The dynamic approach to heterogeneous innovations [Elektronische Ressource] / Anton Bondarev. Fakultät für Wirtschaftswissenschaften. Institut für mathematische Wirtschaftsforschung

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• Publié par: universitat_bielefeld
• Publié le: 01 janvier 2011
• Nombre de lectures: 22
• Langue: English
• Poids de l'ouvrage: 3 Mo

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The Dynamic Approach to Heterogeneous
Innovations
(Anton Bondarev)The author thanks H. Dawid, F. Riedel, J.-M. Bonniseau and I. G. Pospelov.
Abstract. In this work the dynamical framework which combines di erent
aspects of innovative activity is analyzed. First the basic model with nite
time horizon is constructed where the single agent (planner) is optimizing his
stream of investments into the process of creation of new products together
with investments into the improvement of already invented products. The
range of products which might be invented is given by the bounded real inter-
val. Next the role of heterogeneity of the investment characteristics of these
new products is analyzed and it is demonstrated that this heterogeneity plays
the essential role in the dynamics of the model. Further on the analysis is
extended to account for long-run behavior of the planner on the in nite-time
horizon. Steady-states of the system are derived and their stability is ana-
lyzed. Two following chapters of the work deal with two di erent extensions
of the basic model. Possibilities for further analysis of the given approach and
the di erence in conclusions and policy implications with earlierhes
to innovations’ analysis are demonstrated. First the e ect of patenting policy
on the innovative activity is taken into account. There the diversity of pos-
sible outcomes with respect to the patent’s length is demonstrated and it is
argued that this e ect may not be captured without the precense of hetero-
geneity of innovative products under analysis. In the last chapter the extension
which introduces several innovating agents is considered. There the subsequent
optimal control problem is transformed into the di erential game in in nite-
dimensional space. The set of piecewise-constant strategies is derived and it
is shown to be the only one stable set in the class of at most linear feedback
strategies. In an e ect the specialization of innovative activity between agents
is observed and it is demonstrated that this specialization has a foundation
in internal characteristics of these agents. The suggested work provides sev-
eral prospects for further enrichment and development in all the areas being
considered.Contents
Preface 1
Chapter 1. Product and Quality Innovations: A Uni ed Approach 7
1. Introduction 7
2. Assumptions and Basic Framework 10
3. Model 11
4. Theoretical Results 12
5. General Solution 14
6. Homogeneous Products 16
7. Linear Model 19
8. Quality Investments 22
9. Parametric Analysis 24
10. Discussion 26
Chapter 2. In nite Time Horizon Problem 29
1. Introduction 29
2. Monopolist Problem Formulation 29
3. Quality Growth Problem 30
4. Variety Expansion 32
5. Steady States 33
6. Parameter In uence 35
7. Discussion 39
Chapter 3. Patents in Heterogeneous Innovations Framework 43
1. Introduction 43
2. Finite Time Patents 44
3. Quality Growth in Patent Model 46
4. Variety Expansion Process in the Patent Model 48
5. Homogeneous vs Heterogeneous Products in Finite-Time Patents
Setting 52
6. Compensation E ect vs Potential Pro t E ect 55
7. Distributional E ects 60
8. Parameters’ In uence in the Patenting Model 63
9. Discussion 66
Chapter 4. Strategic Interactions in Heterogeneous Innovations Framework 69
1. Introduction 69
2. Strategic Interactions in Heterogeneous Innovations Framework 71
3. Basic Problem Formulation 73
4. Decomposition Method in Di erential Game Setting 74
5. Quality Growth Problem 76
6. Variety Expansion 106
7. Discussion 120
Bibliography 125
34 CONTENTS
Appendix 127Preface
One of the basic sources of economic growth is technological progress, as it is
argued by economic growth theory. Technological progress emerges as a result of
the innovative activity of economic agents. That’s why modeling innovations is one
of the key areas of modern economics. Starting from 1960’s there have been a lot
of attempts of such modeling and incorporation of innovations into macroeconomic
models. This strand of literature is concentrated on the e ects of technological
progress on the economic growth, rather then on the nature and source of this
progress. That’s why nowadays these theories are referred to as theories of exoge-
nous technological progress and/or exogenous economic growth. It was soon recog-
nized, that it is important to model explicitly the process of innovations themselves
to endogenize the technological progress. First such attempts have been made in
the era of classical growth theory in 1960’s. All these theories may be divided into
three groups: disembodied technological change, embodied technological change
and induced technological change.
In the framework of neoclassical growth theory the technological change has
been treated as the only source of economic growth and this source of growth re-
ceived much of the attention of economists. First explicit models of technological
change were that of disembodied one. They assumed that technological progress is
re ected in the growth of productivity of labour and capital in the aggregate pro-
duction function. There was no explicit formulation of micro-foundations of such
growth of productivity of factors. They have been assumed to grow with some ex-
ogenous rate. Such an approach was not satisfying to explain technological change
as it was not compatible with stylized facts and moreover, such a technological
progress had to be Harrod-neutral all the time (that is, only the productivity of
capital may increase over time, not that of labour) which is not the case.
Another approach, that of induced technological change, endogenized techno-
logical progress and made it the object of pro t maximization on the rms’ level.
However, this rate of progress does not depend on any resources and is bounded
from above by some invention frontier which is not allowed to drift in time. This
approach is much closer to present-day ones and bears signs of the microfoundation
of technological progress. Examples of such models may be found in [47], [48]. It
is this strand of literature where the research sector of economy was rst modeled
as a separate one and the role of human capital has been recognized, [50], [51]. At
that time the interest in patent’s length has risen. This is closely related to the
discussion of the role of innovative entities in the economy , see [20].
Last neoclassical concept is that of embodied technological change. There the
technological growth is embodied in factors of production and is distributed over
time when these factors have been produced. This is one of the foundations for
recent vintage models and methods being used in this literature are also employed
in the suggested work for other purposes. One of the scarce works on this is [53].
In summary, some of the neoclassical models already contained ideas of product va-
rieties, developed further on and that of distributed nature of technological progress.
However these concepts have been developed in full only later on.
12 PREFACE
At the beginning of 1990’s two new approaches to innovations in growth the-
ory emerged, namely, Romer’s (1990) model of expanding variety of products and
Aghion&Howitt’s (1993) model of quality ladders. Each of them addressed di er-
ent aspects of innovative activity, but they both have been built on the idea of
endogenizing technological change through means of modeling innovative activity.
First of them explained technological progress as the process of invention of
new goods. This idea originated from works of Dixit&Stigliz, Ethier, Spence [45],
[44], [46]. The nal widely accepted form of this approach is represented by works
of Romer (1990) and Grossman&Helpman (1991). In these works the technological
progress is modeled as the process that expands the variety of products available
on the market, thus stimulating growth through increase in the consumer demand
(Dixit-Stigliz theory) or through increase in the productivity (Romer’s model).
However, quality (or productivity in the case of investment goods) was assumed to
be constant. This idea lacked the precense of capital or other durable goods which
would grant rise in productivity and this approach was sensitive to scale e ects.
To overcome these di culties a number of extensions to this approach has been
considered in last two decades. Namely the assumption of rising costs of R&D has
been employed to weaken the scaling e ect and this is also one of the reasons of
adoption of the similar assumption in the given work. Some competitive e ects
has been considered also, as well as introduction of knowledge as one of the factors
of production [54], [55], [26]. Current work bene ts from some of the ideas used
in these extensions, namely the initial knowledge about varieties is one of the key
factors of the dynamics as well as rising costs of innovations at the quality side
(decreasing e ciency of investments).
Second approach explained technological change as the process of creative de-
struction of products, based on the idea of Schumpeter, [7]. Every product is as-
sumed to have varying quality, which may be increased through investments, while
the outcome of these investments is assumed to be uncertain. However, quantity
or variety of goods available on the market is assumed to be