Growth theory began with Solow (1956) and Swan (1956) formalizing an economic growth framework. Later models endogenized technical progress, including Arrow (1962) on learning by doing, Lucas (1988) on human capital accumulation, and Romer (1990) on R&D-driven innovation. The book provides an overview of these models and extensions, examining issues like the role of public policy, demographics, money, and sustainable development. It aims to demonstrate how growth theory tools can be applied to answer different economic questions.

1. I Introduction
I.1 Evolution of growth theory
Growth Theory is a young field in economics relative to others. The first
formalization of an economic growth framework can be attributed to Solow (1956,
1957) and Swan (1956), though the main ideas and issues discussed nowadays in
growth theory were developed for years by authors such as Smith (1776), Malthus
(1798), Ricardo (1817), Ramsey (1928), Young (1928), Schumpeter (1934). Solow’s
and Swan’s frameworks were considered as the main reference until the mid-eighties,
the period of emergence of the new theory of growth. Although the new growth
theory appears to be radically different from the first formalization of growth
proposed by Solow (1956, 1957) and Swan (1956), it is worthwhile to mention that
understanding the mechanisms which are working in this canonical model is essential
to further extend the analysis to more modern theories. Thus, it will be the starting
point of this book.
Based on this framework, economists who have attempted to identify the
determinants of economic growth estimated that technical progress accounted for
approximately two thirds of growth during the first half of the 20th century. The main
question, which was raised, was the following: how can technical progress be
formalized? As we will see, in a first step, technical progress was formalized as a

2. variable which grows at an exogenous rate. Such formalization helped to explain
several stylized facts and empirical regularities. However, it quickly appeared that to
address the central questions of growth theory, it was necessary to go beyond the
Solow-Swan framework. Many progresses have been realized when economists have
attempted to answer the following questions:
• What are the determinants of technical progress?
• How does technical progress affect the various components (variables) of the
economy?
• How does technical progress manifest itself in the economy?
To answer these questions, economists have attempted to endogenize technical
progress. The first attempt is due to Arrow (1962). He observed the case of an
empirical regularity in aeronautics. Once a new plane was made, the time required to
make a new one was inversely proportional to the cubic root of the number of planes
already made. Based on this feature, Arrow argued that the repetition of an activity
can generate new knowledge. Individuals improve their productivities through
practices, that is nicknamed learning-by-doing. In the same vain, in the mid-eighties,
Romer (1986) reexamined the model of Frankel (1962) assuming that new
knowledge is the outcome of investments of firms. When firms invest, they
simultaneously learn how to produce more efficiently: this is called learning-by-
investing. As we will see, the main contribution of Arrow (1962), Frankel (1962) and
Romer (1986) has been to formalize the idea that technical progress is the outcome of
external effects. A consequence of this formalization is that the competitive
equilibrium is not optimal and displays an insufficient rate of growth compared to the
optimum. Since the decentralized market fails to allocate resources optimally, public
policies are called upon in order to implement the optimum. In these frameworks, then, the
novelty is that the government can play an active role both in affecting the level of the
variables and also their long-run level of growth.
More progress has been made in growth theory following the newer wave of growth
models initiated by Lucas (1988). In his seminal article, Lucas put in evidence the
2 | Growth Theory: Basic Models with Alternative Applications

3. key role of human capital in economic development. Human capital is a broad
concept. It can be defined as a means of production of a person comprising his/her
level of education (knowledge), health status, motivation, and other skills (innate or
acquired on the job, through training and experience). Paradoxically, despite its
various dimensions, human capital has been reduced to its simplest form by a
majority of growth theorists who took this variable as a proxy for education, i.e. the
stock of knowledge embedded in individuals. One reason which induced this
simplifying choice is perhaps the empirical findings of Mankiw, Romer and Weil
(1992). In their influential work, they added the factor education in the form of years
of schooling to a standard growth regression and showed that to become a rich
country, it is necessary not only to work hard but also to invest in schooling
activities. Ceteris paribus, an interpretation is that individuals accumulate skills, a
form of which being knowledge. In this respect, Lucas’ (1988) main contribution is
to introduce an explicit theory where new knowledge is produced through an
independent activity. Individuals decide on their own about investments to be made
in education. That is, they decide whether to attend school and increase their
productivity or to enter in the labor market and earn a wage-income.
The idea of private investments in the knowledge production sector is fundamental in
growth literature. In the early nineties, Romer (1990), Grossman and Helpman
(1991a), Aghion and Howitt (1992) have extended this notion and developed
frameworks in which knowledge is the outcome of private decisions of firms to
invest in research and development (R&D). These frameworks have largely
contributed to give a new interpretation on the determinants of technical progress, in
particular, by taking into account the existence of intellectual property rights. They
show how knowledge may appear as a key factor for long-run growth and how
technological progress may take place in the economy: firms invest in research and
are granted a monopoly on the production and the sale of innovations. In this kind of
framework, technical progress is the outcome of innovative activities which allow
firms to introduce new technologies or to improve the existing ones. The crucial
contribution of R&D-based models is to put the private production of knowledge at
the center of the analysis.
Introduction | 3

4. Since the emergence of the R&D-based literature, no fundamental progress has
changed the face of Growth Theory, although few adjustments that we will review in
this book have been made. Hence, to summarize, we can say that knowledge
accumulation, which is the key ingredient to sustain long-term per-capita growth, can
take various forms, the main ones being: (i) an unintended learning by doing or
investing process; (ii) a human capital accumulation process; (iii) an innovation
process coming from a R&D activity. These ideas will be developed in turn. The
detail of the plan of the book is given in the next sub-section.
I.2 Structure of the book
This book is designed (i) to provide a comprehensive overview to the various
theoretical works that have been developed for the analysis of the process of long-
term income per-capita growth and (ii) to show how we can apply the various tools
developed in growth models to answer a number of very different questions which
have the potential for interesting future research. For this purpose, the structure of
this book is very simple. In reviewing the central questions that have been treated in
growth theory, we present a series of topical issues which have been the subject of
intensive research in the past few years. The plan is as follows.
In chapter 1, we present an augmented version of the so-called Solow (1956) model
in that we introduce technical progress growing at an exogenous and constant rate.
This formalization, which is in line with Swan (1956) and Solow (1957), builds the
main foundations of the more sophisticated models presented in the next chapters.
We show the main principle of growth theory via the fundamental law of motion of
physical capital and clearly distinguish between steady state or balanced growth path
and transitional dynamics.
In chapter 2, we analyze the Ramsey-Cass-Koopmans model initiated by Cass (1965)
and Koopmans (1965). This chapter will allow us to capture in a deeper way the main
mechanisms surrounding growth models. Although, long-term growth is still
exogenous, we show that this framework can be interpreted as a simple extension of
the original frameworks of Solow (1956, 1957) and Swan (1956). In this model, the
4 | Growth Theory: Basic Models with Alternative Applications

5. shares of income that are saved and consumed are endogenously determined by
individuals who have preferences represented by a utility function. In other words,
we capture a fundamental individual’s intertemporal behavior that is the trade-off
between consumption and savings. In an extension of this basic framework and to
further analyze the other potential trade-offs that individuals face in the real world,
we introduce the concept of endogenous labor supply. That is, we examine the trade-
off between leisure and consumption in a dynamic setting.
In chapter 3, we analyze the broad family of AK frameworks or one-sector models of
endogenous growth. These are the most basic models in which growth arises in an
endogenous manner. It includes the standard “AK” model, but also the model of
learning by investing due to Frankel (1962), re-examined by Romer (1986), and the
model of government expenditures due to Barro (1990). Importantly, these
frameworks have allowed economists to raise various issues related to the factors
affecting economic development, among which government policies play a key role.
We provide various and very different examples of research articles which have been
developed using these kinds of models. First, we show how to integrate the notion of
demography and analyze its effects on long-term growth. To proceed, we follow
Blanchard (1985) and construct an endogenous growth model in continuous time in
which individuals have a finite lifetime. In another extension, we show how to
introduce money in a growth model and analyze the effects of monetary policy on the
long-term growth rate. Then, in extending the Frankel-Romer model, we discuss the
role of socioeconomic factors as a possible ingredient promoting or deterring
investments in growth enhancing activities. In particular, based on Tournemaine and
Tsoukis (2008), we show the role of social aspirations in consumption and wealth on
the trade-off between consumption and savings. Finally, following Alesina and
Rodrik (1994), we raise the issue of the relationship between growth and inequality
and examine it from a political economy perspective.
In chapter 4, we deal with a more refined concept of endogenous growth as we show
how human capital accumulation (in the sense of educating individuals) can be
interpreted as a crucial ingredient to sustain long-term per-capita growth. After
examining a simple version of the seminal model of Lucas (1988), which itself
Introduction | 5

6. strongly builds on the model of Uzawa (1965), we follow the steps of Glomm and
Ravikumar (1992), Saint-Paul and Verdier (1993), Zhang (1996). We raise the issue
of the democratic choice between a publicly funded educational regime and a
privately funded one. Interestingly, beyond this issue, this extension also allows us to
discuss about the relation between growth and distribution. In our continuing
investigation of how to apply the basic tools of growth theory, we then show how to
introduce endogenous population growth to account for the idea that individuals
choose not only the amount of resources to allocate to education and working
activities (such as output production), but also those to be devoted to bring up
children. That is, in line with Becker, Murphy and Tamura (1990), we discuss the
role of the quality-quantity trade-off on children for economic development. Finally,
following authors such as Grimaud (1999, 2009) and Schou (2000, 2002), we discuss
the fundamental question of sustainable development in the presence of a polluting
and exhaustible resource such as coal or oil.
In chapter 5, we examine how the R&D-based literature initiated by Romer (1990),
Grossman and Helpman (1991a), Aghion and Howitt (1992) has formalized the
existence of intellectual property rights to capture the idea that profit maximizing
firms invest resources in R&D to produce knowledge which fosters technical
progress and economic development. To proceed, we first review a simple model of
expanding variety of products which captures the main elements of the original
Romer’s (1990) framework and analyze a simple model of vertical differentiation
that accounts for the ideas developed by Grossman and Helpman (1991a), Aghion
and Howitt (1992). Then, we discuss the various developments which have followed
the emergence of this literature. In particular, we present the semi-endogenous
growth literature initiated by Jones (1995a), Kortum (1997), Segerstrom (1998),
extended by Redding (1996), Arnold (1998), Blackburn, Hung and Pozzolo (2000),
Dalgaard and Kreiner (2001), Strulik (2005), Boonprakaikawe and Tournemaine
(2006), in that it combines the ideas of the basic R&D-based models with the model
of endogenous human capital accumulation developed by Lucas (1988). Finally, we
discuss about the recent evolution of intellectual property law which has followed the
emergence of new technologies. Based on Grimaud and Tournemaine (2006),
Chantrel, Grimaud and Tournemaine (2011), we argue that the basic R&D-based
6 | Growth Theory: Basic Models with Alternative Applications

7. models need to be slightly modified to account correctly for this evolution and we
propose a simple manner to account for this feature.
To close this book, in chapter 6, we discuss about the issue dealing with the
relationship between population growth and economic development. There are two
main reasons. First, the idea whereby people’s standard of living can continue to
grow over-time along with an increasing population caused a continuing debate in
economic literature. As we will see there is no clear consensus regarding the relation
between population growth and long-term economic growth: both empirical and
theoretical studies suggest either a positive or a negative correlation. Second,
population growth is rarely a focus of its own in growth theory. This variable is often
treated as an exogenous parameter although it is obviously endogenous. It is
influenced by various factors: some may be under the control of individuals such as
the decision to have or not children; while others can be external such as the
mortality of people which can for instance be affected by the quality of the
environment in which they live. In this book, we will discuss about population
growth as the outcome of the decision of individuals to bring up children. Based on
Tournemaine (2007), we will discuss about this issue in a unified framework in
which technical progress, human capital and population arise endogenously. Such
framework, will allow us to show that population and income per-capita growth can
either be positively or negatively correlated. That is, we embrace a balanced
perspective which certainly places the population debate on a firmer and more
conductive direction for future research.
Introduction | 7