MERIT Research Memorandum 2/94-032. MERIT Research Memoranda can be ordered from the MERIT secretariat, or by anonymous ftp at meritbbs.rulimburg.nl (WWW: http://meritbbs.rulimburg.nl) A Closed Economy Model of Horizontal and Vertical Product Differentiation: The Case of Innovation in Biotechnology Rohini Acharya and Thomas Ziesemer Maastricht Economic Research Institute on Innovation and Technology University of Limburg/Maastricht, The Netherlands Paper Presented to the Conference on the Evolutionary Economics of Technological Change: Assessment of Results and New Frontiers, Strasbourg, October 6-8, 1994. Abstract In endogenous growth theory models have either increasing or constant ranges of product variety. Developments in modern biotechnology however show cases of increasing, decreasing or constant ranges of product variants. We present a simple endogenous growth model allowing for all of these three cases in one model. Quality weights that are exponential in the index of goods are multiplied to the quantity of goods in a love-of-variety utility function. Consumers prefer not to buy goods which are too expensive relative to their quality. The presence or absence of cumulated knowledge determines whether licensing fees, endogenous fixed costs for and the number of producers and the quantities produced are falling or constant, thereby allowing for more or less room for variety in household budgets. Whereas new goods always appear, old goods may be selected away or are even reselected. The case of pure love-of-variety and total creative destruction are limiting cases in this model and cases of decreasing variety or initially increasing and later decreasing variety are additions to the present literature. The highly non-linear dynamics of the model are presented in simulations. 1. Introduction The study of technological change and especially its impact on economic growth through the production function or through increasing R&D has become increasingly relevant in economics. The development of new growth models based on the seminal Solowian contribution to the literature, followed by Arrow (1962) and Shell (1967) have made technological change especially through private sector investment in R&D or human capital accumulation a cornerstone of economic growth. Many such as Grossman and Helpman (for example 1990) have presented innovation as a series of new products which add to the variety of products available in the market, whereas in
Transcript
MERIT Research Memorandum 2/94-032. MERIT Research Memoranda can be ordered fromthe MERIT secretariat, or by anonymous ftp at meritbbs.rulimburg.nl (WWW:
http://meritbbs.rulimburg.nl)
A Closed Economy Model of Horizontal and Vertical Product Differentiation:The Case of Innovation in Biotechnology
Rohini Acharya and Thomas Ziesemer
Maastricht Economic Research Institute on Innovation and TechnologyUniversity of Limburg/Maastricht, The Netherlands
Paper Presented to the Conference on theEvolutionary Economics of Technological Change:Assessment of Results and New Frontiers, Strasbourg, October 6-8, 1994.
Abstract
In endogenous growth theory models have either increasing or constant ranges of product variety.Developments in modern biotechnology however show cases of increasing, decreasing or constantranges of product variants. We present a simple endogenous growth model allowing for all of thesethree cases in one model. Quality weights that are exponential in the index of goods are multipliedto the quantity of goods in a love-of-variety utility function. Consumers prefer not to buy goodswhich are too expensive relative to their quality. The presence or absence of cumulated knowledgedetermines whether licensing fees, endogenous fixed costs for and the number of producers and thequantities produced are falling or constant, thereby allowing for more or less room for variety inhousehold budgets. Whereas new goods always appear, old goods may be selected away or are evenreselected. The case of pure love-of-variety and total creative destruction are limiting cases in thismodel and cases of decreasing variety or initially increasing and later decreasing variety areadditions to the present literature. The highly non-linear dynamics of the model are presented insimulations.
1. Introduction
The study of technological change and especially its impact on economic growth through the
production function or through increasing R&D has become increasingly relevant in economics.
The development of new growth models based on the seminal Solowian contribution to the
literature, followed by Arrow (1962) and Shell (1967) have made technological change especially
through private sector investment in R&D or human capital accumulation a cornerstone of economic
growth. Many such as Grossman and Helpman (for example 1990) have presented innovation as
a series of new products which add to the variety of products available in the market, whereas in
Grossman and Helpman (1991b and c), the product of innovation is the development of new
products which are of a higher quality and keep variety in the market constant. The models by
Young (1991 and 1993) show increasing product variety as a result of higher quality innovations
(in the case of Young 1991) and constant variety as a result of higher quality innovations (in Young
1993).
In this paper, we develop a model which borrows characteristics from the new growth
models, but the results here are different in a number of ways. In specific, we show with the help
of simulations that the dynamics of innovation combined with consumer preferences produce the
results of all these models as special cases. In one case, we have increasing product variety, with
a reselection of older products which were previously rejected by consumers; in another, we have
a range of varieties which resembles a product cycle kind of configuration, with the range of variety
constant for an extended period of time, before new products eventually drive out older technologies
and qualities; in yet another case, we show that innovation in the form of higher quality products
results in older qualities being driven out almost instantly as in the case of Grossman and Helpman
(1991 b and c). In the closed economy model which assumes no capital markets, and therefore no
borrowing and consumer savings, we use examples from a study of biotechnology in industrialized
countries to set up the structure and relate the structure of consumer preferences to biotechnology,
particularly in the sector which is strongest in industrialized countries, namely pharmaceutical and
medical biotechnologies.
The emergence of biotechnology as an important new technology, has been documented
widely, both for industrialized countries (Sharp 1985, 1990, Orsenigo 1990, US OTA 1991 among
others), and for developing countries (see for example Clark and Juma 1989, Acharya and Mugabe
1994). Although still in a stage of infancy, it is quite clear that the high degree of pervasiveness
and its ability to affect a wide range of sectors, will make it an important new addition to the range
of new technologies contributing to the improvement of economic growth and development. It
would therefore be interesting to examine the main features of this technology and the impact it
may have on technological change and the interaction between R&D and economic growth. The
sectoral role of biotechnology R&D especially in industrialized countries is already becoming quite
clear with the emergence of clear cut sectoral demarcations between research and industrial
production. In developing countries as well, although the technology lag is considerable, the
concentration of biotechnologies in particular sectors is also becoming apparent. We use the
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pharmaceutical sector, particularly in industrialized countries in order to establish the structural
pattern of biotechnology R&D and of consumer preferences.
The results as we mentioned above, are interesting because they show a range of possible
results using a very simple structure of consumer preferences and of innovation, adding to the
previous literature in two respects: firstly, consumer preferences in this model reflect a desire for
higher quality as well as for a variety of products, rather than one or the other, as is the case with
most other previous growth models of this kind; secondly, by showing a range of different results
for product variety, we add to the literature on innovation through the emergence of new products.
In the next section, we describe developments in biotechnology and how these relate to the
structure of the model. In section 3, we describe the basic structure of the model and its dynamics.
Section 4 presents the results of simulations which as described above, show a range of implications
for product variety. The final section draws conclusions.
2. Sectoral Developments in Biotechnology: The Case of Pharmaceuticals
Biotechnology, or bioengineering, as its name suggests, straddles a number of scientific
disciplines, including molecular biology and chemistry1, and involves the engineering of biological
material to produce a new product with completely different characteristics. Two major discoveries,
that of the structure of Deoxyribonucleic acid (DNA), by Watson and Crick in Cambridge, England
in 1953 followed two decades later by the insertion of a foreign gene in between two ends of DNA,
resulting in recombinant DNA (rDNA) or genetic engineering, formed the major turning points in
modern biotechnology research. Since, then "new" biotechnology (as opposed to "old"
biotechnologies such as fermentation and plant breeding, which were not based on changes to the
genetic structure of organisms), has enabled radical new changes in both processes and products,
within established sectors, both in industrialized and in developing countries.
1 In fact the Nobel prize for Chemistry in 1993 was awarded to two Chemists for their workon the genetic modification of DNA. K. Mullis developed the technique of Polymerase ChainReaction (PCR) which has subsequently been used in gene sequencing and gene cloning researchwhile M. Smith’s work on changing the structure of an amino acid is being used by biotechnologistsworking on human diseases to insert altered genes into organisms (Economic Times (N. Delhi), 30October 1993. Similarly, the work done by Watson and Crick in the early 1950s was done at theDepartment of Physics at Cambridge.
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One of the fastest growing sectors in biotechnology, especially in the industrialized
countries, is pharmaceuticals. The US patent office approved the first modern biotechnology based
drug, recombinant human insulin in 1982. Since then, the number of patents granted to
pharmaceutical products has increased rapidly especially on the US market2.
Historical links between the first breakthroughs made in biotechnology such as Monoclonal
Antibodies and the medical and pharmaceutical sector has resulted in this sector becoming the
largest and most successful. Although dominated by the US and especially small New
Biotechnology Companies (NBTFs) there are also a number of European multinationals such as
Hoffman LaRoche, Glaxo, Bayer etc. who rank as important contributors to biotechnology research
and product development. Hoffman LaRoche’s merger with Genentech and its involvement in
Cetus and most recently, Syntex, demonstrates the interest these companies are expressing in
biotechnology research. Similarly, Eli Lilly has ongoing alliances with at least 11 biotechnology
firms 3. If this is any indication of its potential, biotechnology seems to be poised for an illustrious
future in the pharmaceutical industry, innovation not only adding to the variety of products
available, but also to quality, in the form of new products which offer treatments for diseases which
were unavailable previously. Thus, from a list of products, which are now available on the
international market (US OTA 1991, Ernst and Young, 1992, Bio/Technology, various issues, 1994),
it appears that innovation will result in an improvement in consumer utility through the production
of both higher quality and also greater variety in this sector.
While sectoral analysis shows that the pharmaceutical sector is the fastest growing, the
success has gone through various stages of research and development. Part of the reason for this
sector emerging before the others, as mentioned above, is the concentration of biotechnology
research in medical and biological faculties at universities. This was evident from the early stages
of biotechnology R&D in the 1970s which led to some of the important breakthroughs, notably the
demonstration of the gene splicing technique by Cohen and Boyer in the early 1970s. The 1980s
however were characterised by a privatization of both research and of product development. In the
USA especially, the emergence of the New Biotechnology Firms (NBTFs), created a new player
in the structure of biotechnology R&D. The NBTFs were specialized and functioned as a bridge
between generic research and commercialization. Although they did not have the marketing base
of large pharmaceutical companies, their success was largely due to their scientific base and
willingness to invest in high risk, applied biotechnology research. However, the lack of a marketing
network resulted in a number of failures by the late 1980s and early 1990s. This period was also
characterized by a number of takeovers of the NBTFs by large multinational pharmaceutical
companies, the most infamous perhaps being the merger between the first NBTF, Genentech and
the pharmaceutical giant, Hoffman LaRoche. Despite this however, a number of the NBTFs have
been able to maintain their market position largely by forming networks and marketing and
production arrangements with other companies. The modern pharmaceutical sector therefore appears
to be characterised by two kinds of players, both private but while one is specialized in research,
the other appears to be largely confined to using the new innovations to commercialize and market
the new products.
The use of modern biotechnology has resulted in a better understanding of diseases,
allowing new research to be targeted to more specific problmes. According to the US OTA (1991),
there are two basic approaches to using biotechnology in this sector: firstly to develop previously
artificially non-creatable human proteins such as human growth hormone using rDNA techniques,
and secondly to design synthetic molecules which can then be used to examine the workings of the
disease thereby enabling the use of the technology in designing drugs which interact in the disease
process. The first biotechnology based drug, recombinant human insulin developed in 1982 was
one such protein which was either not available or only in small quantities before biotechnology.
Human growth hormone is another such protein as are some of the cancer related drugs such as
Tissue plasminogen activator (tPA) which dissolves blood clots and is known to reduce the
incidence of heart attacks. Epogen, the best selling biotechnology drug so far, has been used in
dialysis related anaemia and a number of other drugs have been developed for treating different
strains of hepatitis, as well as AIDS related illnesses.
Thus biotechnology is being used to improve the quality of a number of vaccines and
diagnostics, among other medical products. The variety of products available to consumers will also
increase. Pharmaceuticals however, are never bought directly by the consumer or the patient from
the producer or the manufacturer. Instead, they are usually sold to doctors, or hospitals or retailers
5
such as chemists4. Demand for pharmaceuticals can therefore be expected to combine quality and
variety, as hospitals have to maintain a supply of all major drugs which can be demanded by
patients, even those with a lower quality. In fact, both horizontal variety, as in brand names and
like products, as well as vertical quality improvements, may increase in the long run. Another
argument for preferences for increasing variety is the number of diseases or different strains of the
same illness which prevail among patients. In many cases, a combination of different medicines
are prescribed for the same illness to different patients because of differences such as allergic
reactions to particular medicines. For these reasons therefore, a social planner or a doctor will
always ensure that a sufficient variety of medicines or treatments are available for use. Preferences
will therefore always be for increasing variety in this case.
The implications therefore appear to be, (i) that the various steps of invention and
innovation take place in different stages and are dominated by different players. In the
pharmaceutical sector, this is the case with small, specialized biotechnology companies, known as
the New Biotechnology Firms (NBTFs) that have dominated the process of applied R&D and
invention. The process of commercialization has placed demands upon these companies that are
often beyond their capabilities and they have had to turn to the large established firms, who often
have a long tradition of activity in this particular sector; and (ii) that society during each time period
will demand a variety of biotechnology based products, of different qualities. This is because for
a number of reasons peculiar to biology and medicine we argue that society will continue to demand
a variety of products of different qualities, even though the highest quality is available for the same
(quality adjusted) price. The sectoral structure of the particular model we develop below, is
therefore based upon these observations from biotechnology and consumer preferences reflect a
demand for variety but also a preference for higher quality products. In the next section, we set
up the model along the lines discussed above.
3. The Model
The economy is endowed with one factor, labour, with quality . There are two
4 US OTA (1991), p 83.
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sectors, one doing research while the other produces differentiated products. Innovations take place
in the R&D sector and are patented. The innovations become an input into the commercial sector,
resulting in the production of goods with higher quality. In each period, innovations in the R&D
sector result in new variants with improved quality and lower variable costs produced by the
differentiated sector. Quality weights as described in Flam and Helpman (1987), for quantities are
used in a love-of-variety utility function.
Because of the characteristics of the pharmaceutical sector where society’s preferences as
a whole were identified as being more relevant than those of individual consumers, we concentrate
here on society’s demand rather than that of the individual. The utility function specified therefore
relates to society’s utility function of the Spence-Dixit-Stiglitz type (see Helpman and Krugman,
1985, pp.118-120):
where is the quantity of quality demanded, while is the lowest and the highest quality
(1)
demanded by consumers. The parameter represents society’s constant utility elasticity for
quantity and as in the love of variety models, we specify theta to lie between 0 and 1. However,
in contrast to the love of variety utility functions, the specification here includes a quality weight.
In the exponential function, more importance is given to quality by society, the greater is the size
of alpha, while choice is independent of quality if (see Flam and Helpman, 1987).
According to this Spence-Dixit and Stiglitz specification, the number of varieties demanded
in each period is infinitely large whereas its integral measure is finite. As n grows, ceteris paribus
utility increases. A society with this utility specification maximises its utility, subject to the budget
constraint
where is price of quality and is the consumer’s labour income in each period. Maximiza-
(2)
tion of (1) with respect to (2) yields first-order conditions (see app.I.1 available upon request) from
which we can derive the relationship between price and quantity for values and of :
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where a relatively higher price implies lower preference given to quantity, and from this, we can
(3)
calculate the demand elasticity for differentiated goods,
This result is identical to the one obtained from the Spence-Dixit-Stiglitz function without quality
(4)
weights.
Next we turn to supply. We begin by specifying the structure of production in the
differentiated sector first, and then doing the same for the R&D sector. Labour , is allocated
between the two sectors, and has human capital of .
Producers in the differentiated sector licence the blueprint produced by the innovator in the
R&D sector, and produce higher quality products. The production function is assumed to be
where is quantity of quality and is an index of varieties, for which blueprints are
(5)
produced by the R&D sector and which are licensed by the producer in the differentiated sector.
As in Young (1991), labour input coefficients are lower for more recent varieties. By licensing
blueprint from the R&D sector, the producer in the differentiated sector becomes a monopolist
because of his impact on price according to (4). The monopolist minimizes production costs
where w is wage per efficient labour unit and is total variable cost. The producer earns
(6)
instantaneous profits
where is the cost of licensing from the R&D sector and is included in the cost because the
(7)
innovation is assumed to be licensed in each period from the innovator in the R&D sector. From
the first order conditions for cost minimization and profit maximization (see app. I.2), we get
. Profits have to be zero because under the assumption of free entry into the differen -
tiated sector, each potential producer offers all profits for every users right on a blueprint being
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auctioned off (see Romer, 1990). Thus, the minimized value for the cost function and the monopoly
price in the zero profit condition yield:
The R&D firm is characterised by innovators who are granted infinitely lived patents for
(8)
their innovations. The production function of the research sector is assumed to be
where is the flow of innovations and is a measure of cumulated learning, from each
(9)
innovation. Delta measures the elasticity of learning. If , the specification corresponds to that
of Shell (1967) and if , there is no learning as in Phelps (1966). Each innovation is patented
by its innovator and licensed out to the producer of a differentiated good. The producer maximizes
the sum of discounted cash flows over time from to infinity subject to the production function
(9) where is wage and is the licensing charge for innovation . is the rate of time
preference indicating that they prefer to receive profits earlier rather than later. The R&D firm
maximises the sum of profits from t to infinity. The Lagrangean is
From the first order conditions we can calculate (see app. I.3 below) the price of the most recent
(10)
blueprint:
The licensing fee for the most recent variant is therefore equal to the rate of time preference,
(11)
corrected for productivity of R&D or the value of new patents per efficient labour hour in R&D
equals the rate of time preference. determined in this way, one can solve for according to
(8) as a function of and .
Thus to briefly describe the basic elements of the model thus far, the economy is
characterised by an R&D sector which produces a flow of innovations based on labour , with
human capital and cumulated learning . Each innovation is granted an infinite
patent and the producer has to pay the innovator for licensing each innovation, . Access to
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the innovation grants the producer a monopoly over the production of that quality and the price of
the new good is equivalent to the monopolist’s marginal revenue or cost divided by theta. Having
completed the basic specification of the production and consumption sectors, we now move on to
calculating the labour market allocation between the two production sectors.
If we assume a regulation of monopoly that ensures zero profits each period, the costs of
innovation must be exactly equal to the revenues from licensing to the production sector, implying
that
We use this condition along with the zero profit condition in the differentiated sector, to calculate
(12)
the allocation of labour in each sector (see app. I.4). The result is
Thus, having calculated the labour allocation between the two sectors, we can now move
(13)
on to the dynamics of the system in equilibrium. The economy we have just described is
characterised by a constant share of labour in innovation, whose growth rate is described by the
production function of the R&D sector and can be shown as
From equation (3), the solution for prices, and the zero profit condition of the firm (8), we get the
(14)
following relationship between and where and are variants selected by the household
Hence and grow at the same rate, as do and . More recent variants yield higher fees
(15)
because they are produced at a lower cost and are desired more. Relative fees are constant over
time. From equations (8), (15) (5) and (11), it follows that
and where
(16)
(17)
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In the case of Shellian learning effects, the value of the license according to (11) is
negatively related to the learning or spillover effect. The growth rate of fees, quantities and labour
input for each variant is constant, and negatively related to the growth rate of innovations. If
learning is Phelpsian, then is only dependant on the rate of time preference and the growth rate
is zero. This is because since we have already established the growth rate of in (14), we can
conclude from this that as time goes to infinity, approaches but never exactly reaches zero in
the case of learning. If , approaches zero in the long run and .
The next step is to calculate the rate of change of . In equation (2) income equals expenditure
each period. We insert values of and of from the zero profit condition (8), in the
differentiated sector
which can be rewritten
(18)
From here we can calculate the differential equation for (see app. I.5). The dynamics of and
(19)
are described in (14) and (17) above. Thus we can write the general equations for and as
if and otherwise. If , only the most recent variant remains in the market.
(20)
This qualification will be dropped henceforth. The sign of depends on .
determines the level of , determines the speed of the decline in , and . If the
decline in these variables is strong (weak) enough in relation to the level of or , there will be
(no) room for a decrease in and (no) reselection of variety.
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Next, since we want to examine both the cases of perfect learning as in Shell and no
learning as in Phelps, we examine the specific solution for equation (20) in each case.
3.1. The Case of Delta = 1 (Shell)
The growth rate of has been calculated from (17) above. Using the case of delta = 1,
we insert in (20) and write
From which, putting ,
(21)
The growth rate thus becoming , or determines whether is
(22)
(23)
increasing or falling.
3.2 Delta = 0 (No Learning as in Phelps)
If we assume no learning, ie. delta = 0, then we have the following result for the change
in , where the only differences lie in the calculation of and the growth rate of . The value
of equals because delta is equal to 0. We can therefore rewrite equation (20)
(24)
Thus we have two variants of the differential equation (20), describing the dynamics of the re-
emergence and displacement of old products. In the Shellian case of strong learning (delta = 1),
new products enter and old products are displaced according to
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and in the case of no learning as in Phelps, delta = 0 and the two differential equations which
(25)
describe the range of varieties available in the economy at each time can be written
Thus while in the first case, strong learning effects, as expected, have a positive influence on the
(26)
rate of innovation, but also on the rate by which older products are dropped or reselected from the
consumption bundle (i) via the term in (23) and (ii) via the term in (20) which becomesn
in the Shellian case in (23). This is due to two reasons: firstly, the budget constraint
ensures that older products are dropped as the value of new products consumed increases. As the
latter rate increases, due to learning, the faster the rate of rejection of older products due to the
budget constraint. Secondly, with learning, the fixed cost of producers, , are decreasing.
Therefore the equilibrium quantity produced, according to (8), is also decreasing. The consumer
therefore buys less of each good, and has more room in the budget for old varieties. In the case
of no learning, the fixed cost of production, is not declining, resulting in the production of a
non-declining quantity. The consumer will therefore buy the same amount of each good and has
no more room in the budget for older varieties. In sum, given the price of each variety , as a
fixed mark up over marginal costs, the room for variety is determined by the dynamics of fixed
costs. Besides learning, the level of fixed costs from new varieties, matters as well. If it is high,
relative to the rate of decline of licensing fees, varieties will be selected away by consumers.
In more formal terms, if is increasing, contributing to decreasing variety. In the case
that , is decreasing, implying increasing variety, as older varieties are reselected.
Whereas determines the sign of , the exponential term from the quality weights in
preferences determines the speed of the change.
The second case of no learning is more straightforward, with both innovation and
replacement being driven by the demand elasticity, theta, and in addition, quality preferences. No
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learning implies that the fixed cost stays constant and since consumers have a fixed budget, old
varieties are rejected in favour of new varieties which enter the consumer’s consumption bundle.
An interesting case may arise from if initially , but makes fall according
to (14) such that after some time. Thus initially is decreasing, resulting in products
being reselected, but at a later stage, is increasing and converges to because (24) or (26) hold
in the limit as approaches zero.n̂
4. Implications for Product Variety: Some Results from Simulations
In order to study the dynamic system, we ran simulations using different parameter values
and combinations thereof. Before the simulations could be run however, the initial values of both
upper and lower bounds of the integral, i.e. and had to be established. With respect to the
first, different initial values can be chosen by assumption. However, for the latter, initial values had
to be calculated for each set of parameter values and the initial value used for . In this section
we present some of the more interesting results of these simulations, especially as they relate to the
earlier discussions on biotechnology and innovation. We describe first the case of strong learning
effects as in Shell and then the case of delta = 0.
4.1 The Case of Strong Learning Effects
Two separate trends are recorded in the case of strong private learning effects. In the
simulations, three different initial values of were used, 2, 4 and 8. The results from the first set
of simulations revealed that for higher values of and for higher values of , the two differential
equations go out of bounds very quickly. Thus the base values used were 0.83 for and 0.1 and
0.2 for . The value for the time preference rate , was varied. In the first instance low values
were used for this parameter, ranging from 3 percent to 10 percent5. In all the figures below6,
5 The range of values used for theta have been estimated using different models, to lie between0.83 to 0.9; see for example Gasiorek, Smith and Venables (1991) quoted in Abraham (1994). Therange of values estimated for time preference appear in general to lie between 1 and 4 percent (seeTrostel, 1993, p335).
6 Additional figures showing the results of simulations for a range of parameter values are available fromthe authors on request.
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the legends at the bottom of each graph, indicateinitial values for and for .
In the second instance, the case of was evaluated. The values for used,
ranged from 18 percent to 21 percent7. The case of 18 percent is shown below infigures 5 to 8.
As can be seen from these figures, the high rate of time preference completely offsets the negative
growth of in the previous case. With equal to 18 and equal to 0.1, i.e. low quality
weights, the result is an initial increase in variety, as the differential equation for increases faster
than that for (see for examplefigure 5). This is followed by a period of equal growth, with the
two curves almost parallel to each other (as infigure 6), and finally resulting in the crossing the
curve, which indicates that older varieties are eventually driven out by innovations (figures 7 and
8). The reason for this change from an increase to a decline in variety, is a higher rate of time
preference, implying that fixed costs and equilibrium quantity of are initially high and
therefore variety is low. However, the exponential impact of quality finally comes through,
crowding out variety through quality. A higher initial value for implies greater variety in the
beginning because the values are lower as are those for , thus leaving more room for variety.
7 This value of time preference, i.e. > 17% may seem rather large. However, if comparing thisgrowth rate to the results of estimates using patent data from the European Patent Office and theUS Patent Office which range from 10.27 in the US and 10.71 in Europe, then the rate of timepreference used here does not seem to be as large as at first. In the simulations however, it shouldbe noted that each time period is therefore greater than one year because of these differences in theactual growth rates as estimated from patent data, and the growth rates used in the model.
out and total variety declines. This case resembles descriptive accounts of the product cycle as new
products go through different stages of production associated with declining costs, eventually
driving out old products.
3. In the third case of no learning, the result is one of new products almost immediately driving out
older products. Here, because the fixed costs and equilibrium output levels are constant, consumers,
22
given their budget constraints are unable to buy a larger variety of products, and given preferences
for quality, older products are dropped in favour of higher quality, new products.
5. Conclusions
We have presented a closed economy growth model based on an R&D sector which
innovates and licenses its patented innovations to a production sector which produces differentiated
products. Only one factor of production is present.
The results of the simulations used to examine the dynamics of the system, presented a
number of interesting implications for variety, showing in specific, that depending upon the values
of certain parameters, the system had a wide range of implications for variety, ranging from the
creative destruction result of previous models such as Aghion and Howitt (1992) and Grossman and
Helpman, where only one variety is present, to the constant range of Flam and Helpman (1987) and
Young (1993) for long time periods, although not for the steady state, and to increasing variety,
such as in Young (1991).
This range of results also has interesting parallels with the empirical impact of quality
improvements through biotechnology, upon older products, and traditional technologies. For
example, in the case of genetic engineering, there is a case to be made for creative destruction as
in Grossman and Helpman, with a new product completely displacing an old product from the
consumer demand function. However, in a number of cases, old products are increasingly facing
competition, not from just one product, but from a number of different products and processes. For
example, in the case of sugar, although there was an initial fear that High Fructose Corn Syrup
(HFCS), would replace sugar over the years, despite a decline in the use of sugar, especially for
industrial use, there has also been a rise in the variety of substitutes being used as sweeteners. It
is estimated that more than 20 different sweeteners were in use in the 1980s8. In this instance,
therefore, a case can be made for increasing variety as in Young (1991) and as in this model, in the
case strong learning effects and .
Although it is relatively early to draw conclusions about a product cycle, there is some
evidence for this again from the case of HFCS. When HFCS was first developed, its costs were
too high for industrial use. A combination of declining costs of production and higher internal
prices especially in the EC, have ensured that HFCS is now the most widely used substitute for
sugar and although it has not succeeded in completely displacing sugar, this is probably due to the
fact that the two are imperfect substitutes for each other. A more recent sweetener such as
thaumatin which is used in crystallized form such as sugar, may pose a more strong challenge,
although due to its high cost of production, this is only likely in the distant future. For some cases
8 Panchamukhi and Kumar (1988).
23
however such as vanilla, substitutes are considerably cheaper, implying a faster rate of substitution
than was the case with sugar.
Finally, the reselection of older products one can argue, is also taking place in conjunction
with new technologies. For example, biotechnologies are making it increasingly possible to reselect
traditional products, whether through conservation of traditional products, or the use of tissue culture
and micropropagation techniques to multiply traditional agricultural products. The example of the
neemtree, a tree with astringent properties which is widely used across the Indian subcontinent by
indigenous medicine, can be used to illustrate this, where patents are now being granted to
traditional products and compounds developed from the properties of the tree, which is likely to
increase their consumption by a larger group of consumers, as the products become more widely
marketed.
Thus the model presents interesting dynamics with respect to innovation and substitution
of products driven by quality weights and the dynamics of variable and fixed costs.
References
Abraham, F. (1994), "Social Protection and Regional Convergence in an EMU",Open EconomiesReview,Vol.5, No. 1, pp 89-112.
Acharya, R. and J. Mugabe (1994), "Biotechnology in Developing Countries: Criticial Issue ofCapability Development", inBiotechnology Annual Review(Amsterdam: Elsevier SciencePublishers), Forthcoming.
Aghion, P. and P. Howitt (1992), "A Model of Growth Through Creative Destruction",Econometrica, Vol. 60, No. 2, pp 323-351.
Arrow, K. (1962), "The Economic Implications of Learning by Doing",Review of EconomicStudies, no. 29, pp 155-173.
Bio/Technology, Various Issues (1993 and 1994).
Clark, N. and C. Juma (1991),Biotechnology for Sustainable Development: Policy Options forDeveloping Countries, IFIAS and ACTS (Nairobi, Kenya: African Centre for Technology Studies).
Ernst and Young (1992),Biotech 93: Accelerating Commercialization, Ernst and Young’s SeventhAnnual Report on the Biotech Industry, (San Francisco: Ernst and Young).
Flam, H. and E. Helpman (1987), "Vertical Product Differentiation and North-South Trade",American Economic Review, Vol 77, No 5, pp 810-822.
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Grossman, G. and E. Helpman (1991b), "Quality Ladders in the Theory of Growth"Review ofEconomic Studies,no. 58, pp 43-61.
Helpman, E. and P. Krugman (1985),Market Structure and Foreign Trade: Increasing Returns,Imperfect Competition and the International Economy(Cambridge: MIT Press).
Orsenigo, L. (1989),The Emergence of Biotechnology: Institutions and Markets in IndustrialInnovations, (London: Pinter Publishers).
Panchamukhi, V.R. and N. Kumar (1988), "Impact of Biotechnology Revolution on CommodityExports of Developing Countries," (New Delhi: Research and Information System (RIS) for theNon-Aligned and Other Developing Countries).
Phelps, E.S. (1966), "Models of Technical Progress and the Golden Rule of Research",Review ofEconomic Studies, pp 133-145.
Romer, P. M. (1990), "Endogenous Technological Change",Journal of Political Economy, Vol. 98,pp S72-S102.
Scherer, F.M. (1984),Innovation and Growth: Schumpeterian Perspectives(Cambridge: MIT Press).
Sharp, M. (1990),Technological Trajectories and Corporate Strategies in the Diffusion ofBiotechnologyin E. Deiaco, E. Hörnell and G. Vickery (eds),Technology and Investment: CriticalIssues for the 1990s(London: Pinter Publishers).
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Shell, K. (1967), "A Model of Inventive Activity and Capital Accumulation" in K. Shell (ed),Essays in the Theory of Optimal Growth, (Cambridge, Ma.: MIT Press).
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25
NOT FOR PUBLICATION
Appendix I.1: First Order Conditions of Consumers
Society maximizes its utility subject to the budget constraint:
(1.1)
We specify the Lagrangean,
(1.2)
The time index of , and , and has been ignored. The first order conditions from thisproblem are (1.1) with equality and
(1.3)
I
Given the inequality in (1.3) above, . If (1.3) above holds with equality, it generates
the following price, quantity relationship for values and of :
(1.4)
We can calculate the demand elasticity for differentiated goods as,
(1.5)
This result is identical to the one obtained from the Spence-Dixit-Stiglitz function without qualityweights. Multiplying to equation (1.3) and integrating over yields
(1.6)
and the resulting equation after cancellation becomes
(1.7)
Since income equals expenditure, equation (1.7) reduces to
(1.8)
The solution for therefore is
(1.9)
where we take to be equal to 1. Defining , we can write
(1.10)
Appendix I.2: First Order Conditions in the Differentiated Sector
The producers’ first order condition for cost minimization with respect to is
II
(2.1)
which can be rewritten
(2.2)
which is the marginal cost of the monopolist. The first order condition from profit maximizationis
(2.3)
which means that marginal revenue equals marginal cost which is the monopolist’s optimal pricingcondition. From the first order conditions for consumer demand we have determined the priceelasticity of demand and from (2.3), we can calculate the marginal revenue of the monopolist:
(2.4)
implying that
(2.5)
and using equation (2.2)
(2.6)
Appendix I.3: First Order Conditions in the R&D Sector
The current value Hamiltonian for the R&D sector
(3.1)
yields the first order conditions
(3.2)
and an equation of motion for lambda
III
(3.3)
implying
(3.4)
The future impact of on is taken fully into account. Here we differ from Grossman and
Helpman where is a public factor.
From equation (3.2)
(3.5)
Inserting equation (3.5) in (3.3), this yields
(3.6)
If we take as the numeraire, multiplying with
(3.7)
and inserting from the production function (9) we solve
(3.8)
Appendix I.4: The Allocation of Labour
Taking the zero profit condition in the differentiated sector, equation (8), substituting for fromequation (5) and inserting we obtain
(4.1)
Equation (4.1) can be inserted into the zero profit condition of the R&D sector. This yields:
The second equation can be rewritten as
IV
(4.2)
(4.3)
Inserting according to (4.2) into the labour market equilibrium equation
(4.4)
we obtain the resource allocation
(4.5)
and
(4.6)
Appendix I.5: Calculating the Differential Equation for
Taking the derivative of (19) with respect to time t yields:
(5.1)
Multipling and dividing by in the integral term yields
(5.2)
Licensing fees do not fall over time if there is no learning, i.e., . With learning, thestronger the learning effect, the quicker licensing fees fall. From (15) in the text, we establishedthe relative relationship between and . From this we also concluded that the growth rate of
is independent of . We can therefore rewrite equation (5.2) taking the growth rate of before
V
the integral
(5.3)
inserting values for from (11) in the text, and the time derivative of n from the production
function, (9), and (4.6) for andN R
(5.4)
which, after cancellation can be rewritten
(5.5)
Solving for yields
(5.6)
From which we can calculate
(5.7)
From (15) we can calculate the value of as a function of and write
