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Introduction to Economic Growth

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8. Creative destruction

The essential point to grasp is that in dealing with capitalism we are dealing with an evolutionary process [Joseph Schumpeter].

Learning Goals:

Understand the process through which innovations destroy existing rents

Understand the analogy between creative destruction and the Darwin theory of evolution

Identify the factors that influence the market value of a discovery and the optimal investment in R&D

Acknowledge the alternative approaches that have been proposed to remove the scale effect from endogenous growth models

8.1 Introduction

In today’s world, much competition between firms takes the form of firms trying to develop new and better products or less costly methods of producing existing products. This competition forces incumbents to continuously revise their plans and production techniques, in a process of permanent adaptation. In this process, there are winners and losers. Firms that fail do adapt, experiment losses and some are forced out of business.

The view that technological change comes along with the destruction of existing businesses is on the basis of the Schumpeterian paradigm of economic growth. In light of this paradigm, the disappearance of old activities and firms and the emergence of new activities and firms is an important vehicle through which technological progress materializes. Joseph Schumpeter labelled this process as of “creative destruction”. Creative destruction is a form of competition through innovation that delivers rapid productivity growth.

This chapter examines the argument, focusing on the competitive nature of R&D. Section 8.2 explains what is meant by creative destruction. Section 8.3 presents a simplified version of the basic Schumpeterian model. Section 8.4 gives the intuition od extending the analysis to more than one sector. Section 8.5 analyses the question as to whether more product market competition is good or bad for innovation. Section 8.6 concludes.

8.2. Creative destruction

Destroying a monopolist’ rents



A distinctive feature of the Schumpeterian model is that monopoly rents last only until the arrival of a competing innovation. Hence, in choosing their research effort, firms have to balance the potential gain of gaining market power against the cost of losing it to a competing innovation.

To illustrate the concept of creative destruction, let’s consider again the case of a vertical innovation, with a small novelty. In Figure 7.2 it was assumed that prior to the innovation the market was under perfect competition. Hence, in that example, there were no economic rents to destroy. In Figure 8.1, on the contrary, it is assumed that prior to innovation the market was run by an incumbent with full monopoly power.

Figure 8.1. Creative Destruction

x

1w

Bxp 1 111 wp

Mx0

0w

100 wp

Mx1

(a)

(b)

p

0M

1M

The equilibrium prior to innovation is described in Figure 8.1 by point M0. This equilibrium corresponds to the intersection of the incumbent’ marginal costs curve ( 0w ) with the locus of marginal revenues (the dashed curve), implying a price equal

to 100 wp and a total demand equal to Mx0 (the suffix j is omitted to save

algebra). The incumbent’ operational profits (7.12) corresponds to the area (a).

Now assume that an entrepreneur achieves a drastic vertical innovation, corresponding to a productivity gain from 0 to 01 . With this innovation, the

entrepreneur achieves a marginal cost equal to 1w (it is assumed that the market for this variety is small in respect to the labour market, so the wage rate remains constant). The innovation allows the entrepreneur to undercut its rival and still capture all the market. The new monopoly price falls to 111 wp , implying an increase in

production of this variety from Mx0 to Mx1 .

With the innovation, the entrepreneur achieves operational profits equal to area (b). The incumbent monopolist, in turn, looses area (a) to consumers. Hence, the arrival of a new rent (b) comes along with the destruction of an old rend (a). This is why the process is called Creative Destruction.

Note that, since the innovation is drastic, the consumer gain (area [p0M0 M1 p1]) more than offsets the incumbent loss. Hence, s long as the innovation is profitable for



the entrant (that is, if (b) is greater than the sunk cost of the innovation), there will be a gain for the society as a whole157.

Box 8.1. Joseph Schumpeter

Joseph A. Schumpeter (1883-1950) was one of the most prominent economists of the 20th century and is sometimes referred to as the “father of economic development”. In two famous books, The Theory of Economic Development, published in 1911, and Capitalism, Socialism and Democracy, first published in 1943, Schumpeter argued that the process of economic development resembles the Charles Darwin’s theory of evolution.

Schumpeter theorized that the introduction of new products, new production processes and new forms of industrial organization by innovating firms undermine the marketability and the value of existing designs and production techniques. This allows inventing firms to achieve a new dominant position in the market and, by then, to reap a return on their research effort. According to Schumpeter, that dominant position should not last for long: sooner or later other firms will come up with new and better technologies, causing the incumbent’ rents to erode.

The process through which firms bringing new technology enter in the market and undercut incumbents destroying their rents, “revolutionizing the economic structure from within”, was labelled by Schumpeter as of “creative destruction”. According to the author, creative destruction allows the market economy to incessantly revitalize itself, reallocating resources from old and failing business to newer and more promising areas. Creative destruction, the author defended, is the essential mechanism through which the market economy adapts to technological change.

Box 8.2. Peas, dark moths and the theory of natural selection

In its primitive form, the pea plant evolves a gene that makes its pods explode when peas are ready for germination. This mechanism allows peas to be scattered on the ground, ensuring the survival of the species. In each generation of pea plants, however, a number of mutants grow by accident lacking this key genetic ingredient: pods of mutant peas fail to pop up. In the wild, mutant peas die entombed in their pods. The natural selection assures that only the healthy pods pass on their genes.

When the man invented agriculture, however, the direction of natural selection was changed. Humans were not interested in the primitive version of the pea plant, because it is much more convenient to gather pods with peas enclosed than to search for scattered peas on the ground. Thus, once the man became a farmer, it started growing the mutant version. Today, the pea plants we see in our fields are the mutant version, not the primitive. Farmers reversed the direction of natural selection: the formerly successful gene became lethal and the formerly lethal mutant became successful.

By the end of 19thb century a darker variant of moths became far more abundant than the paler varieties, in regions of England with carbon intensive manufactures. The

157 Note that this is not a general case: if the sunk cost of R&D was too large, the net welfare gain could end up being negative. Also note that, in case the innovation is non-drastic, there will be no consumer gain at all (we will examine the later case in Box 8.3).



reason is that, as the environment became dirtier, dark moths resting on dirty trees were more likely to escape the attention of the predators than the pale moths. The sudden change in environment caused a significant evolutionary change within a time period corresponding to only hundreds of generations.

These two examples, described by Jared Diamond in his famous book Guns, Germs and Steel158, illustrate the Darwin’s concept of “natural selection”: in the nature, each new generation of a species produces a number of mutants. Because in general mutants are not endowed with the same genetic information that their ancestral developed for thousands of years, they are in principle more vulnerable to the environmental challenges. The natural processes of differential surviving and reproduction does the selection. In certain moments, however, the mutant “competencies” may turn out to become an advantage instead of a threat: changes in the natural environment may cause a mutant variety to become naturally selected. In these cases, the population undergoes an evolutionary change.

Like living species, economic agents respond to changes in the economic environment. Each moment in time, agents tend to use strategies that they observed or they learned to be successful in the past. The behaviour of each economic agent each moment in time reflects thus a learning process and an interaction between its competences and the economic environment. Occasionally, agents experiment new strategies. This is innovation. When the new strategy fails, agents retreat to the old strategies. Whenever the new strategy succeeds, the innovating agent gains a competitive advantage. This advantage will render the previous strategies obsolete. As time goes by, other agents copy the more efficient strategy, until it becomes dominant in the market. This is Creative Destruction.

8.3 The optimal level of R&D

The Schumpeterian model of economic growth focuses on vertical innovations. Vertical innovations are by definition, those that improve productivity along a given product line, rendering previous technologies obsolete. A key feature of growth models with vertical innovations is that entrepreneurs bringing new technologies drive the previous incumbents out of the market, destroying their rents, until they are themselves displaced by other entrepreneurs bringing newer and even more efficient technologies.

The analytical model in this chapter builds on the one already introduced in Chapter 7 - described by equations (7.1) to (7.12) 159 . The main features are the following: first, chance matters for innovation; second, inventions are achieved by newcomers; third, successful innovations allows the innovator to displace the previous incumbent (that is, all innovations are assumed to be drastic); fourth, future inventions displace current inventions, so monopoly rents are temporary.

158 Diamond (1997).

159 The first successful model to describe the Schumpeterian argument is due to Aghion and Howitt (1992). Earlier attempts to formalize R&D as a rent seeking activity include Nordhaus (1969) and Shell (1973). Both authors faced, however, difficulties in dealing with increasing returns in a general equilibrium framework.



For simplicity, we start out with the case in which there is only one intermediate input (that is, m=1). Later (section 8.4) we’ll discuss the implications of extending the analysis to multiple intermediate inputs.

A production function for knowledge

By now, we have been abstracting from the question of how the arrival of a new idea relates to the R&D effort. This is, however, a very important question: when firms invest in R&D, they expect to achieve some innovation in the future, and the relationship between resources employed and the expected output in terms of new ideas is critical to find out the optimal level of research.

The problem is that the relationship between R&D effort and technological change is not easy to model:

- First, knowledge is something that we don’t know how to measure: shall we count ideas? Shall all ideas be counted as valuing the same? If not, how to evaluate each particular idea?

- Second, there is an element of risk: researchers may not succeed in inventing a new technology .

- Third, the likelihood of an agent discovering a particular idea may depend on the success of other agents discovering complementary ideas (we labelled this as the “standing on shoulders” effect).

- Fourth, the research effort at the individual level may reveal useless if a competing researcher independently discovers a similar idea (this problem is labelled “stepping on shoes”).

- Finally, even if the key ingredients of a “knowledge production function” were well known, a question remained as to the choice of its functional form: shall output knowledge vary linearly with the research effort, or shall the production function for new ideas exhibit diminishing returns? That is, in order to sustain a given rate of technological progress (and therefore a given rate of per capita output growth) will it be sufficient to have a constant number of researchers or do we need instead an increasing number of researchers over time?��

All these questions mean that the relationship between the production of ideas and the resources allocated to such endeavours is much more difficult to formalize than for other goods. And yet, the shape of such a production function is an essential ingredient to determine the optimal level of R&D. With no surprise, the choice of an appropriate specification for the production function of knowledge became a matter of dispute in the research arena. In Box 8.4, we’ll discuss alternative specifications that have been proposed in the literature. In this section, we stick with basic formulation of the Schumpeterian model.

The Schumpeterian approach assumes that innovations arise randomly, with an “arrival rate” that is proportional to the amount of working time devoted to R&D. Formally, it is assumed that, when one unit of labour is devoted to the search for technology 1 , that technology will be discovered with probability b. For the economy

as a whole, when N units of labour are allocated to R&D, the probability of the next vintage being discovered is bN. Thus, the higher the number of researchers, the more ideas will be produced. The parameter b is assumed exogenous and shall be interpreted as capturing the productivity of the research effort.

An arbitrage condition



To find out the optimal level of R&D, let’s recall our earlier assumption that working time can be split into two basic functions, only: final good production and R&D (equation 7.4). The implication is that the opportunity cost of devoting one unit of time to R&D is the wage rate that the worker abdicates for not engaging in final good production.

With this ingredient, the model develops in an intuitive manner: labour is deviated away from production with the aim to obtain rents. Depending on how expected rents compare with the wage rate, workers allocate their time to R&D or to output production. At the margin, workers must be indifferent between devoting one unit of time to output production or to research160. Formally, the following arbitrage condition should hold:

10 bVw , (8.1)

where 0w denotes for the wage rate and 1V denotes the “market value” of technology

1 . Both variables are evaluated prior to the innovation. Condition (8.1) states that the expected gain of an individual researcher allocating one unit of time to research (the probability b of an innovation times the value of the innovation, 1V ) shall be equal to the wage rate.

Note that the suffixes 0 and 1 do not refer to time, but instead to the moments before and after the innovation: because of the stochastic nature of innovations, the period of time between two successive innovations in this model has a random length.

The market value of a drastic innovation under creative destruction

To find out the value of the licence to produce with technology 1 , one shall take into account not only the implied profits, but also the time length during which these profits materialize. In the Schumpeterian model, each new innovation is fated to become obsolete at a given point in the future, when a superior technology (say 2 ) is discovered by a competitor.

In the following, let’s assume that the license to produce with technology 1 can be sold in an auction to whoever makes the higher bid. The question is how much will a potential bidder be willing to pay for that license. To make the story interesting, let’s assume that investors also have the possibility of investing in a capital good, earning the interest rate r161.

In deciding whether to buy the licence or not, investors shall compare two options:

- One, they can buy the license to produce with technology 1 at the price 1V ,

earning the corresponding ex-post monopoly profits 1 per unit of time, but

160 Corner solutions are ignored, for simplicity.

161 The interest rate could be made endogenous, extending (7.1) so as to account for the role of physical capital. For such an extension, you are invited to read Aghion and Howitt (1998), chapter 3.



facing the threat of the next vintage ( 2 ) being discovered, which will

happen with probability bN162;

- Two, they invest the amount 1V in capital, earning an income equal to 1rV per unit of time.

From an investor’ point of view, the optimal allocation of money shall obey to an arbitrage condition stating that, at the margin, the reward of holding the license must be equal to its opportunity cost:

111 rVNVb (8.2)

Condition (8.2) states that the interest-income generated by the value of the license per unit of time, 1rV , shall be equal to the ex-post monopoly profit minus the

expected loss resulting from the arrival of 2 . The later is equal to the value of the

license ( 1V ) times the probability of the next vintage being discovered, bN.

Rearranging (8.2) one obtains:

NbrV

11 (8.3)

The denominator of (8.3) can be interpreted as the “obsolescence-adjusted interest rate” and captures the effect of creative destruction: if there was no threat of competing innovations (=0), the value of the license would be given to the perpetuity’ formula, rV 11 . When however is positive, the expected duration of the monopoly rent is finite and this lowers the expected discounted value of the monopoly rents.

In (8.3), the value of innovation 1 declines with b and . Thus, current research

is discouraged by the intensity and the productivity of future research. This captures the negative externality of new innovations on incumbents.

The ex post monopoly profits

The expression for monopoly profits was already obtained in (7.12):

1

211 w

B jj

According to this expression, profits increase with productivity and decrease with the wage rate. Thus, a vertical innovation, leading to a productivity increase, impacts positively on profits.

Note however that technological progress in general exerts a negative effect on profits, through its influence on wages. The reason is that productivity improvements raise the demand for labour, causing wages to increase. This indirect effect of

162 In sake of simplicity, it is assumed that R&D intensity, , is constant over time. In the Schumpeterian model, this will happen in the steady state, as long as technological improvements are proportional (that

is, 1 0 2 1 3 2 etc). The model above implicitly assumes this, and it can only be used to

compare steady states.



technological change has to be taken into account when assessing the ex post monopoly profits163.

With m=1, equations (7.2) and (7.5) imply:

YNx . (8.4)

Substituting this in (7.1) and using (7.11) one obtains a simple expression for the (aggregate) labour demand in the intermediate input sector:

YN

Yw

21 (8.5)

This equation differs from (2.11) in that the term 21 instead of 1 appears in the numerator. This is an implication of having imperfect competition in the market for the intermediate product164.

Substituting (8.5) in (7.12), the expression for profits becomes

Y 1 . (8.6)

Now, we make use of equation (7.6) of the earlier chapter, to obtain the following relationship between production prior to innovation and after the innovation:

01

011 YY , holding constant the supply of labour. Given this, the ex post

monopoly profits (8.6) become:

01

011 1 Y (8.7).

The equilibrium level of research

The optimal allocation of labour to R&D is determined by equation (8.1). Substituting the left hand side by (8.5), using (8.3) and (8.7) in the right hand side and solving for the equilibrium level of R&D, one obtains:

11

11

101

bNr (8.8)

Equation (8.8) states that the optimal proportion of time devoted to R&D is higher, the lower the interest rate, the larger the size of the labour force N, the higher the productivity of R&D, b, and the bigger the technological jump, 01 .

It is also apparent that is an increasing function of : the lower the elasticity of the demand curve faced by the intermediate monopolist, the larger the monopoly

163 Although we are assuming one sector only, one wants the model to be meaningful for the case with many intermediate inputs, where each intermediate input is small relative to the economy. Thus, while it is reasonable to assume that the innovator takes the wage rate as given (eq. 7.7), the general equilibrium of the model implies that technological change impacts on wages through its influence in the demand for labour.

164 In other words, monopoly profits come at the cost of lower wages. For each employment level, monopoly profits are equal to the difference between the wage rate that would prevail under perfect competition and the wage rate under monopoly, multiplied by the employment level. That is:

YNNYNY YYY 111 2 (conf. equation 7.6).



rents that will be appropriated by successful innovators and hence the larger the incentives to innovate. This accords to the Schumpeter view that market power is good for innovation.

Graphical illustration

To illustrate the trade-offs involved in the choice between allocating time to production and to R&D, lets refer to Figure 8.2. The curves in the figure do not exactly correspond to the two sides of equation (8.1), but rather to the two sides of equation (8.1) divided by per capita income. This small modification is rather convenient, as it allows the horizontal axes to be expressed in terms of .. That is, in Figure 8.2, from left to right we measure the proportion of time devoted to output production, 1 ; from

right to left we measure the proportion of time devoted to R&D, . The size of the horizontal axes is equal to one.

The downward sloping curve (from left to right), describes the demand for labour and is equal to equation (8.5) divided by per capita output:

1

1 2

y

w (8.9)

This equation states that, as the proportion of time devoted to production 1 increases, diminishing returns translate into lower wages per unit of per capita output.

The upward sloping curve (actually, downward sloping, from right to left) describes the demand for research labour, as implied by the right-hand side of (8.1). This is obtained, using (8.3) and (8.7) and dividing by per capita income:

bV1

y

bN 1

0 1 1 r bN

(8.9a)

This is a negative function of because of creative destruction: the greater the fraction of labour devoted to R&D, the more likely is the arrival of a competing innovation. Thus, a larger proportion of workers in the society devoted to R&D reduces the incentives to engage in R&D.

Solving together equations (8.9) and (8.9a), one obtains the equilibrium level of research and development (8.8).

To see how the model works, assume that initially the allocation of labour was as described by points A and B: in that case, the marginal benefit of working time (B) would be lower than the marginal benefit of R&D (point A). Since in that allocation workers had an incentive to devote more time to R&D than they actually do, such allocation cannot be an equilibrium.

The equilibrium level of R&D (as described by equation 8.8) occurs at point E in the figure. In this allocation, wages are higher than in A because there are less workers in production (this reflects diminishing returns) and the expected benefit of research time is lower because there are more researches in the economy (this reflects the negative effect of creative destruction). In E, the arbitrage condition (8.1) holds.



Figure 8.2. The allocation of labour in a laissez faire Schumpeterian economy

E

Work effort

Expected value of R&D (scaled)

Marginal benefit of working time(scaled)

R&D effort

y

Vb 1

1

y

w

A

B

What are the implications of a higher productivity in R&D?

Consider the impact of an increase in the productivity of R&D, as captured by parameter b. Such a change has no effect on the curve describing the demand for labour by the productive sector (equation 8.9).

It has however two effects on the curve describing the marginal benefit of R&D (equation 8.9a): on one hand, it improves the probability of innovation and hence the incentives to innovate (numerator); on the other hand, it increases the likelihood of creative destruction (denominator), reducing the marginal benefit of research. It is easy to check that the former effect turns out to dominate, so when b increases, the curve shifts up and left (Figure 8.3).

Thus, a higher effectiveness of R&D translates in this model into a higher research effort and henceforth to a faster pace of technological progress.

What are the implications of a larger labour force?

Figure 8.3 can also be used to analyse the implication of having a larger labour force.

Since the curve describing the demand for labour by the productive sector does not depend on N, it remains unchanged. The curve describing the demand for research labour, in turn, is hit by two effects (equation 8.9a): on one hand, an increase in population increases the size of the market and henceforth the monopoly profits (numerator); on the other hand, a larger population also implies a higher number of researchers and therefore a higher probability of the monopoly rents being eroded through creative destruction. As before, the first effect dominates, so the curve shifts up and left.



Figure 8.3. The effect of an increase in the effectiveness of R&D

E’

Work effort

Expected value of R&D (scaled)

Marginal benefit of working time(scaled)

R&D effort

y

Vb 1

1

y

wE

This means that a larger population, by raising the size of the market for a successful entrepreneur, increases the incentives to R&D, leading to higher research intensity.

A corollary is that a large economy should grow faster than a small economy. In other words, this model is plagued with the same type of scale effect that is common to many other models of endogenous growth.



8.4 Multiple sector considerations

Extending the model to m intermediate inputs

The model above was solved assuming one intermediate input, only (m=1). This simplification hides some interesting aspects. In this section we discuss the consequences of having more than one intermediate sector.

So, consider the model described by (7.1)-(7.12), with m>1. Each variety is supposed to have its own research sector, with firms competing to invent the next generation of the corresponding technology. A successful entrepreneur in sector j will displace the current incumbent and will become the incumbent of sector j until being displaced itself. As before, it is assumed that innovations in each variety imply productivity improvements that are proportional to the each other.

Because innovations arise randomly, productivity improvements are not synchronized across sectors. Thus, in contrast to what assumed in (7.6), the level of technology will be in general different across sectors. With a large number of sectors, the implication of asynchronous technological progress is that aggregate productivity and wages will evolve in a much smoother way than in the case with one sector only.

Conditional on technology and wages, the price level, production and profits in each intermediate sector j are given by (7.9), (7.10) and (7.12), respectively. With more than one sector, profit opportunities in each sector depend on the other sectors developments: it is the combined effect of all technological improvements that determines the wage rate and henceforth, expected profits and the incentives to innovate.

To see this, let’s first compute the aggregate demand for labour. Substituting (7.11) in (7.5) and solving for the wage rate, one obtains:

121

YN

mBw , (8.10)

where

11

jj is the average technological level in the economy.

Equation (8.10) states that vertical innovations ( ) impact positively on wages. These are defined in average terms, so as to account for asynchronous technological progress across sectors. Because we now have various intermediate sectors, equation (8.10) also accounts for the impact of horizontal innovations (m) on wages.

Substituting (8.10) in (7.11), one obtains the demand for labour in each variety as a function of aggregate productivity:

m

NN Yj

j

1

(8.11)



According to this equation, the share of sector j on aggregate employment,

Yj NN , is higher/lower than 1/m depending on how sector j’ productivity ( j)

compares to the economy average, . In particular, the share of sector j in manufactures employment is higher than the average 1/m, if its own technological level is higher than the average.

Equation (8.11) also reveals that, with a fixed labour supply, as more and more varieties are introduced in the economy (horizontal innovations), the employment level in each sector declines. This is no more no less than the division of labour effect.

Substituting in (7.2) and then in (7.1) one obtains, after some manipulation, the output level in the economy:

1YNBmY (8.12)

This equation replicates (7.6), with one difference, only: we are not imposing the productivity across sectors to be the same. Using (8.8) and (8.11) you’ll find an aggregate demand for manufacture labour exactly equal to (8.5).

Finally, substituting (8.11) in (7.12) and using (8.12), one obtains an expression for the monopoly profits in each sector:

1

1 jj m

Y (8.13)

Comparing to (8.6), we see that the monopoly profits in each individual sector depend positively on that sector productivity ( j ) relative to the economy’ average ( ).

Equation (8.13) also shows that horizontal innovations, by expanding the number of varieties and reducing the demand for each variety, impact negatively on individual profits.

The crowding out effect

Equations (8.11) and (8.13) reveal a form of creative destruction that was not accounted for in the model with one sector: asynchrony in innovation implies a continual reallocation of labour and profits between sectors. In particular, employment and profits will increase in innovating sectors and will decline in non-innovating sectors.

This “crowding out” effect is another negative externality arising from innovators to incumbents, that reduces the incentives to innovate: monopoly profits in each variety not only erode with the arising of a superior variety in the same product line (the “creative destruction effect” in equation 8.2), they also erode through rising wages implied by technological improvement in other product lines.

An implication is that an increase in b not only shortens the duration of the ex-post monopoly rents along the corresponding variety, it also acts to reduce profits on non-innovating sectors along time, through successive increases in the wage rate165.

165 Still, this crowing out effect is never large enough to invert the relationship between b and , which remains positive. For a formal explanation, see Aghion and Howitt (1998), pp 87-92.



Note that the crowding out effect applies both to vertical and horizontal innovations: an increase in the number of varieties, m, impacts positively on aggregate output and productivity, raising real wages and depressing profits (equations 8.10 and 8.13).

Removing the scale effect

In equation (8.8), we saw that the size of the market impacts positively on the incentives to innovate. Thus, the larger the population the higher will be the optimal proportion of time devoted to R&D and henceforth the faster will be the rate of technological progress and of economic growth. Thus, the model displays a scale effect.

It is important to note that this property of the model does not change in the multiple sector case: according to equation (8.13), monopoly profits in each variety are still a positive function of aggregate output, Y. However – and this is the key issue - in the model with many varieties, profits decline with the number of varieties. The reason is that what determines the size of the market to a typical sector is not aggregate output (Y), but rather its market share (Y/m). Thus, when the number of varieties increase, the market share of a typical variety declines and so will do profits.

This property of the model suggests a natural avenue to get rid of the scale effect: if the size of the market and the number of varieties were set to evolve in the exact proportion, the size of the market available to each variety would remain constant and so would do the incentives to innovate.

In fact, this is precisely the avenue explored by some Schumpeterian models of economic growth to get rid of the scale effect. In brief, these models account for two types of technological progress: increases in the total number of varieties, m (horizontal innovations) and productivity gains along a given product line (vertical innovations). In these models, R&D efforts are basically aimed at vertical innovations, while the number of varieties increase proportionally to the size of the workforce166. If the number of varieties increases in direct proportion to the size of the market, the size of the market for each variety remains constant and so will do profits and the incentives to innovate. Hence, the research intensity in each industry does not change when the population expands. Moreover, for each given research intensity, a rising population does not translate into more researchers in each sector: if the number of varieties and the size of the labour force are proportional, the average firm size (and the number of researchers per variety) remains unchanged. Thus, technological progress in each variety will be unaffected by the population size. All in all, the proliferation of product varieties dilutes the effect of population expansion, both on research intensity and on the number of workers per variety, removing the “strong” scale effect167.

166 Note that a proportional relationship between the size of the market and the number of varieties is a conventional property of models with monopolistic competition. This direction was first explored by Young (1998). Other authors include Dinopoulos and Thompson (1998), Peretto (1998), Aghion and Howitt (1998, 2005), Peretto and Smulders (2002). For a survey, see Jones (1999, 2005).

167 Still, a “weak scale effect” arises in this class of models, because aggregate productivity depends positively on the number of varieties (horizontal innovations). That is, while productivity growth through vertical innovations becomes independent of the size of the labour force, the proliferation of varieties leads to a division of labour effect, through which the level of per capita income increases with the size of population.



Box 8.4. The “Fishing out” theory

A main difficulty in models with endogenous technological change is that they give rise to a counterfactual scale effect, according to which the growth rate of per capita income becomes an increasing function of size the economy’s workforce.

To see this, let’s first consider the basic formulation of the knowledge production function introduced in this chapter, but instead of assuming that innovations arrive stochastically, assume that technological improvements follow a deterministic rule along a continuous time168:

ttt Nb . (8.14)

As before, the exogenous parameter b measures the productivity of research labour in the production of knowledge.

The critical assumption in (8.14) is that the creation of new knowledge is proportional to the existing stock of knowledge in the economy ()169. As for the rationale, you may interpret this as capturing the cumulative nature of knowledge or the “standing on shoulders effect” (Box 7.5): if new ideas build on old ideas, a larger stock of current knowledge is likely to increase the productivity of researchers seeking for new ideas. The “standing on shoulders” is a positive externality, whereby each individual researcher contributes to the common pool of knowledge and henceforth to other researchers’ productivity.

Dividing (8.14) by , one obtains the (endogenous) rate of technological progress:

tNb

(8.15)

This model implies a linear relationship between the R&D effort and the rate of productivity growth: when the proportion of workers engaged in R&D increases, the growth rate of per capita income also increases. This model is a cousin of the AK in that a policy change (e.g, a subsidy to R&D) affects long-term growth. It is a model of endogenous growth.

It is important to stress the critical role of the “standing on shoulders” effect in this model. Analytically, the assumption that the knowledge production function is a linear differential equation on is what we need to assure that the productivity of researchers grows over time, even when the number of researchers remains constant. If, in alternative, the knowledge production function did not depend on that is, if

Nb ), then with constant parameters b and and with a constant population, the

flow of new ideas ( ) would be constant over time. Therefore, the growth rate of per

168 In the model analysed in this chapter, subscripts 0, 1, 2 in the variables do not refer to real time, but rather to a sequence of innovations. Thus, the time interval between each two innovations is random. In the formulation above, the subscript t refers to time and proportional improvements in technology take a constant time interval. With large numbers, the two specifications are basically equivalent..

169 Models consistent with (8.14) (e.g, with inventions generating proportional improvements in productivity) include Romer (1990), Grossman and Helpman (1991) and Aghion and Howitt (1992).



capita income ( t ) would fall down to zero as the stock of knowledge

increased. So the model would be incapable of generating sustained growth.

The other side of the coin of assuming linearity is the scale effect: as long as population is constant, (8.15) the growth rate of per capita income will be constant; but with exponential population growth, the growth rate of per capita income will itself grow exponentially.

As explained in the main text, the Schumpeterian model gets rid of the scale effect by linking the number of varieties, m, to the size of population: this allows the number of researchers per variety to remain constant and the same will happen to the rate of technological progress along each variety. This neutralizes the scale effect. Also note that in this model the removal of the scale effect does not change the “endogenous growth” nature of the model: because the knowledge production function is linear in knowledge, a higher R&D intensity translates into faster production of ideas and fastr growth. This property strongly contrasts with the competing attempt to remove the scale effect, by Charles Jones.

Jones170 abandoned the assumption of linearity in the knowledge production function, arguing that new discoveries are increasingly difficult to find. That is, as the stock of accumulated knowledge increases, researchers will find it more difficult to invent new technologies, because the easiest ideas have already being discovered. On the other hand, as technology becomes more complex, it takes more time and effort for a researcher to learn everything it needs just to catch up with cutting hedge.

As for an illustration, note that many breakthrough inventions in the 18th and 19th centuries were achieved by hobbyists or by single individuals. Thomas Edison, for instance, invented alone the light bulb, the phonograph and the motion picture. Today, advances in technology are mostly achieved by scientists engaged in research teams and focusing on very narrow problems. The assumption that new discoveries become increasingly more difficult became known as the “Fishing out effect” 171.

Formally, the “Fishing out effect” is modelled allowing past discoveries to impact on the productivity of current researchers with declining marginal returns:

ttNb , with 0<<1. (8.16)

In this model, the sign and magnitude of parameter captures the net effect of two opposing externalities on productivity growth: the “standing on shoulders” effect (positive), whereby productivity of current research increases with the accumulated knowledge in the society and; the “fishing out effect” (negative) whereby past discoveries turn new ideas more difficult. Jones conjectured that the net effect of these two externalities may lead to 0<<1 : that is, new researchers benefit from previous ideas, but there are diminishing returns to knowledge in knowledge production.

Another novelty in the Jones formulation is a negative externality from researchers to other researchers, due to overlapping research: that is, the waste resulting from the independent researchers trying to achieve the same piece of knowledge. This

170 Jones (1995).

171 The label “fishing out” arises from the classical example of the fishing pound for the Tragedy of the Commons: if the pound is stocked with a fixed number of fish, then it becomes increasingly difficult to catch each new fish. Followers of this approach include Kortum (1997) and Segerstrom (1998).



externality (labelled “stepping on the shoes”) is accounted for in (8.16) by postulating <1 (that is, doubling the number of researchers less than doubles the production of new ideas). This assumption is not, however, necessary to remove the scale effect.

When the knowledge production function takes the form (8.16), the rate of technological progress becomes:

1

ttNb

. (8.17).

With 0<<1, (8.17) implies a negative relationship between the growth rate of and the level of . This means that the model converges to a steady state: like in the Solow model, there is balanced growth path, in which the growth rate of technology is equal to the growth rate of per capita income, .

The steady state growth rate may be obtained log-differentiating both sides of (8.17) and imposing 0ˆ . This gives:

1n . (8.18)

In (8.18), the growth rate of per capita income is not a direct function of the population size, so the strong scale effect is removed. Still, a weak scale effect shows up, as the growth rate of per capita income is a direct function of the population growth rate172.

Another important distinction between (8.15) and (8.18) is that, in the later formulation the steady state growth rate of per capita income is invariant with the fraction of the population engaged in R&D, . Hence, changes in government policy leading to changes in research intensity have no long run effects on economic growth. Because in this, this model is categorised as of exogenous growth. Still, in this model, changes in research intensity do affect the long run level of per capita income (in other words, there is a transitory effect on growth)173. The policy implication is that a subsidy to the research activity would affect the level of income but not its long term growth rate.

Jones (1995, 2005) contended that this prediction of the model fits well with the cross-countries empirical evidence. The author observed that countries with high R&D intensity do not grow systematically faster than other countries, but they do exhibit higher levels of per capita income (similar evidence in Klenow and Rodriguez-Clare, 2005).

172 Note that in this model population growth is necessary to obtain sustained growth of output per worker: the assumption that new ideas become increasingly difficult to discover implies that the growth rate of falls down to zero over time when the population is constant (in other words, once linearity was removed from the knowledge production function, a constant research effort will no longer be sufficient to sustain the continuing proportional increase in the stock of knowledge that is necessary to sustain long run growth). Thus, only with an ever-increasing research community will be possible to maintain a constant rate of technological progress.

173 When the fraction of population devoted to knowledge accumulation () increases, there is an initial fall in output (labour is deviated away from production) but then the rate of technological progress accelerates (8.16). However, such acceleration is only temporary. Because of diminishing returns in knowledge production, the rate of technological progress falls back until reaching its previous (long-run) level, (8.18).



8.5. Competition and innovation

The discussion in this and in the previous chapter stressed the idea that innovations impact on the market structure: by introducing a new product or a cheaper way of producing an existing product, the innovating firm acquires market power.

A different question is whether the existing market structure affects the incentives to innovate. This section addresses precisely the question as to whether more product market competition is good or bad for innovation.

The replacement effect

A conventional wisdom is that established monopolies, because they are already earning profits, have less incentive to innovate than newcomers. Kenneth Arrow coined this idea as the replacement effect174.

To see this, let’s refer again to Figure 8.1. In that figure, the equilibrium previous to innovation is described by M0, with the incumbent monopolist having profits equal to area (a). The innovation described in Figure 8.1 corresponds to an increase in productivity from 0 to 01 .

Consider first the case in which the innovation is achieved by a newcomer: since the innovator moves from a situation with no profits to a full monopoly, its net gain will be area (b) minus the whatever fixed costs associated to the innovation. If instead the same innovation was achieved by the incumbent, its net gain would be (a)-(b) minus the fixed cost.

Comparing the two cases, we see that the monopolist benefits less with the innovation than the newcomer175. The reason is that the later jumps from a situation of zero profits to one with full monopoly profits, while the monopolist was already earning a monopoly profit prior to innovation. When the monopolists innovates, it replaces old profits by new (larger) profits.

The replacement effect thus suggests that leaders have less incentive to innovate than outsiders.

There are, however, some caveats in the analysis above:

First, the analysis presumes that without innovation the incumbent preserves its profits, (a): however, if the incumbent does not innovate, an outsider will most probably replace him. If one assumes that (a) is lost anyway, then the incentives for the incumbent to innovate and prevent entry will exactly match those of an outsider with equal R&D costs.

Second, the analysis abstracts from the possibility of the incumbent having lower costs in achieving the innovation: if learning by doing or any other information advantage translated into lower R&D costs for the

174 Arrow (1962).

175 A different question is whether there will be a difference for the society as a whole. As you may easily check, the social gain of the process innovation does not depend on who is the new monopolist.



incumbent, the later could end up with greater incentive to innovate than the outsider176.

In the real world, innovations are often carried out by industry leaders, which remain leaders for long periods of time.

Neck and neck competition

So far, we have been assuming that outsiders always undercut incumbents. The implication is that each moment in time, there is only one incumbent in each sector. In alternative, one may assume that followers have first to catch up with the leader before becoming monopolists themselves. With such modification, the model will account for the possibility of firms in a sector to be in a state with equal technologies, competing neck-and-neck at the frontier177.

The implication of neck-and-neck competition is that it provides an incentive for incumbents to innovate: since their profits are constrained by the existence of other competitors with the same level of technology, the larger the number of firms competing neck-and-neck, the larger the incentive for an incumbent to innovate, in order to acquire a technological advantage and escape competition, becoming leader.

To illustrate this, we refer to Figure 8.4. Suppose that all innovations are non-drastic and that technological spillovers are such that no firm can get more than one technological step ahead his competitors: that is, if the technological leader innovates (say to 1 ), a competitive fringe automatically learns to copy the leader’ previous

technology ( 0 ). It is however possible for a laggard firm to escape the fringe and catch

up with the leader.

Hence, at any point in time, there will be only two possible market structures in the industry: “neck-and-neck”, in which more than one firm compete using the frontier technology; and “unlevel”, in which only one firm holds the frontier technology and supplies the entire market.

In the “unlevel” case, the leader’ marginal cost is equal to 1w and the

competitive fringe’ marginal cost equals 0w . In this case, the leader sets the price just

marginally below 0w , capturing all the market, and pocketing the difference between

this price and the marginal cost 1w 178. The leader profits are equal to the shaded area in the figure ( ). All its competitors are priced out of the market, so their profits are zero.

Now suppose that an entrepreneur from the fringe successfully innovates and joins the frontier technology, 1 . This means that, from now on, two firms will be

176 For a discussion, see Barro and Sala-i-Martin, (1995, pp. 254-259), or Mukoyama, (2003).

177 The following explanation adapts from Aghion and Howitt (2009), chapter 2.2. The main references are Aghion et al. (1997) and Aghion at el. (2001).

178 Note that the equality between the leader marginal costs ( 1w ) and marginal revenues occurs at point

R, implying a monopoly price (point M) exceeding the competitive price ( 0w ). This means that the

leader’ innovation is non-drastic.



operating in this market, competing neck-and-neck. The profits earned by each firm will depend on how far they will compete with each other: at one extreme, if they engage in open price competition, the equilibrium price will fall to 1w , resulting in zero profits for both; at the other extreme, if they collude, they can set the profit-maximizing price ( 0w ) and share equally the profits, obtaining 2 each (in this case, the newcomer is

said to have “stolen” part of the leader business – see Box 8.3).

If more firms catch up to the frontier technology, the share of obtained by each one declines further and the collusive solution becomes more difficult to implement. Thus, a laggard firm achieving a successful innovation (from 0 to 1 ), will

gain something between 2 and zero, depending on the degree of competition in the neck and neck state.

Figure 8.4. Neck-and-neck competition

x

1w

Cx0

Bxp 1

11w

Mx

C00w

R

jp

Thus, for laggard firms, the higher the degree of competition in the market, the lower the incentives to achieve a successful innovation and join the incumbents in the neck-and-neck state. This captures the conventional “Schumpeterian effect”, according to which increased competition discourages innovation.

For firms already in the neck-and-neck state, however, there will be more incentive to innovate, the higher the level of competition. The reason is that, the more competition in the neck and neck state, the lower the firm’s profits and hence the higher the benefit of discovering a superior technology, to undercut its rivals and become monopolist. Thus, through this “escape competition effect”, there will be a positive relationship between product market competition and innovation.

In sum, once we account for the possibility of neck-and-neck competition, the relationship between product market competition and innovation needs no longer to be negative: true, in industries where competition is better described as “unlevel”, more competition should come along with lower R&D effort, because joining the leader at the frontier becomes less attractive; but in industries better described as “neck-an-neck”, more competition should be associated to a higher research effort, as firms try to “escape competition” and become market leaders.



Box 8.3. The Business Stealing Effect

When an entrepreneur from the fringe successfully innovates and enters in the market joining the leader in a neck-and-neck competition, there will be a partial deviation of rents from the leader to the newcomer. In this case, the innovator is said to steal business from the incumbent.

The business stealing effect implies that some of the rents earned by the innovator are simply deviated from the previous incumbents: they do not correspond to a gain from the social point of view. This fact introduces the possibility of the R&D efforts being excessive under laissez-faire.

In terms of figure 8.4, consider the case in which an entrepreneur from the fringe achieves an innovation that exactly matches the leader’ technology, 1 . In this case, the market price and the total demand for the good will not change, so the only difference is that two incumbents - instead of one - will now share the market. If, for instance, they collude and share equally the profits, then the “business stealing effect” will correspond to half of the shaded area describing profits in Figure 8.2.

Clearly, in this case the innovation comes along with a social loss: the consumer surplus does not change at all, and all the return reaped by the innovating firm will be a mere transfer from the incumbent. As long as the innovation involves a fixed cost, this will be a pure loss for the society as a whole, even if the innovator itself gets a profit.

Note however that this is not a general case: if the innovator achieved some cost advantage relative to the leader, then there will be scope for social gains, even if the previous incumbent was not driven out of the market: there would be a cost saving in the units produced by the newcomer and consumer prices could fall. In this case, the innovation could have a positive or negative social value depending on how these two benefits compared with the fixed cost of the innovation.

Box 8.4. The inverted-U puzzle

On the empirical front, the relationship between competition and innovation has not been free of controversy. Some authors found a positive correlation between competition and innovation179. Other authors, allowing for a non-linear relationship between competition and R&D effort, came out with a new stylized fact, according to which the relationship between R&D and competition follows a inverted U: that is, at low levels of market competition, increasing competition comes along with more innovation; but at high levels of competition the relationship turns out to be negative: that is, more competition is associated with less innovation180.

An inverted-U relationship between competition and innovation is consistent with the story outlined above. The only thing one shall take into account is that the

179 Nickel (1996), Geroski (1995), Blundel et al., (1999).

180 Comanor (1967) found that R&D is smaller when technical entry barriers are too high or too low. Scherer (1967) found an “inverted U” relationship between industry concentration and employment of scientists and engineers. Aghion et al. (2005), found an inverted U relationship between product market competition and R&D output, measured by citation-weighted patents. The later also provide evidence that the positive relationship between competition and innovation is more pronounced in firms that are close to the technological frontier than in laggard firms.



steady state proportion of firms that are in the fringe or in the neck-and-neck state depends on the level of product market competition:

- When competition is very low, there are little incentives for firms in the neck-and-neck state to innovate. Hence, most firms will remain in the neck-and-neck state. In this case, the “escape competition effect” dominates: an increase in competition increases the incentives to innovate.

- On the other hand, when competition is very high, there is little incentive for firms in the fringe to enter in the market. Hence, the markets structure will be “unlevel”: in this case, the Schumpeterian effect dominates: more market competition reduces the incentives to innovate.

Summing up, as the degree of competition increases, the relationship between competition and innovation changes from positive to negative. This captures the stylized fact of an inverted-U-shape relationship between R&D and product market competition.

8.6 Discussion

This chapter discussed the competitive dimension of R&D. Competition through innovation subjects agents in the market to a process of permanent adaptation that resembles the Darwin’ theory of natural selection.

The Schumpeterian paradigm implies that the introduction of a new technology comes along with the destruction of existing rents. In each sector, when a firm manages to discover a technology that renders an older technology obsolete, it obtains a competitive advantage and destroys its rivals’ rents. As time goes by, other firms will imitate the leader or will develop even better technologies, causing the leader’ rents to erode. Sectors that innovate faster are more likely to expand and to absorb the workers released from non-innovating sectors.

The conventional Schumpeterian paradigm implies that product market competition, by eroding the rents that reward successful innovations, discourage R&D. Thus, the higher the intensity of competition in a given market, the lower the incentive for an outsider to innovate and join that market. Creative destruction accounts however to a form of dynamic competition, according to which incumbents, seeing their rents being eroded by competing innovations, try to “escape competition” with faster innovation. This effect is more likely when firms compete neck-and-neck at the technological frontier: in this case, an increase in product market competition leads incumbents to increase their research effort, in an attempt to achieve a technological advantage and become market leaders.

Most endogenous growth models are plagued by a scale effect whereby the growth rate of per capita output becomes a function of the growth rate of population. The Schumpeterian model gets rid of this scale effect by linking R&D to vertical innovations and allowing the number of varieties to expand along with the size of population. This allows the increased population to be diluted by a larger number of varieties, so the number of researchers per variety does not increase. However, a “weak” scale effect arises, due to the “division of labour effect”: since the number of varieties increases proportionally to the size of population, the growth rate of output will be itself a function of the growth rate of population



Key ideas of chapter 8

In our days, many firms compete through innovation. When entrepreneurs achieve a successful innovation, they reap a return that often comes at the cost of losses for non-innovating firms. This competitive nature of R&D is labelled Creative Destruction and resembles the Darwin theory of natural selection.

Because the potential gains of successful innovations materialize after the sunk cost of R&D is incurred, the optimal level of R&D has to be determined “ex ante”. R&D expenditures are decided depending on the expected profits achieved with the innovation compared to the opportunity cost of the resources employed.

In this assessment, entrepreneurs have to take into account both the potential profit in case innovation and also how long this profit will materialize. This, in turn, will depend on the research effort by others: the higher the R&D activity in an economy, the higher the likelihood of a successful innovation to be short-lived, and hence the lower the incentives to innovate. In contrast, when the society devotes only few resources to innovation, the opportunity cost of R&D is low.

In the Schumpeterian model, the optimal level of R&D depends positively on the size of the workforce: a larger workforce implies a larger market and hence more profits, so the optimal R&D intensity increases. This, in turn, leads to higher growth, giving rise to a scale effect.

Extending the model to many sectors, another source of creative destruction is identified: successful innovations across different sectors translate into real wages, shrinking the profits and employment in non-innovating industries.

The model with many sectors offers a natural framework to remove the scale effect: the key assumption is to link the size of population to the number of product varieties. As long as the size of population and the number of varieties are proportional, the fraction of the workforce employed in each variety remains constant. With a constant number of researchers per variety, the arrival rate of vertical innovations will be constant as well, despite the expanding population. Still, the model will display a weak scale effect.

An alternative avenue to remove the scale effect is to assume that ideas become more difficult to achieve as the level of technology increases (the Fishing out effect). With such an assumption, a larger population will not imply a faster rate of technological progress.

The fact that the reward to innovation comes through monopoly profits does not necessarily imply that less competition is good for innovation. True, a market with low competition will be more attractive for newcomers, so through this “Schumpeterian effect”, less competition is good for innovation. However, high product market competition also makes more attractive for firms in that market to “escape competition” by innovation. The total effect is ambiguous.

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