PROPORCIONALIDAD DE SEGMENTOS

Considerfirst the models, such as that in Romer’s (1990) seminal paper, describing technical change and growth in the technology leaders. They point out that the purposeful research and

development activities that often underlie technical change (and cause A to grow in formal models) require inputs of labor and other factors and thus are costly to undertake. They will be undertaken only if investors expect to receive at least enough future reward to cover their costs. When the new technological ideas produced through research and development may be freely copied, potential investors see no way to reap returns on their investments and do not invest because they would be unable to charge for the use of their ideas. Investment in research and development activities takes place only if a system of patent protection or effective trade secrets gives them temporary monopoly power over the use of the new ideas they generate. (We return to these concerns in Chapter 21.)

In Romer’s (1990) model, the costliness of research and development activities is captured by assuming that some of the economy’s labor resources must be allocated to research and development activities if technology is to advance. This creates a tradeoff between the two uses of labor in the economy:final goods production and efforts to improve technology. Total final goods production is shaped by the production function

Y= F K, ALY 4 17

where K represents physical and human capital and LYrepresents the quantity of labor devoted to

final goods production. The level of technology A is now assumed to be the cumulative result of past research and development activity. More specifically, A is interpreted as the total number of ideas generated by research and development activities to date, and the ideas are blueprints for the production of new intermediate capital goods (such as new digital devices and software) that can be used in the production of final goods and services. Producers are assumed to achieve higher productivity (in their transformation of labor and capital intofinal goods) through the use of a richer array of intermediate capital goods. Some clever math, beyond the scope of this chapter, describes a more detailed production function involving multiple capital goods and shows that total output can ultimately be summarized, as in equation 4.17, as a function only of the total value of all the many capital goods K and the cumulative number of ideas A as well as the labor input LY.

Central to the Romer model are its assumptions regarding the production of new techno- logical ideas. The production function for technological change is given by

A= ν LA, A LA 4 18

where A is the rate at which new ideas are created and LA is the quantity of labor devoted to

research and development activities (which must be equal to the difference between the total labor stock and LY).

The quantityν . represents the productivity of labor in producing new ideas. It may be a declining function of LA if larger numbers of researchers are more likely to duplicate one

another’s efforts, so that higher LAresults in a smaller output of ideas per research worker. Per-

researcher productivity,ν . , can rise or fall with the current level of technological attainment A. If researchers who start with a richer body of previous research are equipped to be more productive in their current research, thenν . is an increasing function of A. In principle, however, ν . might instead be a decreasing function of A, if the easiest-to-discover ideas tend to be discoveredfirst, so that as A rises, additional research tends to produce fewer new ideas. In the model these effects of LAand A onν . are assumed to represent externalities, which are true at the level of the economy

as a whole but are ignored by individual investors in research and development, who take the current level ofν . as unaffected by their choices.

Inventors are assumed to have exclusive rights to the use of their new ideas, which take the form of new designs for intermediate goods. They may either use the ideas to produce and sell the new intermediate goods themselves, or they may sell the use of the ideas to

specialized intermediate goods producers. Exclusive use rights give producers of each inter- mediate good monopoly power and monopoly profits in their sales to producers of final goods. It is these monopoly profits that provide the motivation for investment in research.

The technology offinal goods production is such that final producers always want to use some of every intermediate good that has ever been invented and that their demand for any one intermediate good weakens as the number of other intermediate goods rises. Thus, as the number of intermediate goods available in the economy rises, the profit earned by individual producers of intermediate goods falls. This implies that the more labor that is devoted to research, the lower is the expected return to additional investment in research. In equilibrium, researchers devote labor to research only up to the point at which the monopoly profit received from a new design is expected to just cover the cost of producing the design.

This model points to several reasons private individuals might fail to deliver the socially most desirable level of investment in new technology and thus offers additional reasons why well- designed government intervention might enhance growth behavior. First, it seems likely that today’s research discoveries make tomorrow’s research sector more productive, but unlikely that today’s research investors take this positive future impact of their work into account when making their current investment decisions. This provides a reason to suspect that people underinvest in research.

Second, it is possible that when the number of current researchers rises (as the rate of investment in the research sector increases), the tendency for researchers to duplicate one another’s efforts can rise, implying a reduction in the per-researcher production of distinct new ideas. Failing to take this effect into account, research investors might tend to overinvest in research.

Finally, it can be shown in these models that although monopoly profits are crucial as a source of return to research and development activities, they actually understate the benefits to society of the new ideas, suggesting another reason for private investors to underinvest in research. The net impact of all these imperfections is theoretically ambiguous, but they suggest the value of paying careful attention to the context-specific microeconomics of productivity advance.