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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.

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W. W. Norton & Company *OD t 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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Our interactive player makes it easy to find solutions to Introduction to Economic Growth problems you're working on - just go to the chapter for your book.

Hit a particularly tricky question? Bookmark it to easily review again before an exam. The best part? As a Chegg Study subscriber, you can view available interactive solutions manuals for each of your classes for one low monthly price. Because the amount of investment being undertaken exceeds the amount needed to keep the capital-technology ratio constant. This will be true until! From equation 2. An interesting result is apparent from equation 2.

The Solow diagram for this policy change is drawn in Figure 2. At the initial capital-! To see the effects on growth, rewrite equation 2. Since g is con-! The behavior of the growth rate of output per worker over time is displayed in Figure 2.

Prior to the policy change, output per worker is growing at the constant rate g, so that the log of out- put per worker rises linearly. This more rapid growth contin- ues temporarily until the output-technology ratio reaches its new steady state. At this point, growth has returned to its long-run level of g. This exercise illustrates two important points.

First, policy changes in the Solow model increase growth rates, but only temporarily along the transition to the new steady state. That is, policy changes have no long-run growth effect. Second, policy changes can have level effects. That is, a permanent policy change can permanently raise or lower the level of per capita output. First, the Solow model appeals to differences in invest- ment rates and population growth rates and perhaps to exogenous dif- ferences in technology to explain differences in per capita incomes.

Why are we so rich and they so poor? In the next chapter, we will explore this hypothe- sis more carefully and see that it is firmly supported by data across the countries of the world. Second, why do economies exhibit sustained growth in the Solow model? The answer is technological progress. As we saw earlier, without technological progress, per capita growth will eventually cease as dimin- ishing returns to capital set in. Technological progress, however, can offset the tendency for the marginal product of capital to fall, and in the long run, countries exhibit per capita growth at the rate of technological progress.

How, then, does the Solow model account for differences in growth rates across countries? At first glance, it may seem that the Solow model cannot do so, except by appealing to differences in unmodeled techno- logical progress. A more subtle explanation, however, can be found by appealing to transition dynamics. We have seen several examples of how transition dynamics can allow countries to grow at rates different from their long-run growth rates. For example, an economy with a capital- technology ratio below its long-run level will grow rapidly until the capital-technology ratio reaches its steady-state level.

This reasoning may help explain why countries such as Japan and Germany, which had their capital stocks wiped out by World War II, have grown more rapidly than the United States over the last sixty years.

Or it may explain why an econ- omy that increases its investment rate will grow rapidly as it makes the transition to a higher output-technology ratio. This explanation may work well for countries such as South Korea and Taiwan. Their investment rates have increased dramatically since , as shown in Figure 2. This kind of reasoning raises an interesting ques- tion: This question will be discussed in more detail in later chapters. Without technological progress, capital accumulation runs into diminishing returns.

With technologi- cal progress, however, improvements in technology continually offset the diminishing returns to capital accumulation. Since we are primarily interested here in the growth rate of out- put per worker instead of total output, it is helpful to rewrite equation 2.

The U. Its most recent numbers are reported in Table 2. They generalize this equation in a couple of ways. First, the BLS measures labor by calculat- ing total hours worked rather than just the number of workers. Second, the BLS includes an additional term in equation 2. As can be seen from the table, output per hour in the private busi- ness sector for the United States grew at an average annual rate of 2. The contribution from capital per hour worked was 1.

Multifactor productivity growth accounts for the remaining 1. The implication is that about one-half of U. Because of the way in which it is calculated, economists have referred to this 1. This interpretation will be explored in later chapters. Capital per hour worked 1. Bureau of Labor Statistics The table reports average annual growth rates for the private business sector. Table 2. One of the important stylized facts revealed in the table is the productivity growth slowdown that occurred in the s.

The top row shows that growth in output per hour also known as labor productivity slowed dramatically after ; growth between and was nearly 2 percentage points slower than growth between and What was the source of this slow- down? The next few rows show that the changes in the contributions from capital per worker and labor composition are relatively minor.

The primary culprit of the productivity slowdown is a substantial decline in the growth rate of multifactor productivity. Various explanations for the productivity slowdown have been advanced. For example, perhaps the sharp rise in energy prices in and contributed to the slowdown.

Another explanation may involve the changing composition of the labor force or the sectoral shift in the economy away from manufacturing which tends to have high labor productivity toward services many of which have low labor productivity. This explanation receives some support from recent evidence that productivity growth recovered substantially in the s in manufacturing. It is possible that a slowdown in resources spent on research in the late s contributed to the slowdown as well.

Or, perhaps it is not the s and s that need to be explained but rather the s and s: Nevertheless, careful work on the productivity slowdown has failed to provide a complete explanation. As shown in Table 2. Before , this com- ponent of capital accumulation contributed only 0.

In addition, evidence suggests that as much as half of the rise in multifactor productivity growth in recent years is due to increases in efficiency of the production of information technology. Recently, a number of economists have suggested that the informa- tion-technology revolution associated with the widespread adoption of computers might explain both the productivity slowdown after as well as the recent rise in productivity growth.

According to this hypothesis, growth slowed temporarily while the economy adapted its factories to the new production techniques associated with informa- tion technology and as workers learned to take advantage of the new technology. The recent upsurge in productivity growth, then, reflects 14 The fall issue of the Journal of Economic Perspectives contains several papers discussing potential explanations of the productivity slowdown.

Growth accounting has also been used to analyze economic growth in countries other than the United States. Recall from Chapter 1 that average annual growth rates have exceeded 4 percent in these economies since Alwyn Young shows that a large part of this growth is the result of factor accumulation: The vertical axis measures growth in output per worker, while the horizontal axis measures growth in Harrod-neutral i.

Countries growing along a balanced growth path, then, should lie on the degree line in the figure. Two features of Figure 2. First, while the growth rates of output per worker in the East Asian countries are clearly remark- able, their rates of growth in total factor productivity TFP are less so. Total factor productivity growth, while typically higher than in the United States, was not exceptional in the East Asian economies.

Second, the East Asian countries are far above the degree line. This shift means that growth in output per worker is much higher than TFP growth would suggest. Singapore is an extreme example, with slightly negative TFP growth. If we overstate the growth rate of capital per worker, then growth accounting will understate the growth rate of TFP.

If so, then less of their growth can be attributed to capital accumulation. The years over which growth rates are calculated vary across countries: More generally, a key source of the rapid growth performance of these countries is factor accumulation.

Therefore, Young concludes, the framework of the Solow model and the extension of the model in Chap- ter 3 can explain a substantial amount of the rapid growth of the East Asian economies. The derivation of this solution is beyond the scope of this book. The key insight is to recognize that the differ- ential equation for the capital-output ratio in the Solow model is linear and can be solved using standard techniques.

Although the method of solution is beyond the scope of this book, the exact solution is still of interest. Notice that output per worker at any time t is written as a function of the parameters of the model as well as of the exogenous variable A t. At the other extreme, consider what happens as t gets very large, in the limit going off to infinity. In this case, e-lt goes to zero, so we are left with an expression that is exactly that given by equation 2. As time goes on, all that changes are the weights.

The interested reader will find it very useful to go back and reinter- pret the Solow diagram and the various comparative static exercises with this solution in mind. A decrease in the investment rate. Suppose the U. Congress enacts legislation that discourages saving and investment, such as the elimination of the investment tax credit that occurred in Sketch a graph of how the natural log of output per worker evolves over time with and without the policy change.

Make a similar graph for the growth rate of output per worker. Does the policy change perma- nently reduce the level or the growth rate of output per worker? An increase in the labor force.

Shocks to an economy, such as wars, famines, or the unification of two economies, often generate large flows of workers across borders. What are the short-run and long- run effects on an economy of a one-time permanent increase in the stock of labor? An income tax. Congress decides to levy an income tax on both wage income and capital income.

Trace the consequences of this tax for output per worker in the short and long runs, starting from steady state. Manna falls faster. Sketch a graph of the growth rate of output per worker over time. Be sure to pay close attention to the transition dynamics.

Can we save too much? Consumption is equal to output minus investment: In the context of the Solow model with no technological progress, what is the savings rate that maximizes steady-state consumption per worker? What is the marginal product of capital in this steady state? Show this point in a Solow diagram. Be sure to draw the production function on the diagram, and show consumption and saving and a line indicating the marginal product of capital.

Solow versus Solow In the Solow model with tech- nological progress, consider an economy that begins in steady state with a rate of technological progress, g, of 2 percent. Suppose g rises permanently to 3 percent.

How much of the increase in the growth rate of out- put per worker is due to a change in the growth rate of capital per worker, and how much is due to a change in multifactor productivity growth?

Finally, the third section of this chapter merges the discussion of the cross-country distribution of income levels with the convergence lit- erature and examines the evolution of the world income distribution.

Extending the Solow model to include human capital or skilled labor is relatively straightforward, as we shall see in this section. Individuals in this economy accumulate human capital by spend- ing time learning new skills instead of working. By increasing u, a unit of unskilled labor increases the effective units of skilled labor H. To see by how much, take logs and derivatives of equation 3. In this 1The development here differs from that in Mankiw, Romer, and Weil in one important way.

Mankiw, Romer, and Weil allow an economy to accumulate human capi- tal in the same way that it accumulates physical capital: Here, instead, we follow Lucas in assuming that individuals spend time accumulating skills, much like a student going to school. See Exercise 6 at the end of this chapter. The fact that the effects are proportional is driven by the somewhat odd presence of the exponential e in the equa- tion. This formulation is intended to match a large literature in labor economics that finds that an additional year of schooling increases the wages earned by an individual by something like 10 percent.

We solve this model using the same techniques employed in Chap- ter 2. How do agents decide how much time to spend accumulating skills instead of working? Just as we assume that indi- viduals save and invest a constant fraction of their income, we will assume that u is constant and given exogenously. In particular, along a balanced growth path, y and k will grow at the constant rate g, the rate of technological progress. Here, since h is constant, we can define the state variables by dividing by Ah.

Denoting these state variables with a tilde, equation 3. That is, equations 3. This means that all of the results we discussed in Chapter 2 regarding the dynamics of the Solow model apply here. Adding human capital as we have done it does not change the basic flavor of the model. The steady-state values of k and! This last equation summarizes the explanation provided by the extended Solow model for why some countries are rich and others are poor.

Furthermore, in the steady state, per capita output grows at the rate of technological progress, g, just as in the original Solow model. How well does this model perform empirically in terms of explain- ing why some countries are richer than others? Notice, however, that unless countries are all grow- ing at the same rate, even relative incomes will not be constant.

In order for relative incomes to be constant in the steady state, we need to make the assumption that g is the same in all countries—that is, the rate of technological progress in all countries is identical. On the surface, this seems very much at odds with one of our key styl- ized facts from Chapter 1: This may not seem plausible if growth is driven purely by technology. Technolo- gies may flow across international borders through international trade, or in scientific journals and newspapers, or through the immigration of scientists and engineers.

It may be more plausible to think that technol- ogy transfer will keep even the poorest countries from falling too far behind, and one way to interpret this statement is that the growth rates of technology, g, are the same across countries.

We will formalize this argument in Chapter 6. In the meantime, notice that in no way are we requiring the levels of technology to be the same; in fact, differences in technology presumably help to explain why some countries are richer than others. Still, we are left wondering why it is that countries have grown at such different rates over the last thirty years if they have the same underlying growth rate for technology.

A log scale is used for each axis. First, however, we return to the basic question of how well the extended Solow model fits the data. By obtaining estimates of the variables and parameters in equa- tion 3. Figure 3. Finally, we assume that the technology level, A, is the same across countries. That is, we tie one hand behind our back to see how well the model performs without introducing technological differences.

This assumption will be discussed shortly. The data used in this exercise are listed in Appendix C at the end of the book. Without accounting for differences in technology, the neoclassical model still describes the distribution of per capita income across coun- tries fairly well.

Countries such as the United States and Norway are quite rich, as predicted by the model. Countries such as Uganda and Mozambique are decidedly poor. The main failure of the model—that it is ignoring differences in technology—can be seen by the departures from the degree line in Figure 3. How can we incorporate actual technology levels into the analysis?

This is a cheat in that we are simply calculating A to make the model fit the data. However, it is an informative cheat. One can examine the As that are needed to fit the data to see if they are plausible. Solving the production function in equation 3. These estimates are reported in Figure 3. From this figure, one discovers several important things.

First, the lev- els of A calculated from the production function are strongly correlated 5See Jones for additional details. Notice that measuring u as years of schooling means that it is no longer between zero and one. This problem can be addressed by dividing years of schooling by potential life span, which simply changes the value of c proportionally and is therefore ignored.

A log scale is used for each axis, and U. Rich countries gen- erally have high levels of A, and poor countries generally have low levels. Countries that are rich not only have high levels of physical and human capital, but they also manage to use these inputs very productively. Second, although levels of A are highly correlated with levels of income, the correlation is far from perfect.

Countries such as Singa- pore, Trinidad and Tobago, and the United Kingdom have much higher levels of A than would be expected from their GDP per worker, and perhaps have levels that are too high to be plausible. It is difficult to see in the figure, but several countries have levels of A higher than that in the United States; these include Austria, Iceland, the Nether- lands, Norway, and Singapore.

This observation leads to an important remark. Estimates of A computed this way are like the residuals from growth accounting: For example, we have not controlled for differences in the quality of educational systems, the importance of experience at work and on-the-job training, or the general health of the labor force. These differences will therefore be included in A.

In this sense, it is more appropriate to refer to these estimates as total factor productivity levels rather than technology levels. Finally, the differences in total factor productivity across countries are large. The poorest countries of the world have levels of A that are only 10 to 15 percent of those in the richest countries.

With this observation, we can return to equation 3. The richest countries of the world have an output per worker that is roughly forty times that of the poorest countries of the world. This difference can be broken down into differences associated with investment rates in physical capital, investment rates in human capital, and differences in productivity.

For this purpose, it is helpful to refer to the data in Appendix C. The richest countries of the world have investment rates that are around 25 percent, while the poorest countries of the world have investment rates around 5 percent. According to equation 3. Similarly, workers in rich countries have about ten or eleven years of education on average, whereas workers in poor countries have less than three years.

Assuming a return to schooling of 10 percent, this suggests that hn! What accounts for the remainder?

Jones - Introduction to Economic Growth

By construction, differences in total factor productivity contribute the remaining factor of 10 to the differences in output per worker between the rich and poor countries. See Hsieh and Klenow for a review of the latest research on productivity levels. Coun- tries that invest a large fraction of their resources in physical capital and in the accumulation of skills are rich. Countries that use these inputs productively are rich.

The countries that fail in one or more of these dimensions suffer a corresponding reduction in income. Of course, one thing the Solow model does not help us understand is why some countries invest more than others, and why some countries attain higher levels of technology or productivity.

Addressing these questions is the subject of Chapter 7. As a preview, the answers are tied inti- mately to government policies and institutions. This catchup phenomenon is referred to as convergence.

For obvious reasons, questions about convergence have been at the heart of much empirical work on growth. We documented in Chapter 1 the enormous differences in levels of income per person around the world: The question of convergence asks whether these enormous differences are getting smaller over time.

An important cause of convergence might be technology transfer, but the neoclassical growth model provides another explanation for convergence that we will explore in this section.

William Baumol , alert to the analysis provided by eco- nomic historians, was one of the first economists to provide statisti- cal evidence documenting convergence among some countries and the absence of convergence among others. Maddison presented by Baumol is displayed in Figure 3.

The narrowing of the gaps between countries is evident in this figure. The United Kingdom had the second- highest per capita GDP and was recognized as the industrial center of the Western world. Maddison two variables: The simple con- vergence hypothesis seems to do a good job of explaining differences in growth rates, at least among this sample of industrialized economies. Bradford DeLong provides an important criticism of this result.

See Exercise 5 at the end of this chapter. But before we declare the hypothesis a success, note that Figure 3. Baumol also reported this finding: Recall that Table 1. Why, then, do we see convergence among some sets of countries but a lack of convergence among the countries of the world as a whole?

The neoclassical growth model suggests an important explanation for these findings. Consider the key differential equation of the neoclassical growth model, given in equation 3.

This equation can be rewritten as! Remember that! Therefore, the average product of capi-! In particular, it declines as k rises because of the diminishing returns to capital accumulation in the neoclassical model. As in Chapter 2, we can analyze this equation in a simple diagram, shown in Figure 3. The two curves in the figure plot the two terms on the right-hand side of equation 3.

Therefore, the difference! Notice that the growth rate! 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.

Jones - Introduction to Economic Growth 3ed.pdf - W W...

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.

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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.

To growth pdf economic introduction charles jones

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.

Growth charles pdf jones introduction economic to

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.

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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