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 | Growth Theory: Basic Models with Alternative Applications

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

Introduction | 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.

4 | Growth Theory: Basic Models with Alternative Applications

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

Introduction | 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

6 | Growth Theory: Basic Models with Alternative Applications

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

Introduction | 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.