Worth: Mankiw Economics 5e CHAPTER EIGHT Economic growth‖ Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia's or Egypt's? If so, what, exactly? If not, what is it about the "nature of India that makes it so? The conse- quences for human welfare involved in questions like these are simply stag- gering: Once one starts to think about them, it is hard to think about Robert E. Lucas, Jr. This chapter continues our analysis of the forces governing long-run economic rowth. With the basic version of the Solow growth model as our starting point, we take on four new tasks Our first task is to make the Solow model more general and more realistic. In Chapter 3 we saw that capital, labor, and technology are the key determinants of a nations production of goods and services. In Chapter 7 we developed the Solow model to show how changes in capital (saving and investment)and changes in the labor force(population growth) affect the economy s output. We are now ready to add the third source of growth--changes in technology--into the mix Our second task is to examine how a nations public policies can influence the evel and growth of its standard of living. In particular, we address four questions: Should our society save more or save less? How can policy influence the rate of saving? Are there some types of investment that policy should especially encour- age? How can policy increase the rate of technological progress? The Solow growth model provides the theoretical framework within which we consider each of these policy issues. Our third task is to move from theory to empirics. That is, we consider how well the Solow model fits the facts. During the 1990s, a large literature examined the predictions of the Solow model and other models of economic growth. It turns out that the glass is both half full and half empty. The Solow model can shed much light on international growth experiences, but it is far from the last word on the subject. Our fourth and final task is to consider what the solow model leaves out we have discussed previously, models help us understand the world by simplifying it. After completing an analysis of a model, therefore, it is important to consider 207 User JoENA: Job EFFo1424: 6264_ch08: Pg 207: 27096#/eps at 100sl ed,Feb13,20029:584M
User JOEWA:Job EFF01424:6264_ch08:Pg 207:27096#/eps at 100% *27096* Wed, Feb 13, 2002 9:58 AM This chapter continues our analysis of the forces governing long-run economic growth.With the basic version of the Solow growth model as our starting point, we take on four new tasks. Our first task is to make the Solow model more general and more realistic. In Chapter 3 we saw that capital, labor, and technology are the key determinants of a nation’s production of goods and services. In Chapter 7 we developed the Solow model to show how changes in capital (saving and investment) and changes in the labor force (population growth) affect the economy’s output.We are now ready to add the third source of growth—changes in technology—into the mix. Our second task is to examine how a nation’s public policies can influence the level and growth of its standard of living. In particular, we address four questions: Should our society save more or save less? How can policy influence the rate of saving? Are there some types of investment that policy should especially encourage? How can policy increase the rate of technological progress? The Solow growth model provides the theoretical framework within which we consider each of these policy issues. Our third task is to move from theory to empirics.That is, we consider how well the Solow model fits the facts. During the 1990s, a large literature examined the predictions of the Solow model and other models of economic growth. It turns out that the glass is both half full and half empty. The Solow model can shed much light on international growth experiences, but it is far from the last word on the subject. Our fourth and final task is to consider what the Solow model leaves out. As we have discussed previously, models help us understand the world by simplifying it. After completing an analysis of a model, therefore, it is important to consider | 207 Economic Growth II 8CHAPTER Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia’s or Egypt’s? If so,what,exactly? If not, what is it about the “nature of India” that makes it so? The consequences for human welfare involved in questions like these are simply staggering: Once one starts to think about them, it is hard to think about anything else. — Robert E. Lucas, Jr. EIGHT
Worth: Mankiw Economics 5e 208 PART I11 Growth Theory: The Economy in the Very Long Run whether we have oversimplified matters. In the last section, we examine a new set of theories, called endogenous growth theories, that hope to explain the technological progress that the Solow model takes as exogenous 8-1 Technological Progress in the solow model ar, our presentation of the Solow model has assumed an unchanging rela- tionship between the inputs of capital and labor and the output of goods and ser- vices. Yet the model can be modified to include exogenous technological progress, which over time expands society's ability to produce The Efficiency of Labor To incorporate technological progress, we must return to the production func- tion that relates total capital K and total labor L to total output Y. Thus far, the production function has been F(K, L We now write the ction function as Y=F(K, where E is a new(and somewhat abstract) variable called the efficiency of labor. The efficiency of labor is meant to reflect society's knowledge about pro- duction methods: as the available technology improves, the efficiency of labor rises. For instance, the efficiency of labor rose when assembly-line production transformed manufacturing in the early twentieth century, and it rose again when computerization was introduced in the the late twentieth century. The ef- ficiency of labor also rises when there are improvements in the health, education, or skills of the labor force The term L X E measures the number of effective workers. It takes into account the number of workers L and the efficiency of each worker E. This new produc tion function states that total output Y depends on the number of units of capital K and on the number of effective workers L X E Increases in the efficiency of labor e are in effect. like increases in the labor force L. The simplest assumption about technological progress is that it causes the effi ciency of labor e to grow at some constant rate g. For example, if g=0.02, then each unit of labor becomes 2 percent more efficient each year: output increases as if the labor force had increased by an additional 2 percent. This form of tech nological progress is called labor augmenting, and g is called the rate of labor augmenting technological progress. Because the labor force L is growing at rate n,and the efficiency of each unit of labor E is growing at rate g, the number of effective workers LX E is growing at rate n+g. User JoENA: Job EFFo1424: 6264_ ch08: Pg 208: 27097#/eps at 100s ed,Feb13,20029:584M
User JOEWA:Job EFF01424:6264_ch08:Pg 208:27097#/eps at 100% *27097* Wed, Feb 13, 2002 9:58 AM whether we have oversimplified matters. In the last section, we examine a new set of theories, called endogenous growth theories, that hope to explain the technological progress that the Solow model takes as exogenous. 8-1 Technological Progress in the Solow Model So far, our presentation of the Solow model has assumed an unchanging relationship between the inputs of capital and labor and the output of goods and services. Yet the model can be modified to include exogenous technological progress, which over time expands society’s ability to produce. The Efficiency of Labor To incorporate technological progress, we must return to the production function that relates total capital K and total labor L to total output Y.Thus far, the production function has been Y = F(K, L). We now write the production function as Y = F(K, L × E), where E is a new (and somewhat abstract) variable called the efficiency of labor.The efficiency of labor is meant to reflect society’s knowledge about production methods: as the available technology improves, the efficiency of labor rises. For instance, the efficiency of labor rose when assembly-line production transformed manufacturing in the early twentieth century, and it rose again when computerization was introduced in the the late twentieth century. The ef- ficiency of labor also rises when there are improvements in the health, education, or skills of the labor force. The term L × E measures the number of effective workers. It takes into account the number of workers L and the efficiency of each worker E.This new production function states that total output Y depends on the number of units of capital K and on the number of effective workers L × E. Increases in the efficiency of labor E are, in effect, like increases in the labor force L. The simplest assumption about technological progress is that it causes the effi- ciency of labor E to grow at some constant rate g. For example, if g = 0.02, then each unit of labor becomes 2 percent more efficient each year: output increases as if the labor force had increased by an additional 2 percent.This form of technological progress is called labor augmenting, and g is called the rate of laboraugmenting technological progress. Because the labor force L is growing at rate n, and the efficiency of each unit of labor E is growing at rate g, the number of effective workers L × E is growing at rate n + g. 208 | PART III Growth Theory: The Economy in the Very Long Run
Worth: Mankiw Economics 5e CHAPTER 8 Economic Growth Il 209 The Steady State With Technological Progres Expressing technological progress as labor augmenting makes it analogous to population growth. In Chapter 7 we analyzed the economy in terms of quanti- ties per worker and allowed the number of workers to rise over time. now we analyze the economy in terms of quantities per effective worker and allow the number of effective workers to rise To do this, we need to reconsider our notation We now let k= K/(L X E) stand for capital per effective worker and y=Y/(L X E)stand for output per ef- fective worker. With these definitions, we can again write y=f(l) t This notation is not really as new as it seems. If we hold the efficiency of labor constant at the arbitrary value of 1, as we have done implicitly up to now, the these new definitions of k and y reduce to our old ones. When the efficiency of labor is growing, however, we must keep in mind that k and y now refer to quan tities per effective worker(not per actual worker) Our analysis of the economy proceeds just as it did when we examined popu- lation growth. The equation showing the evolution of k over time now changes to △k=$f(k)-(6+n+g)k As before, the change in the capital stock Ak equals investment sf(k)minus break-even investment(8+n+gk. Now, however, because k=K/EL, break even investment includes three terms: to keep k constant, &k is needed to replace depreciating capital, nk is needed to provide capital for new workers, and gk is needed to provide capital for the new "effective workers "created by technologi- As shown in Figure 8-1, the inclusion of technological progress does not sub stantially alter our analysis of the steady state. There is one level of k, denoted figure 8-1 nvestment, Technological Progress and the break-even Break-even investment, (8+n+ g)k Solow Growth Model Labor Investment augmenting technological progress at rate g affects the Solow growth model in much the same way as did population growth at rate n. Now that k is Investment, sf(k) defined as the amount of capital per effective worker, increases in the number of effective workers because of technological progress tend to decrease k In the steady state investment sf(k) exactly offsets the reductions in k attributable k* Capital per effective worker, k to depreciation, population The steady growth, and technological progress User JoENA: Job EFFo1424: 6264_ ch08: Pg 209: 27098#/eps at 100s ed,Feb13,20029:584M
User JOEWA:Job EFF01424:6264_ch08:Pg 209:27098#/eps at 100% *27098* Wed, Feb 13, 2002 9:58 AM The Steady State With Technological Progress Expressing technological progress as labor augmenting makes it analogous to population growth. In Chapter 7 we analyzed the economy in terms of quantities per worker and allowed the number of workers to rise over time. Now we analyze the economy in terms of quantities per effective worker and allow the number of effective workers to rise. To do this, we need to reconsider our notation.We now let k = K/(L × E) stand for capital per effective worker and y = Y/(L × E) stand for output per effective worker.With these definitions, we can again write y = f(k). This notation is not really as new as it seems. If we hold the efficiency of labor E constant at the arbitrary value of 1, as we have done implicitly up to now, then these new definitions of k and y reduce to our old ones.When the efficiency of labor is growing, however, we must keep in mind that k and y now refer to quantities per effective worker (not per actual worker). Our analysis of the economy proceeds just as it did when we examined population growth.The equation showing the evolution of k over time now changes to Dk = sf(k) − ( d + n + g)k. As before, the change in the capital stock Dk equals investment sf(k) minus break-even investment (d + n + g)k. Now, however, because k = K/EL, breakeven investment includes three terms: to keep k constant,d k is needed to replace depreciating capital, nk is needed to provide capital for new workers, and gk is needed to provide capital for the new “effective workers” created by technological progress. As shown in Figure 8-1, the inclusion of technological progress does not substantially alter our analysis of the steady state. There is one level of k, denoted CHAPTER 8 Economic Growth II | 209 figure 8-1 Investment, break-even investment k* Capital per effective worker, k Break-even investment, (d n g)k Investment, sf(k) The steady state Technological Progress and the Solow Growth Model Laboraugmenting technological progress at rate g affects the Solow growth model in much the same way as did population growth at rate n. Now that k is defined as the amount of capital per effective worker, increases in the number of effective workers because of technological progress tend to decrease k. In the steady state, investment sf(k) exactly offsets the reductions in k attributable to depreciation, population growth, and technological progress.
Worth: Mankiw Economics 5e 210 PART I11 Growth Theory: The Economy in the Very Long Run k, at which capital per effective worker and output per effective worker are constant. As before, this steady state represents the long-run equilibrium of th e econom The Effects of Technological Progress able 8-1 shows how four key variables behave in the steady state with technolog ical progress As we have just seen, capital per effective worker k is constant in the steady state. Because y=f(k), output per effective worker is also constant Remem- ber,though, that the efficiency of each actual worker is growing at rate g. Hence, output per worker(Y/L=yXE)also grows at rate g Total output Y=yX(EX LI With the addition of technological progress, our model can finally explain the sustained increases in standards of living that we observe. That is, we have shown that technological progress can lead to sustained growth in output per worker. B contrast, a high rate of saving leads to a high rate of growth only until the steady state is reached. Once the economy is in steady state, the rate of growth of output per worker depends only on the rate of technological progress. Acording to the Solow model, only technological progress can explain persistently rising living standards The introduction of technological progress also modifies the criterion for the Golden Rule. The Golden Rule level of capital is now defined as the steady state chat maximizes consumption per effective worker. Following the same argu ments that we have used before, we can show that steady-state consumption per effective worker is *=f(k*)-(6+n+g)k Steady-state consumption is maximized if MPk=δ+n+g, MPK-6=n+ That is, at the Golden Rule level of capital, the net marginal product of capital, MPK-6, equals the rate of growth of total output, n g. Because actual Steady-State Growth Rates in the Solow Model With Technological Progress Variable Symbol eady-State Growth Rate Output per effective worker y=Y/(EXL)=f(k) Output pe g g User JoENA: Job EFFo1424: 6264_ ch08: Pg 210: 27099#/eps at 100sl ed,Feb13,20029:584M
User JOEWA:Job EFF01424:6264_ch08:Pg 210:27099#/eps at 100% *27099* Wed, Feb 13, 2002 9:58 AM k*, at which capital per effective worker and output per effective worker are constant. As before, this steady state represents the long-run equilibrium of the economy. The Effects of Technological Progress Table 8-1 shows how four key variables behave in the steady state with technological progress.As we have just seen, capital per effective worker k is constant in the steady state. Because y = f(k), output per effective worker is also constant. Remember, though, that the efficiency of each actual worker is growing at rate g. Hence, output per worker (Y/L = y × E) also grows at rate g.Total output [Y = y × (E × L)] grows at rate n + g. With the addition of technological progress, our model can finally explain the sustained increases in standards of living that we observe.That is, we have shown that technological progress can lead to sustained growth in output per worker. By contrast, a high rate of saving leads to a high rate of growth only until the steady state is reached. Once the economy is in steady state, the rate of growth of output per worker depends only on the rate of technological progress. According to the Solow model, only technological progress can explain persistently rising living standards. The introduction of technological progress also modifies the criterion for the Golden Rule.The Golden Rule level of capital is now defined as the steady state that maximizes consumption per effective worker. Following the same arguments that we have used before, we can show that steady-state consumption per effective worker is c* = f(k*) − ( d + n + g)k*. Steady-state consumption is maximized if MPK = d + n + g, or MPK − d = n + g. That is, at the Golden Rule level of capital, the net marginal product of capital, MPK − d , equals the rate of growth of total output, n + g. Because actual 210 | PART III Growth Theory: The Economy in the Very Long Run Variable Symbol Steady-State Growth Rate Capital per effective worker k = K/(E × L) 0 Output per effective worker y = Y/(E × L) = f(k) 0 Output per worker Y/L = y × E g Total output Y = y × (E × L) n + g Steady-State Growth Rates in the Solow Model With Technological Progress table 8-1
Worth: Mankiw Economics 5e CHAPTER 8 Economic Growth Il 211 economies experience both population growth and technological progress, we must use this criterion to evaluate whether they have more or less capital than at the golden rule steady state 8-2 Policies to Promote growth Having used the Solow model to uncover the relationships among the different sources of economic growth, we can now use the theory to help guide our hinking about economic polie Evaluating the Rate of Saving According to the Solow growth model, how much a nation saves and invests is a key determinant of its citizens'standard of living. So let's begin our policy discus sion with a natural question: Is the rate of saving in the U.S. economy too low, too high, or about right? As we have seen, the saving rate determines the steady-state levels of capital and output. One particular saving rate produces the Golden Rule steady state, which maximizes consumption per worker and thus economic well-being. The Golden Rule provides the benchmark against which we can compare the U.S. economy. To decide whether the U.S. economy is at, above, or below the Golden Rule steady state, we need to compare the marginal product of capital net of deprecia tion(MPK-8) with the growth rate of total output(n+g). As we just estab- lished, at the Golden Rule steady state, MPK-8=n+g. If the economy is operating with less capital than in the Golden Rule steady state, then diminish lls us that MPK-8>n+g In this Ite of saving will eventually lead to a steady state with higher consumption However, if the economy is operating with too much capital, then MPK-8<n +8, and the rate of saving should be reduced. To make this comparison for a real economy, such as the U.S. economy, we need an estimate of the growth rate (n+g) and an estimate of the net marginal product of capital (MPK-8) Real GDP in the United States grows an average of 3 percent per year, so +g=0.03. We can estimate the net marginal product of capital from the following three facts 1. The capital stock is about 2.5 times one years GDP. 2. Depreciation of capital is about 10 percent of GDP. 3. Capital income is about 30 percent of GDP. Using the notation of our model (and the result from Chapter 3 that capital owners earn income of MPK for each unit of capital), we can write these facts as 2.6k=0.1 3.MPK×k=0.3y User JOENA: Job EFF01424: 6264_ch08: Pg 211: 27100 #/eps at 100s ed,Feb13,20029:584M
User JOEWA:Job EFF01424:6264_ch08:Pg 211:27100#/eps at 100% *27100* Wed, Feb 13, 2002 9:58 AM economies experience both population growth and technological progress, we must use this criterion to evaluate whether they have more or less capital than at the Golden Rule steady state. 8-2 Policies to Promote Growth Having used the Solow model to uncover the relationships among the different sources of economic growth, we can now use the theory to help guide our thinking about economic policy. Evaluating the Rate of Saving According to the Solow growth model, how much a nation saves and invests is a key determinant of its citizens’standard of living. So let’s begin our policy discussion with a natural question: Is the rate of saving in the U.S. economy too low, too high, or about right? As we have seen,the saving rate determines the steady-state levels of capital and output. One particular saving rate produces the Golden Rule steady state, which maximizes consumption per worker and thus economic well-being.The Golden Rule provides the benchmark against which we can compare the U.S. economy. To decide whether the U.S. economy is at, above, or below the Golden Rule steady state, we need to compare the marginal product of capital net of depreciation (MPK − d ) with the growth rate of total output (n + g). As we just established, at the Golden Rule steady state, MPK − d = n + g. If the economy is operating with less capital than in the Golden Rule steady state, then diminishing marginal product tells us that MPK − d > n + g. In this case, increasing the rate of saving will eventually lead to a steady state with higher consumption. However, if the economy is operating with too much capital, then MPK − d < n + g, and the rate of saving should be reduced. To make this comparison for a real economy, such as the U.S. economy, we need an estimate of the growth rate (n + g) and an estimate of the net marginal product of capital (MPK − d ). Real GDP in the United States grows an average of 3 percent per year, so n + g = 0.03.We can estimate the net marginal product of capital from the following three facts: 1. The capital stock is about 2.5 times one year’s GDP. 2. Depreciation of capital is about 10 percent of GDP. 3. Capital income is about 30 percent of GDP. Using the notation of our model (and the result from Chapter 3 that capital owners earn income of MPK for each unit of capital), we can write these facts as 1. k = 2.5y. 2. d k = 0.1y. 3. MPK × k = 0.3y CHAPTER 8 Economic Growth II | 211