Macro chapter 9 r and d based endogenous growth
in all our growth models the ultimate source of growth in GDP per worker is technological
progress. Up to now technological progress has been either unexplained or
unintentional. In this chapter and the next we will study growth models in wh ich technological
progress is the endogenous and deliberate outcome of a production process which
requires productive inputs.
The exogenous growth models of Part 2 postulated a fixed growth rate in the technological
variable A" so the driving Ioree of economic growth was basically unexplained. In
the externality-based endogenous growth models presented in the previous ch apter, A 1
was linked to aggregate capital (or income), so growth in A1 was endogenous and
'explained' by growth in capital, but technological progress was an unintentional byproduct
of economic activity in general. No agent was concerned with creating technological
progress, and no inputs were used lor the purpose of producing increases in A 1
•
In the real world many people are occupied v.rith producing better technology and
production methods in private companies as well as at private and public universities and
other organizations engaged in the creation of new knowledge. Thus, on the one hand,
the growth models we have considered so far trace economic growth back to tech nological
progress. which is not described as arising from an intentional production process,
and on the other hand. in the real world a lot of production explicitly intended to create
technological progress tal<es place. This is a bit of a paradox.
We will now begin to study growth models that bring research and development,
R&D. production processes explicitly into the picture. Our purposes are the usual ones: if
economic growth is rooted in technological progress, then by better understanding the
production process lor technological progress we gain a deeper understanding of growth.
This is an end in itself. and it may bring us better tools lor engineering growth-promoting
policies.
In our models technological progress will have a very precise meaning: there will still
be a technological variable, A 1• and technological progress '>Viii mean that A 1 increases.
The ultimate output of the R&D sector in period tis thus the total technological progress.
A,+ 1 - A" from period t to period t + 1.
We view the production process in the R&D sector as follows . Economic resources in
research and development (or in innovative ellort in general) produce ideas. These ideas are what ultimately bring better technology, that is. increases in A,. So. better tech11ology is
created by new ideas. where we interpret ideas in a broad sense. Ideas can be new insights in
basic research, such as Nev.rton's mechanics. calculus. Einstein's theory of relativL~m.
Bohr's atomic theory, etc. They can also be more 'close-to-the-factory· inventions of new
machinery, such as the steam engine or a new generation of computers, or better 'tools' for
existing machinery. such as a new or improved piece of software lor existing computers.
Furthermore. they can be ideas for new and more productive ways to organize production,
such as the assembly line, or they can be ideas for new intermediate or tina! products.
Ideas come from people. so the R&D production process has to be labour intensive. We
assume that the only inputs in the R&D sector are the labour power of 'researchers' and
the existing stock of knowledge, although in the real world also some capital is used in
R&D activities. We thus view the R&D sector as follows:
Inputs: The innovative ellort of labour and the existing level of technology
-create as Direct output: new insights and ideas
which result in Lhe
Ultimate output: a new and higher level of technology.
The fact that the direct output of the R&D sector essentially consists of ideas makes
the associated microeconomics more subtle than in the growth models we have considered
earlier. The reason is that ideas, viewed as economic goods, are like public goods.
They are 11on-rival: the fact that one person uses calculus or (the idea behind) a specific
spreadsheet in no way limits another person's ability to use calculus or the same kind of
spreadsheet. Ideas are also impe1jectly excludable, varying from absolutely non-excludable
(no person can be prevented from using calculus) to partly excludable (in principle people
are excluded from using a spreadsheet they h aven't paid for because using it without a
licence is a violation of law. but pirate copying takes place).
The non-rival character of ideas implies. as will be further explained in the next
chapter, that private production of ideas cannot take place under perfect competition .
Imperfect competition is therefore a necessary ingredient in a model of privately conducted
R&D. The fact that ideas are partly or fully n on-excludable implies problems with
private production, be it under perfect or imperfect competition.
We postpone an explicit treatment of the subtle microeconomics associated with
(private) R&D production to the next chapter. In this chapter we present a growth model
of a more conventional macroeconomic character. It abstracts from the underlying
microeconomics and postulates a number of growth and technology relationships. We
study the implications of these. It should be emphasized, however, that the model is not ad
hoc: one conclusion in the next chapter is that the properly micro-founded model studied
there implies (more or less) the macro model we study in this chapter.
2.1 R and d based macro growth model
The model we study in this chapter is meant to explain the relatively constant economic
growth of around 1. S- 2 per cent per year in the developed world. co11sidering tile developed
world as one large eco11omy. Since the economy we conslder will produce all of its technological
progress itself, and thus does not import technology developed elsewhere, it is
implicit that the model covers the entire developed world.
There will be two types of output: 'new technology', and fmal goods that can be used
for consumption or for investment in physical capital. We will now describe the production
processes for each type of output.
Production function of the firm..
Formally, the only new feature is that labour input is now denoted by L1,1 rather th an by
L ,. This is because there '<Viii also be a labour input. LA< . in the R&D sector and we have to
distinguish between the two. Another input is capital services, the amount of which we
assume to be proportional to the stock of capital. K,. Finally the technological variable. A,.
enters as usual.
From now we '<Viii think ofA 1 more as an input in line with K1 and Ly1• The variable A1
is the total productive eflect of the stock of all innovative ideas that have come into existence
up to period t. There are important diflerences between the input A, and the inputs
K1 and L1,1: llrst. the representative llrm cannot adjust its input of technology as it wishes.
From the point of view of each individual llrm, society's stock of ideas or technology. A,. is
given. Second, the fixed amount of technology. A,. can be used in every tirm because the
general level of technology is non-rival.
According to the replication argument. the production function should have constant
returns to the two rival inputs, K1 and Ly1 • as assumed in (1). Doubling production by
undertaking the same activities twice means doubling the inputs of capital and labour .for
a given inp1.tt oft.eclmology. As a consequence. the production function in (1) has increasing
returns in the three inputs, K,. Ly1 and A1, a feature that is important for our conclusions.
The production of new technology
The R&D sector also has one representative llnn. As usual we should distinguish between
its two roles. On the one hand. it produces the entire output. A,+ 1 - A,, of new tech nology
in period t (since there is only this one firm) . On the other hand. the firm is actually to be
considered as one of many small firms and therefore it only has a negligible intluence on
the aggregates of the R&D sector, that is. on the total input oflabour, LAr• and on the total
output. A:+ 1 - A1, produced in the sector in period t. Consequently, the representative
llrm in the R&D sector tal<es the stock of technology as given at any point in time. just lil<e
the firm in the final goods sector does.
progress. Up to now technological progress has been either unexplained or
unintentional. In this chapter and the next we will study growth models in wh ich technological
progress is the endogenous and deliberate outcome of a production process which
requires productive inputs.
The exogenous growth models of Part 2 postulated a fixed growth rate in the technological
variable A" so the driving Ioree of economic growth was basically unexplained. In
the externality-based endogenous growth models presented in the previous ch apter, A 1
was linked to aggregate capital (or income), so growth in A1 was endogenous and
'explained' by growth in capital, but technological progress was an unintentional byproduct
of economic activity in general. No agent was concerned with creating technological
progress, and no inputs were used lor the purpose of producing increases in A 1
•
In the real world many people are occupied v.rith producing better technology and
production methods in private companies as well as at private and public universities and
other organizations engaged in the creation of new knowledge. Thus, on the one hand,
the growth models we have considered so far trace economic growth back to tech nological
progress. which is not described as arising from an intentional production process,
and on the other hand. in the real world a lot of production explicitly intended to create
technological progress tal<es place. This is a bit of a paradox.
We will now begin to study growth models that bring research and development,
R&D. production processes explicitly into the picture. Our purposes are the usual ones: if
economic growth is rooted in technological progress, then by better understanding the
production process lor technological progress we gain a deeper understanding of growth.
This is an end in itself. and it may bring us better tools lor engineering growth-promoting
policies.
In our models technological progress will have a very precise meaning: there will still
be a technological variable, A 1• and technological progress '>Viii mean that A 1 increases.
The ultimate output of the R&D sector in period tis thus the total technological progress.
A,+ 1 - A" from period t to period t + 1.
We view the production process in the R&D sector as follows . Economic resources in
research and development (or in innovative ellort in general) produce ideas. These ideas are what ultimately bring better technology, that is. increases in A,. So. better tech11ology is
created by new ideas. where we interpret ideas in a broad sense. Ideas can be new insights in
basic research, such as Nev.rton's mechanics. calculus. Einstein's theory of relativL~m.
Bohr's atomic theory, etc. They can also be more 'close-to-the-factory· inventions of new
machinery, such as the steam engine or a new generation of computers, or better 'tools' for
existing machinery. such as a new or improved piece of software lor existing computers.
Furthermore. they can be ideas for new and more productive ways to organize production,
such as the assembly line, or they can be ideas for new intermediate or tina! products.
Ideas come from people. so the R&D production process has to be labour intensive. We
assume that the only inputs in the R&D sector are the labour power of 'researchers' and
the existing stock of knowledge, although in the real world also some capital is used in
R&D activities. We thus view the R&D sector as follows:
Inputs: The innovative ellort of labour and the existing level of technology
-create as Direct output: new insights and ideas
which result in Lhe
Ultimate output: a new and higher level of technology.
The fact that the direct output of the R&D sector essentially consists of ideas makes
the associated microeconomics more subtle than in the growth models we have considered
earlier. The reason is that ideas, viewed as economic goods, are like public goods.
They are 11on-rival: the fact that one person uses calculus or (the idea behind) a specific
spreadsheet in no way limits another person's ability to use calculus or the same kind of
spreadsheet. Ideas are also impe1jectly excludable, varying from absolutely non-excludable
(no person can be prevented from using calculus) to partly excludable (in principle people
are excluded from using a spreadsheet they h aven't paid for because using it without a
licence is a violation of law. but pirate copying takes place).
The non-rival character of ideas implies. as will be further explained in the next
chapter, that private production of ideas cannot take place under perfect competition .
Imperfect competition is therefore a necessary ingredient in a model of privately conducted
R&D. The fact that ideas are partly or fully n on-excludable implies problems with
private production, be it under perfect or imperfect competition.
We postpone an explicit treatment of the subtle microeconomics associated with
(private) R&D production to the next chapter. In this chapter we present a growth model
of a more conventional macroeconomic character. It abstracts from the underlying
microeconomics and postulates a number of growth and technology relationships. We
study the implications of these. It should be emphasized, however, that the model is not ad
hoc: one conclusion in the next chapter is that the properly micro-founded model studied
there implies (more or less) the macro model we study in this chapter.
2.1 R and d based macro growth model
The model we study in this chapter is meant to explain the relatively constant economic
growth of around 1. S- 2 per cent per year in the developed world. co11sidering tile developed
world as one large eco11omy. Since the economy we conslder will produce all of its technological
progress itself, and thus does not import technology developed elsewhere, it is
implicit that the model covers the entire developed world.
There will be two types of output: 'new technology', and fmal goods that can be used
for consumption or for investment in physical capital. We will now describe the production
processes for each type of output.
Production function of the firm..
Formally, the only new feature is that labour input is now denoted by L1,1 rather th an by
L ,. This is because there '<Viii also be a labour input. LA< . in the R&D sector and we have to
distinguish between the two. Another input is capital services, the amount of which we
assume to be proportional to the stock of capital. K,. Finally the technological variable. A,.
enters as usual.
From now we '<Viii think ofA 1 more as an input in line with K1 and Ly1• The variable A1
is the total productive eflect of the stock of all innovative ideas that have come into existence
up to period t. There are important diflerences between the input A, and the inputs
K1 and L1,1: llrst. the representative llrm cannot adjust its input of technology as it wishes.
From the point of view of each individual llrm, society's stock of ideas or technology. A,. is
given. Second, the fixed amount of technology. A,. can be used in every tirm because the
general level of technology is non-rival.
According to the replication argument. the production function should have constant
returns to the two rival inputs, K1 and Ly1 • as assumed in (1). Doubling production by
undertaking the same activities twice means doubling the inputs of capital and labour .for
a given inp1.tt oft.eclmology. As a consequence. the production function in (1) has increasing
returns in the three inputs, K,. Ly1 and A1, a feature that is important for our conclusions.
The production of new technology
The R&D sector also has one representative llnn. As usual we should distinguish between
its two roles. On the one hand. it produces the entire output. A,+ 1 - A,, of new tech nology
in period t (since there is only this one firm) . On the other hand. the firm is actually to be
considered as one of many small firms and therefore it only has a negligible intluence on
the aggregates of the R&D sector, that is. on the total input oflabour, LAr• and on the total
output. A:+ 1 - A1, produced in the sector in period t. Consequently, the representative
llrm in the R&D sector tal<es the stock of technology as given at any point in time. just lil<e
the firm in the final goods sector does.
Comments
Post a Comment