present discounted value of the stream of net revenue to be higher. This would mean that firms will see higher future values on capital investments they conduct in the present and would therefore be more inclined to research ideas as research would mature at a future date and require discounting. This would cause an increase in the demand of partially rivalrous. This would lead to more human capital being allocated to research, and therefore the rate of growth should be higher.

If looking at the data for total patents vs. interest rates, a relationship is difficult to see. However, when the percentage change in patents filed vs. interest rates is examined, the graphs show there may be a possible relationship, however econometric testing is required.

Sources:

‘U.S. Design Patents Granted As Distributed By Year Of Patent Grant’ (Quandl)

‘Effective Federal Funds Rate’ (Quandl)

• What is the impact on the returns to research of an increase in the population? Why?

In most cases an increase in the population would lead to a decrease in the returns to research. The reason for this is that the proportion of human capital to labour would decrease, supposing human capital stocks remained constant. If the population increase led to an increase in the human capital stocks, such as a band of researchers migrating to a country, it is possible that an increase in returns to research could occur as the proportion of human capital stocks will have increased.

• What is the impact of an increase in the stock of human capital on the returns to research? Why?

An increase in the stock of human capital increases returns to research. An increase in scale as measured by total human capital H has the effect of speeding up the rate of growth. This effect is illustrated in figure 2, which plots the rate of growth and the amount of human capital used in research as a function of total human capital. As a result, an increase in a scale variable induces an increase in the rate of growth. Human capital is the relevant scale variable in this model because it is the input that is used most intensively in research. A permanent increase in the total stock of human capital in the population leads to an increase in the ratio of A to K and a more than proportional increase in the amount of human capital that is devoted to the research sector.

• Savageland, a new country founded by Jim, is negotiating trade relationships with Malaysia (population 30.5m) and Singapore (population 5.5m). Both countries have about the same GDP. Which trade relationship would be expected to have a larger impact on the returns to research? Why?

Savageland, a new country founded by me, is negotiating trade relationship with Malaysia (population 30.5m) and Singapore (population 5.5m). Both countries have about the same GDP. Which trade relationship would be expected to have a larger impact on the returns to research? Why?

We would prefer Singapore because Singapore has higher productivity despite its population (divide GDP over population). In term of research industry, Singapore appears to be more advanced than Malaysia. If we also would like to compare the education system between those countries, Singapore has better rating in education than Malaysia. Based on these, trade relation with Singapore can improving balance of trade.

Does too little or too much research get done in the Romer model

Romer stipulates that research will reach an equilibrium as too much or too little research will not result in a steady state equilibrium. This is because if there is too much research undertaken the wage paid to researchers will decrease and researchers will then seek higher wages in the non-research sector. Romer highlights historical movements of groups of people in and out of research as a result of aggregate disturbances such as business cycles and shocks, and due to the size of the market and the effect this has on patent demand. This is because human capital used in research has alternative uses in manufacturing and commercial trade.

Romer also highlights the possibility of a mismatch in research volume as the partially rivalrous nature means that the owner of the research cannot completely stop others from copying it, reducing incentive.