W. W. Norton & Company *OD t terney.info INTRODUCTION TO ECONOMIC GROWTH THIRD EDITION Charles I. Jones and Dietrich Vollrath. Charles Jones. / Introduction To Economic Growth 2nd Edition I. Chapter 2. The Solow Model. All theory depends on assumptions which are not quite true. Veja grátis o arquivo Introduction to Economic Growth 3rd E th Charles I. Jones. pdf enviado para a disciplina de Desenvolvimento Econômico Categoria: Outros .
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Charles Jones 2nd ed. Introduction to. 1 Economic Growth. Chapter 5: The Engine of growth. As for the Arts of Delight and Ornalne~~t, they are. Jones - Introduction to Economic Growth - Free download as PDF File .pdf) or read Solutions to Exercises in Introduction to Economic Growth-Charles Jones. The Solow model and the facts of economic growth. research was coined “stepping on shoes” by Charles Jones (), leading to.
Third, an explicit treatment of Schumpeterian growth models has been incorporated alongside the Romer model in Chapter 5. Fourth, new sections on international trade and growth, the misallocation of factors of production, and optimal natural resource usage have been added. Fifth, the list of books and articles that can be used for supplementary reading has been updated and expanded. In smaller classes, combining lectures from the book with discussions of these readings can produce an enlightening course.
Finally, improvements to the exposition have been made in virtually every chapter in an effort to make the book more accessible to students. There are many people to thank for their comments and suggestions. Per Krusell, Christian Kerckhoffs, Sjak Smulders, and Kristoffer Laursen all made helpful comments that have been incorporated into this new edition.
Dietz would like to thank Chad for the opportunity to work on such an interesting book, and Kirstin Vollrath for all her support during this project.
Charles I. It is the theory which decides what we can observe. During the s and to a lesser extent the s, work on economic growth flourished. Taking advantage of new developments in the theory of imperfect competition, Romer introduced the economics of technology to macroeconomists. Following these theoretical advances, empirical work by a number of economists, such as Robert Barro of Harvard University, quantified and tested the theories of growth.
Both theoretical and empirical work has since continued with enormous professional interest. The purpose of this book is to explain and explore the modern theories of economic growth. This exploration is an exciting journey, in which we encounter several ideas that have already earned Nobel Prizes and several more with Nobel potential. The book attempts to make this cutting-edge research accessible to readers with only basic training in economics and calculus.
Like economists, astronomers are unable to perform the controlled experiments that are the hallmark of chemistry and physics. There is observation: planets, stars, and galaxies are laid out across the universe in a particular way. And there is theory: the theory of the Big Bang, for example, provides a coherent explanation for these observations.
This same interplay between observation and theory is used to organize this book. This first chapter will outline the broad empirical regularities associated with growth and development.
How rich are the rich countries; how poor are the poor? How fast do rich and poor countries grow? Unlike static PDF Introduction to Economic Growth solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step.
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Hit a particularly tricky question? Furthermore, because the growth rate of technology is constant, any changes in the growth rates! Suppose the economy of InitiallyBehind starts with the capital-! The output-per-worker gap between the two countries will narrow over time as both economies approach the same steady state.
An important prediction of the neoclassical model is this: For the industrialized countries, the assumption that their econo- mies have similar technology levels, investment rates, and popula- tion growth rates may not be a bad one. The neoclassical model, then, would predict the convergence that we saw in Figures 3.
This same reasoning suggests a compelling explanation for the lack of con- vergence across the world as a whole: In fact, as we saw in Figure 3. Because all countries do not have the same investment rates, population growth rates, or technology levels, they are not generally expected to grow toward the same steady-state target.
Another important prediction of the neoclassical model is related to growth rates. Although it is a key feature of the neoclassical model, the principle of transition dynamics applies much more broadly. In Chapters 5 and 6, for example, we will see that it is also a feature of the models of new growth theory that endogenize technological progress. Mankiw, Romer, and Weil and Barro and Sala-i-Martin show that this prediction of the neoclassical model can explain differ- ences in growth rates across the countries of the world.
This steady state is computed according to equation 3. You will be asked to undertake a similar calculation in Exercise 1 at the end of the chapter. Comparing Figures 3. In , good examples of these countries were Japan, Botswana, and Taiwan—economies that grew rapidly over the next forty years, just as the neoclassical model would predict. For example, Barro and Sala-i-Martin , 8In simple models, including most of those presented in this book, this principle works well. In more complicated models with more state variables, however, it must be modified.
It is simply a confirmation of a result predicted by the neoclassical growth model: It does not mean that all countries in the world are con- verging to the same steady state, only that they are converging to their own steady states according to a common theoretical model.
This matches the prediction of the Solow model if regions within a country are similar in terms of investment and population growth, as seems reasonable. How does the neoclassical model account for the wide differences in growth rates across countries documented in Chapter 1? The princi- ple of transition dynamics provides the answer: As we saw in Chapter 2, there are many reasons why countries may not be in steady state. This gap will change growth rates until the economy returns to its steady-state path.
For example, large changes in oil prices will have important effects on the economic performance of oil-exporting countries.
Mismanage- ment of the macroeconomy can similarly generate temporary changes in growth performance. The hyperinflations in many Latin American countries during the s or in Zimbabwe more recently are a good example of this. In terms of the neoclassical model, these shocks are interpreted as discrete changes in TFP. A negative shock to TFP would! A host of cross-country empirical work has been done, beginning with Barro and Easterly, Kremer, et al. Durlauf, Johnson, and Temple provide a comprehensive overview of this literature, counting !
This abundance of explanations for growth rates does not mean that economists can completely describe economic growth. With as many variables as countries, there is no way to actually test all of the expla- nations at once.
Sala-i-Martin, Doppelhofer, and Miller attempt to identify which of the candidates are most important for growth by using a statistical technique called Bayesian averaging to compare the results by using different combinations of varibles.
They find that higher rates of primary schooling in and higher life expectancy in are among the most relevant factors positively associated with higher growth in the following decades. In contrast, higher prices for investment goods and the prevalence of malaria in the s are nega- tively related to growth in the same period.
In short, this empirical work has not identified whether these variables are casual for growth as opposed to simply correlated with growth. Increases in the investment rate, skill accumulation, or the level of technology will have this effect. Or perhaps countries are not getting any closer together at all but are instead fanning out, with the rich countries getting richer and the poor countries getting poorer.
More generally, these questions are really about the evolution of the distribution of per capita incomes around the world. This figure plots the ratio of GDP per worker for the country at the 90th percentile of the world distribution to the country at the 10th percentile.
In , GDP per worker in the country at the 90th percentile was about twenty times that of the country at the 10th percentile. By this ratio had risen to forty, and after jumping to about forty-five for a few years, it has returned to around forty in The widening of the world income distribution is a fact that almost certainly characterizes the world economy over its entire history.
This number provides a lower bound on incomes at any date in the past, and this lower bound comes close to being attained by the poorest countries in the world even today. On the other hand, the incomes of the richest countries have been growing over time. This suggests that the ratio of the incomes in the richest to those in the poorest countries has also been rising. Quah , discusses this topic in more detail. Before , the ratio was presumably even lower. Whether this widening will continue in the future is an open ques- tion.
As long as there are some countries that have yet to get on, the world income distribution widens. Once all countries get on, however, this widening may reverse. The figure shows the percentage of world population at 12Robert E. A point x, y in the figure indicates that x percent of countries had relative GDP per worker less than or equal to y.
One hundred ten countries are represented. This is simi- lar to Figure 1. Accord- ing to this figure, in about 60 percent of the world population had GDP per worker less than 10 percent of the U. By the frac- tion of population this far below the United States was only about 20 percent. Because GDP per worker in the United States was growing steadily from to , the gains in relative income for the low end of the distribution also translate to absolute gains in living standards.
By only million were at this low level of income, and they accounted for only 6 percent of world population. Absolute poverty has been decreasing over time for the world population. This holds despite the fact that the number of countries as opposed to the number of people with very low relative GDP per worker has not fallen demonstrably. In , the poorest thirty-three countries in the world had an average GDP per worker relative to the United States of 3.
In , the poorest thirty-three countries had an aver- age of only 3. In relative terms, the poorest countries in the world are poorer than they were about fifty years ago, suggesting that there is a divergence across countries over time. The information in Figure 3. While the poorest countries in the world are not gaining on the richest, these countries have relatively small popula- tions compared to the countries that are gaining: China and India.
There is more optimism regarding convergence if we look at population-based measures than if we look only at country-based measures. Where are these economies headed? Consider the following data: Using equation 3. Consider two extreme cases: For each case, which economy will grow fast- est in the next decade and which slowest?
Policy reforms and growth. Suppose an economy, starting from an initial steady state, undertakes new policy reforms that raise its steady-state level of output per worker. For each of the following cases, calculate the proportion by which steady-state output per worker increases and, using the slope of the relationship shown in Figure 3. What are state variables? The basic idea of solving dynamic models that contain a differential equation is to first write the model so that along a balanced growth path, some state variable is constant.
Recall, however, that h is a constant. Do this. That is, solve the growth model in equations 3. During the late s, Sir Fran- cis Galton, a famous statistician in England, studied the distribution of heights in the British population and how the distribution was evolv- ing over time. In particular, Galton noticed that the sons of tall fathers tended to be shorter than their fathers, and vice versa. Suppose that their heights are determined as follows.
Draw a number from the hat and let that be the height for a mother. Without replacing the sheet just drawn, continue. Now suppose that the heights of the daughters are determined in the same way, starting with the hat full again and drawing new heights. Make a graph of the change in height between daughter and mother against the height of the mother. Will tall mothers tend to have shorter daughters, and vice versa? Let the heights correspond to income levels, and consider observ- ing income levels at two points in time, say and Does this mean the figures in this chapter are useless?
Reconsidering the Baumol results. In particular, DeLong noted two things. First, only countries that were rich at the end of the sample i.
Second, several countries not included, such as Argentina, were richer than Japan in Use these points to criticize and discuss the Baumol results. Do these criticisms apply to the results for the OECD? For the world? The Mankiw-Romer-Weil model. As mentioned in this chap- ter, the extended Solow model that we have considered differs slightly from that in Mankiw, Romer, and Weil This problem asks you to solve their model.
The key difference is the treatment of human capital. Mankiw, Romer, and Weil assume that human capi- tal is accumulated just like physical capital, so that it is measured in units of output instead of years of time. Human capital is accumulated just like physical capital: Assume that physical capital is accumulated as in equation 3. Discuss how the solution differs from that in equation 3.
These theories focus on modeling the accumulation of physical and human capital. In another sense, however, the theories emphasize the importance of technology. For example, the models do not generate economic growth in the absence of technological progress, and productivity differences help to explain why some countries are rich and others are poor.
In this way, neoclassical growth theory highlights its own shortcoming: Technological improvements arrive exogenously at a constant rate, g, and differences in technologies across economies are unexplained. In this chapter, we will explore the broad issues associ- ated with creating an economic model of technology and technological improvement. A new idea allows a given bundle of inputs to produce more or better output.
A good exam- ple is the use of tin throughout history. The ancient Bronze Age circa BCE to BCE is named for the alloy of tin and copper that was used extensively in weapons, armor, and household items like plates and cups. By 1 CE tin was alloyed with copper, lead, and antimony to create pewter, which was used up through the twentieth century for flat- ware.
Tin has a low toxicity, and in the early nineteenth century it was discovered that steel plated with tin could be used to create air-tight food containers, the tin cans you can still find on grocery shelves today. In the last decade, it was discovered that mixing tin with indium resulted in a solid solution that was both transparent and electrically conductive.
There is a good chance you were in contact with it today, as it is used to make the touch screen on smartphones. In the context of the production function above, each new idea generates an increase in the technology index, A.
Examples of ideas and technological improvements abound. In , light was provided by candles and oil lamps, whereas today we have very efficient fluorescent bulbs. William Nordhaus has calculated that the quality-adjusted price of light has fallen by a factor of 4, since the year The multiplex the- ater and diet soft drinks are innovations that allowed firms to combine inputs in new ways that consumers, according to revealed preference, have found very valuable.
Increasing h Imperfect Ideas h Nonrivalry h Returns Competition According to Romer, an inherent characteristic of ideas is that they are nonrivalrous.
This nonrivalry implies the presence of increasing returns to scale. And to model these increasing returns in a competitive environment with intentional research necessarily requires imperfect competition. Each of these terms and the links between them will now be discussed in detail. In the next chapter, we will develop the math- ematical model that integrates this reasoning. A crucial observation emphasized by Romer is that ideas are very different from most other economic goods.
Most goods, such as a smartphone or lawyer services are rivalrous. That is, your use of a smartphone excludes our use of the same phone, or your seeing a par- ticular attorney today from 1: Most economic goods share this property: If one thousand people each want to use a smartphone, we have to pro- vide them with one thousand phones.
The fact that Toyota takes advan- tage of just-in-time inventory methods does not preclude GM from tak- ing advantage of the same technique. Once an idea has been created, anyone with knowledge of the idea can take advantage of it.
Consider the design for the next-generation computer chip. Once the design itself has been created, factories throughout the country and even the world can use the design simultaneously to produce computer chips, provided they have the plans in hand. The paper the plans are written on is rival- rous; an engineer, whose skills are needed to understand the plans, is rivalrous; but the instructions written on the paper—the ideas—are not.
This last observation suggests another important characteristic of ideas, one that ideas share with most economic goods: The degree to which a good is excludable is the degree to which the owner of the good can charge a fee for its use. The firm that invents the design for the next computer chip can presumably lock the plans in a safe and restrict access to the design, at least for some period of time.
Alternatively, copyright and patent systems grant inventors who receive copyrights or patents the right to charge for the use of their ideas. Figure 4. Both rivalrous and nonrivalrous goods vary in the degree to which they are excludable. Goods such as a smartphone or the services of a lawyer are highly excludable. The result is an inefficiently high level of grazing that can potentially destroy the com- mons. A similar outcome occurs when a group of friends goes to a nice restaurant and divides the bill evenly at the end of the evening— suddenly everyone wants to order an expensive bottle of wine and a rich chocolate dessert.
A modern example of the commons problem is the overfishing of international waters. This is a slightly altered version of Figure 1 in Romer Ideas are nonrivalrous goods, but they vary substantially in their degree of excludability.
Cable TV transmissions are highly excludable, whereas computer software is less excludable. The digital signals of an cable TV transmission are scrambled so as to be useful only to someone with an appropriate receiver. Digital rights management DRM on music, movies, or software is an attempt to keep those items excludable, but once the DRM is cracked these items can be shared without cost. Similar con- siderations apply to the operating manual for Wal-Mart.
Sam Walton details his ideas for efficiently running a retail operation in the manual and gives it to all of his stores. Nonrivalrous goods that are essentially unexcludable are often called public goods. A traditional example is national defense. If the shield is going to protect some citizens in Washington, D. Some ideas may also be both nonrivalrous and un- excludable.
Calculus, our scientific understanding of med- icine, and the Black-Scholes formula for pricing financial options are other examples. Such spillovers are called exter- nalities. Goods with positive spillovers tend to be underproduced by markets, providing a classic opportunity for government intervention to improve welfare. Goods with negative spillovers may be overproduced by markets, and government regulation may be needed if property rights cannot be well defined.
The tragedy of the commons is a good example. Goods that are rivalrous must be produced each time they are sold; goods that are nonrivalrous need be produced only once. That is, non- rivalrous goods such as ideas involve a fixed cost of production and zero marginal cost.
For example, it costs a great deal to produce the first unit of the latest app for your phone, but subsequent units are pro- duced simply by copying the software from the first unit. It required a great deal of inspiration and perspiration for Thomas Edison and his lab to produce the first commercially viable electric light. But once the first light was produced, additional lights could be produced at a much lower per-unit cost.
In the lightbulb examples, notice that the only reason for a nonzero marginal cost is that the nonrivalrous good—the idea—is embodied in a rivalrous good: The formula, the basis for the Nobel Prize in Economics, is widely used on Wall Street and throughout the financial community.
The link to increasing returns is almost immediate once we grant that ideas are associated with fixed costs. Once it is developed, each pill is produced with constant returns to scale: In other words, this process can be viewed as production with a fixed cost and a constant marginal cost. In this example, F units of labor are required to produce the first copy of ColdAway. After the first pill is created, additional copies can be produced very cheaply.
In our example, one hour of labor input can produce one hundred pills. Recall that a production function exhibits increasing returns to scale if f ax 7 af x where a is some number greater than one—for example, doubling the inputs more than doubles output.
Clearly, this is the case for the production function in Figure 4. However, the inefficiency is in many ways a necessary one. To explain why, Figure 4. This fig- ure shows the costs of production as a function of the number of units produced. But the average cost is declining. The first unit costs F to produce because of the fixed cost of the idea, which is also the average cost of the first unit.
At higher levels of production, this fixed cost is spread over more and more units so that the average cost declines with scale. Now consider what happens if this firm sets price equal to marginal cost. With increasing returns to scale, average cost is always greater than marginal cost and therefore marginal cost pricing results in nega- tive profits. In other words, no firm would enter this market and pay the fixed cost F to develop the cold vaccine if it could not set the price above the marginal cost of producing additional units.
In practice, of course, this is exactly what we see: Firms will enter only if they can charge a price higher than marginal cost that allows them to recoup the fixed cost of creating the good in the first place. The production of new goods, or new ideas, requires the possibility of earning profits and therefore necessitates a move away from perfect competition.
Central among these features is that the economics of ideas involves potentially large one-time costs to create inventions. Think of the cost of creating the first touch-screen phone or the first jet engine. Inventors will not incur these one-time costs unless they have some expectation of being able to capture some of the gains to society, in the form of profit, after they create the invention.
Patents and copyrights are legal mechanisms that grant inventors monopoly power for a time in order to allow them to reap a return from their inventions.
They are attempts to use the legal system to influence the degree of excludability of ideas. According to some economic historians such as Nobel laureate Douglass C. North, this reasoning is quite impor- tant in understanding the broad history of economic growth, as we will now explain.
Recall from Figure 1. While the growth rate of world GDP per capita is around 2. Furthermore, the best data we have indicate that there was no sustained growth in income per capita from the origins of humanity in one million BCE to For now, we want to concentrate on the fact that sustained economic growth only began within the last years.
This raises one of the fundamental questions of economic history. How did sustained growth get started in the first place? The thesis of North and a number of other economic historians is that the develop- ment of intellectual property rights, a cumulative process that occurred over centuries, is responsible for modern economic growth. It is not until individuals are encouraged by the credible promise of large returns via the marketplace that sustained innovation occurs.
To quote a concise statement of this thesis: What determines the rate of development of new technology and of pure scientific knowledge? In the case of technological change, the social rate of return from developing new techniques had probably always been high; but we would expect that until the means to raise the private rate of return on developing new techniques was devised, there would be slow progress in producing new techniques.
The primary reason has been that the incentives for developing new techniques have occurred only sporadically. Typically, innovations could be copied at no cost by others and without any reward to the inventor or innovator. The failure to develop systematic property rights in innovation up until fairly modern times was a major source of the slow pace of techno- logical change.
North , p. Latitude was easily discerned by the angle of the North Star above the horizon. When Columbus landed in the Americas, he thought he had discovered a new route to India because he had no idea of his longitude. Several astronomical observatories built in western Europe during the seventeenth and eighteenth centuries were sponsored by govern- ments for the express purpose of solving the problem of longitude.
The rulers of Spain, Holland, and Britain offered large monetary prizes for the solution. Finally, the problem was solved in the mids, on the eve of the Industrial Revolution, by a poorly educated but eminently skilled clockmaker in England named John Harrison. Harrison spent his lifetime building and perfecting a mechanical clock, the chronometer, whose accuracy could be maintained despite turbulence and frequent changes in weather over the course of an ocean voyage that might last for months.
This chronometer, rather than any astronomical observation, provided the first practical solution to the determination of longitude. How does a chronometer solve the problem? Imagine taking two wristwatches with you on a cruise from London to New York. Maintain London Greenwich! From this standpoint, the astounding fact is that there was no market mechanism generating the enormous investments required to find a solution.
It is not that Harrison or anyone else would become rich from selling the solution to the navies and merchants of western Europe, despite the fact that the benefits to the world from the solution were enormous.
Instead, the main financial incentive seems to have been the prizes offered by the governments. Although the Statute of Monopolies in established a patent law in Britain and the institutions to secure property rights 7Sobel discusses the history of longitude in much more detail.
Exactly why this change occurred remains one of the great mysteries of economics and history. It is tempting to conclude that one of the causes was the establishment of long-lasting institutions that allowed entrepreneurs to capture as a private return some of the enormous social returns their innovations create.
But the number of potential innovators will also be crucial in determining the total number of new ideas that the economy produces.
If one hundred people can come up with ten new ideas every year, then two hundred people can come up with twenty. Edmund Phelps expresses this intuition in a far more elegant manner: One can hardly imagine, I think, how poor we would be today were it not for the rapid population growth of the past to which we owe the enormous number of technological advances enjoyed today. If I could re-do the history of the world, halving population size each year from the beginning of time on some random basis, I would not do it for fear of losing Mozart in the process.
In addition to the beginning of the Industrial Revolution, we have the drafting of the Declaration of Independence, the U. DATA ON I DEAS 91 The concept that increasing population size is actually a boon for economic growth can seem counterintuitive, as we often have in mind that this would result in less food, less oil, and less physical capital per person.
Even the Solow model in Chapter 2 implies that faster popu- lation growth will permanently lower the level of income per capita along the balanced growth path. Note that our intuition, and the Solow model, rely on a world of rivalrous goods.
That is, if we are eating some food, burning some oil, or working with some physical capital, you cannot. It was this rea- soning that led Thomas Malthus, in , to predict that living standards were doomed to remain stagnant.
Malthus presumed that any increase in living standards would simply lead to greater population growth, which would spread the supply of rivalrous natural resources more thinly, lower- ing living standards back to a minimum subsistence level. What Malthus did not consider, however, was the presence of nonri- valrous goods like ideas. As the absolute population increases, so does the absolute number of new ideas, and these can be copied an infinite number of times without reducing their availability.
The rate of economic growth in the world accelerated as the growth rate of population rose around In 1 CE, there were only about million humans on the planet, living stan- dards were poor, and both population and income per capita were growing at less than one-tenth of 1 percent per year. By , there were over six billion people, twenty times as many, and population was growing at well over 1 percent per year, slightly down from the maximum growth rate of around 2 percent in the s.
Yet income per capita was growing at about 1. At some fundamental level it is dif- ficult to measure both the inputs to the production function for ideas and the output of that production function, the ideas themselves. Average annual population growth rate. To the extent that the most important or valuable ideas are patented, patent counts may provide a simple measure of the number of ideas produced. Of course, both of these measures have their problems.
The Wal-Mart operation manual and multiplex movie theaters are good examples. In addition, a simple count of the number of patents granted in any particular year does not convey the economic value of the pat- ents. Among the thousands of patents awarded every year, only one may be for the transistor or the laser. A patent is a legal document that describes an inven- tion and entitles the patent owner to a monopoly over the invention for some period of time, typically seventeen to twenty years.
The first feature apparent from the graph is the rise in the number of patents awarded. In , approximately 25, patents were issued; in , more than , patents were issued. Presumably, the num- ber of ideas used in the U. This large increase masks several important features of the data, however.
First, over half of all patents granted in were of foreign origin. Second, nearly all of the increase in patents over the last cen- tury reflects an increase in foreign patents, at least until the s; the number of patents awarded in the United States to U. Does this mean that the number of new ideas generated within the United States has been relatively constant from to the present? Probably not. Patent and Trademark Office The formula for Coca-Cola, for example, is a quietly kept trade secret that has never been patented.
What about the inputs into the production of ideas? A similar rise can be seen for the five most highly developed countries as a whole. The number of U. Jones and OECD For example, the share in Japan rose from 0.
Ideas are nonrivalrous: This distinguishing fea- ture of ideas implies that the size of the economy—its scale—plays an important role in the economics of ideas. In particular, the nonrivalry of ideas implies that production will be characterized by increasing returns to scale.
In turn, the presence of increasing returns suggests that we must move away from models of perfect competition. The only reason an inventor is willing to undertake the large one-time costs of creating a new idea is because the inventor expects to be able to charge a price greater than marginal cost and earn profits. New ideas often create benefits that the inventor is unable to cap- ture.
This is what is meant when we say that ideas are only partially excludable. The incentive to create new ideas depends on the profits that an inventor can expect to earn the private benefit , not on the entire social benefit generated by the idea. Whether or not an idea gets created depends on the magnitude of the private benefit relative to the one-time invention costs.
It is easy to see, then, how ideas that are socially very valuable may fail to be invented if private benefits and social benefits are too far apart. Patents and copyrights are legal mecha- nisms that attempt to bring the private benefits of invention closer in line with the social benefits. The absolute number of individuals also plays an important role in producing new ideas.
The increas- ing scale of population along with the development of intellectual property rights—and of property rights more generally—combined to play a critical role in sparking the Industrial Revolution and the sus- tained economic growth that has followed. Classifying goods. Place the following goods on a chart like that in Figure 4. Provision of goods. Explain the role of the market and the govern- ment in providing each of the goods in the previous question.
Pricing with increasing returns to scale. Consider the following pro- duction function similar to that used earlier for ColdAway: Each unit of labor L costs the wage w to hire. That is, find the cost function C Y that tells the minimum cost required to produce Y units of output.
And it is more likely that one ingenious curious man may rather be found among 4 million than among persons. In this chapter, we incorporate the insights from the previous chapters to develop an explicit theory of technological progress.
The model we develop allows us to explore the engine of economic growth, thus addressing the sec- ond main question posed at the beginning of this book. We seek an understanding of why the advanced economies of the world, such as the United States, have grown at something like 2 percent per year for the last century. Where does the technological progress that underlies this growth come from?
Why is the growth rate 2 percent per year instead of 1 percent or 10 percent? Can we expect this growth to continue, or is there some limit to economic growth? Much of the work by economists to address these questions has been labeled endogenous growth theory or new growth theory. Instead of assuming that growth occurs because of automatic and unmodeled exogenous improvements in technology, the theory focuses on under- standing the economic forces underlying technological progress.
Similarly, it is the possibility of earning a profit that drives firms to develop a computer that can fit in your hand, a soft drink with only a single calorie, or a way to record TV programs and movies to be replayed at your convenience. In this way, improvements in technology, and the process of economic growth itself, are under- stood as an endogenous outcome of the economy. After we have gone through the Romer model, we present an alternative specification of technology based on improving the quality of existing products: Devel- oped by Aghion and Howitt and Grossman and Helpman originally, this alternative is often referred to as a Schumpeterian growth model, as they were anticipated by the work of Joseph Schumpeter in the late s and early s.
The market structure and economic incentives that 1 The version of the Romer model that we will present in this chapter is based on Jones a. There is one key difference between the two models, which will be discussed at the appropriate time. First, though, we will outline the basic elements of the model and their implications for economic growth.
The model is designed to explain why and how the advanced coun- tries of the world exhibit sustained growth. In contrast to the neoclas- sical models in earlier chapters, which could be applied to different countries, the model in this chapter describes the advanced countries of the world as a whole.
In the next chapter we will explore the important pro- cess of technology transfer and why different economies have different levels of technology. For the moment, we will concern ourselves with how the world technological frontier is continually pushed outward. As was the case with the Solow model, there are two main elements in the Romer model of endogenous technological change: The main equations will be similar to the equations for the Solow model, with one important difference.
The aggregate production function in the Romer model describes how the capital stock, K, and labor, LY, combine to produce output, Y, using the stock of ideas, A: For the moment, we take this production function as given; in Section 5.
For a given level of technology, A, the production function in equa- tion 5. However, when we recognize that ideas A are also an input into production, then there are increasing returns. To double the pro- duction of personal computers, Jobs and Wozniak needed only to dou- ble the number of integrated circuits, semiconductors, and so on, and find a larger garage.
That is, the production function exhibits constant returns to scale with respect to the capital and labor inputs, and there- fore must exhibit increasing returns with respect to all three inputs: As discussed in Chapter 4, the presence of increas- ing returns to scale results fundamentally from the nonrivalrous nature of ideas. The accumulation equations for capital and labor are identical to those for the Solow model.
Capital accumulates as people in the econ- omy forgo consumption at some given rate, sK, and depreciates at the exogenous rate d: Labor, which is equivalent to the population, grows exponentially at some constant and exogenous rate n: In the neoclassical model, the productivity term A grows exogenously at a constant rate.
In the Romer model, growth in A is endogenized. How is this accom- plished? The answer is with a production function for new ideas: According to the Romer model, A t is the stock of knowledge or the number of ideas that have been invented over the course of history up until time t.
Then, A is the number of new ideas produced at any given point in time.