"Both the consumer-surplus and business-stealing effects are pecuniary externalities: they operate through markets rather than outside them. As described in Chapter 2, such externalities do not cause inefficiency in a competitive market. For example, the fact that an individuals love of carrots drives up the price of carrots harms other carrot buyers, but benefits carrot producers. In the competitive case, these harms and benefits balance, and so the competitive equilibrium is Pareto-efficient. But when there are departures from perfect competition, pecuniary externahties can cause inefficiency.

The Romer, Grossman-Helpman, and Aghion-Howitt models provide examples of complete models that formalize these notions. At the macroeconomic level, the models are sinular to the third case in the previous section (6 +13 1 and n = 0), since that model is tractable and since it implies that the quantity of resources engaged in R&D may affect long-run growth. The models microeconomic structures, however, are much richer.

Since economies like these are not perfectly competitive, their equilibria are not in general optimal. In particular, the decentralized equilibria may have inefficient divisions of resources between R&D and conventional goods production. Three externalities from R&D have been identified: the consumer-surplus effect, the business-stealing effect, and the R&D effect.

The consumer-surplus effect is that the individuals or firms licensing ideas from innovators obtain some surplus, since innovators cannot engage in perfect price discrimination. Thus this is a positive externaUly from R&D.

The business-stealing effect is that the introduction of a superior technology typically makes existing technologies less attractive, and therefore harms the owners of those technologies. This externality is negative.

Finally, the R&D effect is that innovators are generally assumed not to control the use of their knowledge in the production of additional knowledge. In terms of the model of the previous section, innovators are assumed to earn returns on the use of their knowledge in goods production (equation [3.1]) but not in knowledge production (equation [3.3]). This assumption matches the institutional fact that a description of a new technology must be made available after a patent is granted, so that the knowledge can be used by other inventors. Thus the development of new knowledge has a positive externality on others engaged in R&D.

The net effect of these three externaUties is ambiguous. It is possible to construct examples where the business-stealing externahty outweighs both the consumer-surplus and R&D externalities. In this case the incentives to capture the profits being earned by other innovators cause too many resources to be devoted to R&D. The result is that the economys equilibrium growth rate may be inefficiently high (Aghion and Howiit, 1992). It is generally believed, however, that the normal silualion is for the overall externality from R&D to be positive. In the model developed by Romer (1990), for example, the consumer-surplus and business-stealing effects just balance, so on net only the positive R&D effect remains. In this case the equilibrium level of R&D is inefficiently low, and R&D subsidies can increase welfare.

There can be additional externalities as well For example, if innovators have only incomplete control over the use of their ideas in goods production

Alternative Opportunities for Talented Individuals

Baumol (IDgO) and Murphy, Shleifer, and Vishny (1991) observe that major innovations and advances in knowledge are often the result of the work of extremely talented individuals. They also observe that highly talented individuals typically have choices other than just pursuing innovations and producing goods. These observations suggest that the economic incentives and social forces influencing the activities of highly talented Individuals may be important to the accumulation of knowledge.

Baumol takes a historical view of this issue. He argues that, in various places and times, military conquest, political and religious leadership, tax collection, criminal activity, philosophical contemplation, financial dealings, and manipulation of the legal system have been attractive to the most talented members of society. He also argues that these activities often have negligible (or even negative) social returns. That is, his argument is that these activities are often forms of renf-seekzng-attempts to capture existing wealth rather than to create new wealth. Finally, he argues that there has been a strong link between how societies direct the energies of their most able members and whether societies flourish over the long term.

Murphy, Shleifer, and Vishny provide a general discussion of the forces that influence talented individuals decisions whether to pursue activities that are socially productive. They emphasize three factors in particular. The first is the size of the relevant market: the larger is the market from which a talented individual can reap returns, the greater are the incentives to enter a given activity. Thus, for example, low transportation costs and an absence of barriers to trade encourage entrepreneurship; poorly defined property rights that make much of an economys wealth vulnerable to expropriation encourage rent-seeking. The second factor is the degree of diminishing returns. Activities whose scale is limited by the entrepreneurs time (such as performing surgeries, for example) do not offer the same potential returns as activities whose returns are limited only by the scale of the market (such as creating inventions, for instance). Thus, for example, well-functioning capital markets that permit firms to expand rapidly tend to promote entrepreneurship over rent-seeking. The final factor

See Reinganum (1989) for an introduction to some of the issues raised by such patent races.

(that is, if there is only partial excludabiUty), there is an additional reason that the private return to R&D is below the social return. On the other hand, the fact that the first individual to create an invention is awarded exclusive rights to the invention can create excessive incentives for some kinds of R&D; for example, the private returns to activities that cause one inventor to complete an invention just ahead of a competitor can exceed the social returns.

Learning-by-Doing

The final determinant of knowledge accumulation is somewhat different in character. The central idea is that, as individuals produce goods, they inevitably think of ways of improving the production process. For example. Arrow (1962) cites the empirical regularity that after a new airplane design is introduced, the time required to build the frame of the marginal aircraft is inversely proportional to the cube root of the number of aircraft of that model that have already been produced; this improvement in productivity occurs without any evident innovations in the production process. Thus the accumulation of knowledge occurs in part not as a result of deliberate efforts, but as a side effect of conventional economic activity. This type of knowledge accumulation is known as learning-by-doing.

When learning-by-doing is the source of technological progress, the rate of knowledge accumulation depends not on the fraction of the economys resources engaged in R&D, but on how much new knowledge is generated by conventional economic activity. Analyzing learning-by-doing therefore requires some slight changes to our model. All inputs are now engaged in goods production; thus the production function becomes

Y(t) = K{tnA(,mt)V-". (3.22)

The simplest case of learning-by-doing is when learning occurs as a side effect of the production of new capital. With this formulation, since the increase in knowledge is a function of the increase in capital, the stock of knowledge is a function of the stock of capital. Thus there is only one stock variable whose behavior is endogenous. Making our usual choice of a power function, we have

A(f) = EK(tY, >0, >0. (3.23)

Equations (3.22)-(3.23), together with (3.4)-(3.5) describmg the accumulation of capital and labor, characterize the economy.

To analyze the properties of this economy, begin by substituting (3.23) into (3.22); this yields

nt) = X(t)"Bi-"X(f)*<i-«>L(f)i". (3.24)

"See Problem 3.7 for the case in which knowledge accumulation occurs as a side effect of goods production rather than of capital accumulation.

is the ability to keep the returns from ones activities. Thus, clear property rights tend to encourage entrepreneurship, whereas legally sanctioned rent-seeking (through government or religion, for example) tends to encourage socially unproductive activities.