Can Endogenous Growth Theories Explain Growth in South Tyrol and Luxembourg?

Table of Contents

Abstract

Zusammenfassung

Riassunto

Table of Contents

List of Equations

List of Figures

List of Abbreviations

1 Introduction
1.1 Object of Analysis: Growth in South Tyrol & Luxembourg
1.2 Structure

2 The Evolution of Endogenous Growth Theories
2.1 Neoclassical Growth Theory with Exogenous Growth
2.1.1 The Solow-Model
2.1.2 Shortcomings of Neoclassical Conceptions
2.1.2.1 Assumptions
2.1.2.2 Convergence Controversy
2.2 The Origins of Endogenous Growth Models
2.2.1 The Passing of Perfect Competition – 5 Facts
2.2.2 Learning by Doing – Arrow’s Approach
2.2.3 Adding Human Capital – Lucas’ Approach
2.2.4 Knowledge Spillovers & Increasing Returns – Romer’s Approach
2.2.4.1 Romer’s Work of 1986
2.2.4.2 Romer’s Work of 1990
2.2.5 Neo-Schumpeterian Growth Models
2.3 Critical Reflections on Endogenous Growth Theory
2.3.1 Critique
2.3.2 Practical Relevance

3 Matching Growth in South Tyrol & Luxembourg
3.1 Background Facts
3.1.1 South Tyrol
3.1.2 Luxembourg
3.2 Data & Methods
3.3 Historical Growth Observations
3.4 Composition of GDP’s & Characterization of the Economies
3.4.1 Tourism in South Tyrol
3.4.2 Financial Intermediation in Luxembourg
3.5 Analysis of One Major Growth Factor Suggested by EGT – Human Capital
3.5.1 Mahroum’s 3D Framework
3.5.2 The Cumulative Growth of Human Capital
3.5.3 The Human Development Index
3.6 Alternative Explanations outside Endogenous Growth Theories
3.6.1 The Case of South Tyrol
3.6.2 The Case of Luxembourg

4 Conclusion

References

Appendix

List of Equations

Equation 1: Solow's Basic Production Function

Equation 2: Change in Stock of Capital

Equation 3: Extension of Solow's Production Function

Equation 4: Aggregate Production Function in a Competitive Market (including Human Capital)

Equation 5: Arrow's Model

Equation 6: Lucas' Model

Equation 7: Romer’s Spillover Model

Equation 8: Romer’s Production Function for Firm j

Equation 9: Romer’s Production Function for Firm j - Learning by Doing included

Equation 10: Romer’s Aggregate Production Function with Increasing Returns

Equation 11: Romer's Production Function with Separable Inputs

List of Figures

Figure 1: Self-built Table with Key Data of both Regions

Figure 2: Map of South Tyrol – Districts and their Principal Towns

Figure 3: Map of Luxembourg – Districts and their Principal Towns

Figure 4: GDP per Capita (PPP)

Figure 5: Population Growth

Figure 6: Gross Value Added 2007 at Market Prices

Figure 7: Gross Value Added 2007 at Market Prices - Broken Down

Figure 8: Gross Value Added in Services 2007 in South Tyrol at Market Prices

Figure 9: Gross Value Added in Services 2007 in Luxembourg at Market Prices

Figure 10: Value Added of Tourism, divided by Sub-Sectors in 2008

Figure 11: Effects of Tourism on Sub-Sectors 2008

Figure 12: Growth of Holding Companies in Luxembourg

Figure 13: Growth of Banks in Luxembourg

Figure 14: HDI Trends 1980 – Present

Figure 15: Trend in HDI Component Indices

Figure 16: History of Arrivals and Overnight Stays in South Tyrol

Figure 17: GDP per Capita (PPP) (US$)

Figure 18: Population Structure of Luxembourg

Figure 19: Share of Foreigners & Foreign-Born of Total Population 2010.

List of Abbreviations

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1 Introduction

The analysis of economic growth has always been a fascinating science and has bred a lot of research from notable economists. Especially the theories and views of how an economy transforms from a lower level to a higher level of welfare are frequently discussed.

Aghion et al. (1998, p. 1) stated that “economic growth involves a two-way interaction between technology and economic life: technological progress transforms the very economic system that creates it. The purpose of endogenous growth theory is to seek some understanding of this interplay between technological knowledge and the various structural characteristics of an economy and the society, and how such an interplay results in economic growth.”

1.1 Object of Analysis: Growth in South Tyrol & Luxembourg

The aim of this thesis is the analysis of the two economies of South Tyrol and Luxembourg regarding their economic growth. The question is not only how and why they grow, but more specific whether their growth can be explained by arguments of endogenous growth theory.

One might ask now two questions:

Why endogenous growth theories? And why exactly are these two economies of interest?

The advantage of endogenous growth models in contrast to neoclassical concepts is that they provide tools to handle endogenous technological change, innovation and other factors within a dynamic general equilibrium setting. Therefore, they allow for the application of tractable and flexible models that display the vision of economic life as an endless succession of innovation and change caused by competition. Well-known economists like Schumpeter have long pointed out the importance of endogenous technological progress for growth. Aghion et al. (1998) hence argue that endogenous growth theory is indeed ideally suited for studying the problem of sustainable economic development. In order stay within the scope of this thesis, only one major factor suggested by endogenous growth theory will be analyzed – human capital.

The answer to the second question is that South Tyrol and Luxembourg are highly comparable because both are very small economies with a scarcity of natural resources; they have an almost equal number of inhabitants, lie at a relatively close geographical position to each other and exhibit a multilingual population.

For the analysis of the possible relationships and interconnections, it is important to look closely at the historical economic development and anatomize both economies. Investigating about the engines of growth by disassembling the economies’ value added can give insights and provide tools to answer the questions about their growth factors.

Since human capital is a very complex concept and nearly impossible to measure in a quantitative manner, we will search for its indicators like levels of education, income, etc. To identify its components and driving forces, we will utilize Mahroum’s 3D Framework-concept and the Human Development Index which is issued every year by the United Nations.

In case this analysis does not yield significant results, alternative explanations outside endogenous growth theory will be considered as well.

1.2 Structure

In order to guarantee a comprehensible framework, the structure and methods will be briefly presented. This thesis consists of two major sections.

The first will discuss the evolution of endogenous growth theories from a theoretical point of view. Highlighting chronologically the important contributions from the most known authors, the chapter aims to give a basic understanding of how and why endogenous growth theories have developed. Therefore, we will start with the explanation of the neoclassical growth models and exogenous growth. To demonstrate this principle, the well-known neoclassical Solow-Model will briefly be discussed. Afterwards its assumptions as well as its shortcomings will be examined. The concept of convergence is also worth mentioning in this context.

This leads us to the origins of endogenous growth models. The passing of perfect competition will be explained based on the five facts which Romer pointed out in his work of 1994. Subsequently, the different approaches of Arrow, Lucas and Romer will be introduced, discussing their models regarding the influences of learning-by-doing, human capital, knowledge spillovers and increasing returns, respectively. To complete this section, neo-Schumpeterian models will be presented as well. Finally, potential critiques will be discussed and the practical relevance of endogenous growth models will be reviewed.

The second part of the thesis is of empirical nature. Starting with the provision of background facts about South Tyrol and Luxembourg, their histories as well as their economies, geographies and populations will be exhibited. Afterward the data sources, which were utilized for this thesis, will be shortly introduced.

After this step, historical growth observations of both regions will be presented and analyzed. In order to characterize both economies, the compositions of GDP’s will be reviewed, with an emphasis on tourism in South Tyrol and on financial intermediation in Luxembourg. Then, the following chapter will try to explain their growth with a major factor suggested by endogenous growth theory – human capital. For this matter Mahroum’s 3D framework will be introduced and the nature of human capital will be examined. With the help of the United Nations’ Human Development Index, the correlations between the two economies will be drawn and the results of both compared. In the case this will not lead to a conclusive result, alternative explanations outside endogenous growth theories will be sought. Possibly, foreign income increase for South Tyrol and high dynamic capabilities for Luxembourg may come into question.

At the end, the result and final evaluation will be presented in the conclusion.

2 The Evolution of Endogenous Growth Theories

Growth within an economy can be defined either as change of output or as change of output per capita. Most often the latter definition is used in growth models. The term “endogenous growth” embraces a diverse collection of theoretical and empirical work that emerged in the 1980s. As in neoclassical growth theory, the focus in endogenous growth is on the behavior of the economy as a whole. However, it distinguishes itself from neoclassical growth by emphasizing that economic growth is an endogenous outcome of an economic system, not the result of forces that irrupt from outside (Romer 1994).

In this section, an overview of the origins of endogenous growth theory will be given and how it differs from more traditional views. In order to do so, a selection of models from several authors will be looked at, each of them focusing on a different aspect.

To set a frame of reference for endogenous growth models to be discussed later, an outline of neoclassical growth theory will be drawn.

2.1 Neoclassical Growth Theory with Exogenous Growth

The most basic proposition of growth theory is that in order to sustain a positive growth rate of output per capita in the long run, continual advances in technological knowledge in the form of new goods, new markets or new processes have to be made. This proposition can be demonstrated using the neoclassical growth model developed by Solow (1956), which shows that if there were no technological progress, the effects of diminishing returns would eventually cause economic growth to cease (Aghion et al. 1998).

Neoclassical growth theory, in particular, is a formulated collectivity of models that had its peak in the 1950s and 1960s. In a narrower sense, the neoclassical paradigm contains the assumption that all economic decisions are made under boundless rationality (Christiaans 2004).

The basic building block of a neoclassical growth model is an aggregate production function exhibiting constant returns in labor and reproducible capital. (Aghion et al 1998).

2.1.1 The Solow-Model

The Solow-Model (1956) assumes the production of only one commodity, whose rate of production is designated Y(t). The production of this good is described by a production function in which capital K(t) and labor L(t) are deployed to variable proportions.

illustration not visible in this excerpt

Equation 1: Solow's Basic Production Function

The commodity, so called output Y, can either be consumed or it can be used for productive purposes, i.e. investment. This means that the not-consumed income s increases the stock of capital.

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Equation 2: Change in Stock of Capital

The existing stock of capital wears out, which continuously causes a constant percentage of capital to become defective. The population of this theoretical world consumes a constant percentage of its income. Furthermore the number of inhabitants increases with a constant growth rate. In addition the model assumes full employment and perfect competition (Solow 1956; Christiaans 2004).

One crucial property of the aggregate production function is that there are diminishing returns to the accumulation of capital. If you continue to equip people with more and more of the same capital goods, without inventing new uses for the capital, then a point will eventually be reached where the extra capital goods become redundant, except those used as spare parts in the event of multiple equipment failure, and where therefore the marginal product of capital is negligible (Aghion et al. 1998).

The growth equilibria, with which growth theory deals, are usually so-called “steady state” equilibria. These are situations in which all variables, that are expressed as per capita factors (like per capita income, per capita consume, etc.), grow at the same rate. The neoclassical model described here determines an equilibrium with an exogenous steady state growth rate, i.e. the growth trend is solely dictated by an exogenous factor, not by interactions within the model ^[1]. Why is that?

Intuitively one can answer the question in the following way: imagine that per capita capital stock grows with a positive rate. Hence, per capita income increases over time as well. Because of the diminishing returns on capital, per capita income grows less than per capita capital. ^[2] This means in turn that the only growth rate, which per capita income and per capita capital can have in common, is zero. The equilibrium capital stock per capital is reached at the point, where the savings, diverted from the income, are just enough to hold the per capita capital stock constant, despite increasing population and capital erosion. The described state is an equilibrium because the modeled economy tends towards it, regardless of what its initial position might have been (Jones 2008).

The neoclassical model describes therefore an equilibrium in which the population growth rate determines the growth trend of the economy. The result is exogenous growth because national income, stock of capital and consumption increase with the growth-rate of population, which is not explained in the model.

One of the most important implications of the steady state result is that there is no long run growth in the Solow-Model. In the long run, the economy settles down to a constant level of production and a constant amount of capital. Output per person is constant as well, as is consumption per person. As we can see, this basic version of the Solow-Model can lead to economic growth for a while, but eventually growth stops as the capital stock and production converge to constant levels in the steady state (Jones 2008). ^[3]

However, to account for historical growth trends, neoclassical growth theory needs another element, as in most countries, positive growth trends for the above mentioned per capita factors have been recorded for quite some time. Neoclassical theory pays tribute to this development through a second exogenous factor: technological progress A(t).

As a result the extended production function followed:

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Equation 3: Extension of Solow's Production Function

Technological progress increases constantly the productivity of capital and labor, so the central statement of the Solow-Model is that, in the long run, only technological progress is of importance for permanent growth. Subsequently, growth politics can only be successful, if they nurture technological advance (Solow 1956; Mankiw et al. 1992; Rötheli 1993; Christiaans 2004).

2.1.2 Shortcomings of Neoclassical Conceptions

In the following, several shortcomings of neoclassical growth theory will be discussed. These, among others, led to the emergence of endogenous growth models.

2.1.2.1 Assumptions

Taking a look at the assumptions of neoclassical growth theory, one can easily discover the boundedness of these models:

- Closed Economy
- Perfect Competition
- Diminishing returns to capital
- Exogeneity of technological progress
- Exogeneity of population growth
- Savings and population growth determine the steady state income per capita

An often expressed critique about macroeconomic assumptions is that they simplify the proofs of desired conclusions. However, in order to model such a complex, organic matter like the aggregate economy, it is of course necessary to build a framework with certain limitations, in which the models can work. Prominent economists such as Keynes (1924) and Joskow have observed that much of economics is conceptual rather than quantitative and difficult to model and formalize quantitatively.

Nevertheless, neoclassical models cannot force someone to address the complicated issues that arise in the economic analysis like non-perfect competition, diffusion of technology, knowledge and information (Romer 1994).

In 1992, N. Gregory Mankiw, David Romer (not to be confused with Paul M. Romer, mentioned above and below) and David N. Weil analyzed Solow’s Model in their paper “Contribution to the Empirics of Economic Growth”. They showed that Solow correctly predicts the directions of saving and population growth, but not the orders of magnitude. Furthermore they pointed out that, if the model was augmented by the factor of human capital H, it would fit reality better, because human capital is in fact correlated with saving and population growth (Mankiw et al. 1992).

A few years later, Aghion, Howitt and García-Peñalosa (1998, p.3) summarized the neoclassical model as follows: “… the general equilibrium theory that has dominated the mainstream is one in which the product space is given, technology is given, firms are mere placeholders for technological possibilities available to everyone and there is no discernible process of competition, Schumpeterian or otherwise. Thus the neoclassical growth model of Solow (…) assumed technological progress to be exogenous not because this was a realistic assumption, but because it was the only manageable one.”

Romer (1994, p. 13) is of the same opinion, he states “like any model, the neoclassical model is a compromise between what we would like from a model and what is feasible given the state of our modeling skills”.

2.1.2.2 Convergence Controversy

Another stimulus for the birth of endogenous growth theory was the convergence controversy. The term “convergence” describes the observed phenomenon that poorer countries grow faster than richer countries (Mankiw et al. 1992; Barro / Sala-i-Martin 1992).

This question attracted a lot of attention in the beginning of the 1990s. In the analysis of the Maddison data set ^[4], William Baumol (1986) found that poorer countries like Japan and Italy substantially closed the per capita income gap with richer countries like the United States and Canada 1870 to 1979.

But two objections became soon apparent: within the data set, convergence has taken place only in the years since World War II. In fact, between 1870 and 1950, income per capita tended to diverge. Because the Maddison data set included only those economies that had successfully industrialized by the end of the sample period, it induces a sample selection bias that apparently accounts for most of the evidence in favor of convergence (Abramovitz 1986; Romer 1994).

As a result the attention then shifted to a broader sample of countries in the Heston-Summers data set ^[5]. In 1994, Romer tested for convergence and he clearly failed to prove it. On average, poor countries in this sample did not grow any faster than the rich countries.

The question that poses itself is why do poor countries as a group not catch up with the rich countries in the same way that, e.g. low income states in the US have been catching up with the high income states?

Robert Lucas (1988) and Romer (1986) cited the failure of cross-country convergence to motivate models of growth that drop two central assumptions of the neoclassical model: “that technological change is exogenous and that the same technological opportunities are available in all countries of the world” (Romer 1994, p. 4).

Romer (1994) saw the assumption that the level of technology can be different in different regions as particularly attractive in the context of an analysis of the state data. It removes the prediction of the closed-economy and identical-technology neoclassical model, which means that the marginal productivity of capital can be many times larger in poorer regions than in richer regions. Reality proves this point: if the same technology were available in all countries, human capital would not move from places where it is scarce to places where it is abundant and the same worker would not earn a higher wage after moving from the Philippines to the US.

Given all that, many economists felt that neoclassical theory was not satisfactory to explain growth. The time for less convenient but more realistic models had come.

2.2 The Origins of Endogenous Growth Models

In this section, we will have a look at various contributions to endogenous growth theory (EGT) and discuss their similarities, differences and arguments. The aim is to get a feeling for how findings are connected, what is assured and what is still a mystery.

First of all, the object of EGT is not to supplant capital accumulation as an explanation of economic growth, but to supplement it. The purpose of EGT is to fill the gaps in neoclassical theory – to open up technological progress and innovation to systematic analysis as well as to study its effects on growth, not to show that it is the solution to everything (Aghion et al. 1998).

2.2.1 The Passing of Perfect Competition – 5 Facts

In the 1980s, researchers made the observation that there was enough evidence to reject all the available growth models throughout the 1950s, 1960s and 1970s. What they lacked were good aggregate models, because there has always been the struggle to construct a viable alternative to perfect competition (Romer 1994; Aghion et al. 1998).

Following Romer (1994), the evidence about growth that poses a challenge for growth theorists can be distilled to five basic facts:

Fact #1: No Monopoly

There are many firms in a market economy that produce equal goods.

Fact #2: Non-Rivalry of Technology

Discoveries differ from other inputs in the sense that more than one person or firm can use them at the same time. The concept of double-entry bookkeeping or the recipe of how to produce steel – all these pieces of information and many more like them have the property that it is technologically possible for everybody and every firm to make use of them at the same time. Ordinary goods are rival goods, but information is non-rival (Jones 2008).

Fact #3: Replication

It is possible to replicate physical activities. Replication implies that the aggregate production function indicating a competitive market should be characterized by homogeneity of degree one in all of its conventional – that means rival – inputs. If we typify output in the form of

Equation 4: Aggregate Production Function in a Competitive Market (including Human Capital)

then doubling all three of K, H and L should lead to double output. ^[6] There is no need to double the non-rival inputs represented by A because the existing pieces of information can be used in both instances of the productive activity at the same time (Jones 2008).

If aggregate output is homogeneous of degree one in the rival inputs and firms are price-takers, Euler’s theorem implies that the compensation paid to the rival inputs must exactly equal the value of output produced. This is part of what makes the neoclassical model so simple and makes growth accounting feasible. The only problem is that this leaves nothing to compensate any inputs that were used to produce the discoveries that lead to increases in A.

In his article “Toward a Theory of Inventive Activity and Capital Accumulation”, Karl Shell (1966) showed this matter. He proposed a model in which A is financed from tax revenue collected by the government.

Fact #4: Technology Costs

Innovations do not fall like manna from heaven, instead, technological progress comes from things that people do. Romer states, a little tongue-in-cheek, that he wouldn’t know any economist that has ever been willing to make a serious defense of the proposition that technological change is literally a function of elapsed calendar time. However, being explicit about the issues here is important because it can help untangle a link that is sometimes made between exogeneity and randomness: if I’m prospecting for gold, success for me will be dominated by chance. So, discovery will seem to be an exogenous event in the sense that forces outside of my control appear to determine whether I succeed. But the aggregate rate of discovery is endogenous. When more people start prospecting for gold, more valuable discoveries will be found. This will be true even if discoveries are accidental side effects of some other activity (for instance finding gold as side effect of ditch digging) or if market incentives play no role in encouraging the activity. The aggregate rate of discovery will still be determined by things that people do (Romer 1994; Aghion et al. 1998).

Fact #5: Excludability

Many individuals and companies have market power and earn monopoly rents on discoveries. Even though information from discoveries is non-rival (fact #2), economically important discoveries usually do not meet the other criterion for public good ^[7], which is non-excludability. Most often they are partially excludable; or excludable for at least some time (patents). Hence, they cannot be treated as a pure public good. But if a firm can control access to a discovery, it can charge a price that is higher than zero. It therefore earns monopoly profits because information has no opportunity costs.

The neoclassical model captured the facts #1, #2 and #3, but postponed the considerations about facts #4 and #5. From a theoretical point of view, one key advantage of the model is its treatment of technology as a public good. This assumption also implies that knowledge is non-excludable and this is clearly inconsistent with fact #5, namely that it is possible to earn profits from discoveries (Romer 1994).

Endogenous growth models try to take the next step and accommodate fact #4. Work in this direction started in the 1960s. With the benefit of hindsight, it is obvious that growth theorists would eventually have to do what economists working at firm level have done: abandon the assumption of price-taking competition. Otherwise there would be no hope of capturing fact #5. Even at the time, the point received at least some attention. In his paper, Solow (1956) remarked in a footnote the desirability of extending the model to allow for monopolistic competition. One of his students, William Nordhaus (1969), subsequently outlined a growth model that did have patents, monopoly power and many firms. For technical reasons, the model still invoked exogenous growth – but following Romer (1994) it could have been extended to become a model of endogenous growth.

The next sections will show different approaches of various economists to incorporate the facts #4 and #5.

2.2.2 Learning by Doing – Arrow’s Approach

Kenneth Arrow was the first pioneer in EGT. He developed the key concept of “learning by doing” in 1962, published in his paper “The Economic Implications of Learning by Doing”. Therein he suggested an endogenous theory of the changes in knowledge, which underlie intertemporal and international shifts in production functions. Thus, he introduced changes in knowledge in order to explain increasing returns to capital. In his model, the acquisition of knowledge is termed “learning” (Arrow 1962).

Learning is a product of experience (“doing”) that takes place during activity, since it usually occurs through the attempt to solve a problem (Segura / Rodríguez Braun 2004).

Arrow (1962) refers to the study of Lundberg that supports this idea by analyzing the Horndal Iron Works in Sweden. Although no new investments were made (and therefore presumably no significant changes in the methods of production) during a period of 15 years, the productivity ^[8] of the firm increased on average 2% per annum (Lundberg 1961). This can only be explained by the increases in the cumulative output, thus, learning by doing. Lundberg named the phenomenon “Horndal Effect”.

This observation has proved the capability of workers to improve their productivity by regularly repeating the same type of action. The increased productivity is achieved through practice, self-perfection and minor innovations (Rötheli 1993).

In a simplified form, output Y for firm j can be written as

illustration not visible in this excerpt

Equation 5: Arrow's Model

whereas before, K without a subscript denotes the aggregate stock of capital. Arrow’s view is that at least part of the technological progress does not depend on the passage of time as such, but grows out of experience caught by cumulative gross investment, that is, a vehicle for improvements in skill and technical knowledge. Although his model may be considered as a precursor to EGT, for technical reasons, he did not emphasize the fact that this model could lead to sustained, endogenous growth. For the parameter values that he studied, if the size of the population is held constant, growth eventually comes to a halt (Romer 1994; Segura / Rodríguez Braun 2004).

Arrow’s approach differs from more recent literature in the way that in his model, the improved production conditions are only an accidental by-product of capital accumulation. This means that in Arrow’s model nobody earns a living through inventions or technical improvements, as a theory in which research and development (R&D) were object of employment would face a severe problem: if a separate factor of production “knowledge” was applied directly in the production of goods and compensated to its corresponding marginal product, the production function could not show constant returns to scale for capital and labor only. In this case, total production would not be sufficient to compensate all factors in an equilibrium (Rötheli 1993; Segura / Rodríguez Braun 2004).

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^[1] The existence of a steady state equilibrium presupposes that the production function fulfills certain conditions. The often used Cobb-Douglas-Function complies with all these conditions.

^[2] It is assumed that the production function shows constant returns to scale. I.e. income increases only proportionally to deployed capital, if, at the same time, deployed labor increases with the same proportion.

^[3] This process – the movement of the economy towards the steady state – is called transition dynamics.

^[4] The Maddison data set includes population by country, GDP’s, and GDP per capita back to 1820. http://www.worldeconomics.com/Data/MadisonHistoricalGDP/Madison%20Historical%20GDP%20Data.efp.

^[5] The Heston-Summers data set, or Penn World Table, has been the foundation of most empirical growth research since the mid-1980's. http://pwt.econ.upenn.edu/php_site/pwt_index.php.

^[6] The assumption that the market is competitive means that the existing activity already operates at the minimum efficient scale, so there are no economies of scale from building a single plant that is twice as large as the existing one.

^[7] Definition of Public Good: A product that one individual can consume without reducing its availability to another individual and from which no one is excluded. Economists refer to public goods as “non-rivalrous” and “non-excludable”. National defense, public parks and radio broadcasts could all be considered public goods.http://www.investopedia.com/terms/p/public-good.asp#axzz26vCVdPXw.

^[8] Productivity was measured in output per man-hour.