CH-9 Economic Growth II: Technology, Empirics, and Policy – Macroeconomics : Book Guide

Answers to Textbook Questions and Problems CHAPTER 9 Economic Growth II: Technology, Empirics, and Policy Questions for Review 1. In the Solow model, we find that only technological progress can affect the steady-state rate of growth in income per worker. Growth in the capital stock (through high saving) has no effect on the steadystate growth rate of income per worker; neither does population growth. But technological progress can lead to sustained growth. 2. In the steady state, output per person in the Solow model grows at the rate of technological progress g. Capital per person also grows at rate g. Note that this implies that output and capital per effective worker are constant in steady state. In the U.S. data, output and capital per worker have both grown at about 2 percent per year for the past half-century. 3. To decide whether an economy has more or less capital than the Golden Rule, we need to compare the marginal product of capital net of depreciation (MPK – δ) with the growth rate of total output (n + g). The growth rate of GDP is readily available. Estimating the net marginal product of capital requires a little more work but, as shown in the text, can be backed out of available data on the capital stock relative to GDP, the total amount of depreciation relative to GDP, and capital’s share in GDP. 4. Economic policy can influence the saving rate by either increasing public saving or providing incentives to stimulate private saving. Public saving is the difference between government revenue and government spending. If spending exceeds revenue, the government runs a budget deficit, which is negative saving. Policies that decrease the deficit (such as reductions in government purchases or increases in taxes) increase public saving, whereas policies that increase the deficit decrease saving. A variety of government policies affect private saving. The decision by a household to save may depend on the rate of return; the greater the return to saving, the more attractive saving becomes. Tax incentives such as tax-exempt retirement accounts for individuals and investment tax credits for corporations increase the rate of return and encourage private saving. 5. The legal system is an example of an institutional difference between countries that might explain differences in income per person. Countries that have adopted the English style common law system tend to have better developed capital markets, and this leads to more rapid growth because it is easier for businesses to obtain financing. The quality of government is also important. Countries with more government corruption tend to have lower levels of income per person. 6. Endogenous growth theories attempt to explain the rate of technological progress by explaining the decisions that determine the creation of knowledge through research and development. By contrast, the Solow model simply took this rate as exogenous. In the Solow model, the saving rate affects growth temporarily, but diminishing returns to capital eventually force the economy to approach a steady state in which growth depends only on exogenous technological progress. By contrast, many endogenous growth models in essence assume that there are constant (rather than diminishing) returns to capital, interpreted to include knowledge. Hence, changes in the saving rate can lead to persistent growth. Problems and Applications 1. a. In the Solow model with technological progress, y is defined as output per effective worker, and k is defined as capital per effective worker. The number of effective workers is defined as L  E (or LE), where L is the number of workers, and E measures the efficiency of each worker. To find output per effective worker y, divide total output by the number of effective workers: LE Ł LEł y=k b. To solve for the steady-state value of y as a function of s, n, g, and δ, we begin with the equation for the change in the capital stock in the steady state: Δk = sf(k) – (δ + n + g)k = 0. The production function y= k can also be rewritten as y2 = k. Plugging this production function into the equation for the change in the capital stock, we find that in the steady state: sy – (δ + n + g)y2 = 0. Solving this, we find the steady-state value of y: y* = s/(δ + n + g). c. The question provides us with the following information about each country: Atlantis: s = 0.28 Xanadu: s = 0.10 n = 0.01 n = 0.04 g = 0.02 g = 0.02 δ = 0.04 δ = 0.04 Using the equation for y* that we derived in part (a), we can calculate the steady-state values of y for each country. Developed country: y* = 0.28/(0.04 + 0.01 + 0.02) = 4 Less-developed country: y* = 0.10/(0.04 + 0.04 + 0.02) = 1 2. a. In the steady state, capital per effective worker is constant, and this leads to a constant level of output per effective worker. Given that the growth rate of output per effective worker is zero, this means the growth rate of output is equal to the growth rate of effective workers (LE). We know labor grows at the rate of population growth n and the efficiency of labor (E) grows at rate g. Therefore, output grows at rate n+g. Given output grows at rate n+g and labor grows at rate n, output per worker must grow at rate g. This follows from the rule that the growth rate of Y/L is equal to the growth rate of Y minus the growth rate of L. b. First find the output per effective worker production function by dividing both sides of the production function by the number of effective workers LE: = LE ŁLEł y=k To solve for capital per effective worker, we start with the steady state condition: Δk = sf(k) – (δ + n + g)k = 0. Now substitute in the given parameter values and solve for capital per effective worker (k): Substitute the value for k back into the per effective worker production function to find output per effective worker is equal to 2. The marginal product of capital is given by Substitute the value for capital per effective worker to find the marginal product of capital is equal to 1/12. c. According to the Golden Rule, the marginal product of capital is equal to (δ + n + g) or 0.06. In the current steady state, the marginal product of capital is equal to 1/12 or 0.083. Therefore, we have less capital per effective worker in comparison to the Golden Rule. As the level of capital per effective worker rises, the marginal product of capital will fall until it is equal to 0.06. To increase capital per effective worker, there must be an increase in the saving rate. d. During the transition to the Golden Rule steady state, the growth rate of output per worker will increase. In the steady state, output per worker grows at rate g. The increase in the saving rate will increase output per effective worker, and this will increase output per effective worker. In the new steady state, output per effective worker is constant at a new higher level, and output per worker is growing at rate g. During the transition, the growth rate of output per worker jumps up, and then transitions back down to rate g. 3. To solve this problem, it is useful to establish what we know about the U.S. economy: • A Cobb–Douglas production function has the form y = kα, where α is capital’s share of income. The question tells us that α = 0.3, so we know that the production function is y = k0.3. • In the steady state, we know that the growth rate of output equals 3 percent, so we know that (n + g) = 0.03. • The depreciation rate δ = 0.04. • The capital–output ratio K/Y = 2.5. Because k/y = [K/(LE)]/[Y/(LE)] = K/Y, we also know that k/y = 2.5. (That is, the capital–output ratio is the same in terms of effective workers as it is in levels.) a. Begin with the steady-state condition, sy = (δ + n + g)k. Rewriting this equation leads to a formula for saving in the steady state: s = (δ + n + g)(k/y). Plugging in the values established above: s = (0.04 + 0.03)(2.5) = 0.175. The initial saving rate is 17.5 percent. b. We know from Chapter 3 that with a Cobb–Douglas production function, capital’s share of income α = MPK(K/Y). Rewriting, we have MPK = α/(K/Y). Plugging in the values established above, we find MPK = 0.3/2.5 = 0.12. c. We know that at the Golden Rule steady state: MPK = (n + g + δ). Plugging in the values established above: MPK = (0.03 + 0.04) = 0.07. At the Golden Rule steady state, the marginal product of capital is 7 percent, whereas it is 12 percent in the initial steady state. Hence, from the initial steady state we need to increase k to achieve the Golden Rule steady state. d. We know from Chapter 3 that for a Cobb–Douglas production function, MPK = α (Y/K). Solving this for the capital–output ratio, we find K/Y = α/MPK. We can solve for the Golden Rule capital–output ratio using this equation. If we plug in the value 0.07 for the Golden Rule steady-state marginal product of capital, and the value 0.3 for α, we find K/Y = 0.3/0.07 = 4.29. In the Golden Rule steady state, the capital–output ratio equals 4.29, compared to the current capital–output ratio of 2.5. e. We know from part (a) that in the steady state s = (δ + n + g)(k/y), where k/y is the steady-state capital–output ratio. In the introduction to this answer, we showed that k/y = K/Y, and in part (d) we found that the Golden Rule K/Y = 4.29. Plugging in this value and those established above: s = (0.04 + 0.03)(4.29) = 0.30. To reach the Golden Rule steady state, the saving rate must rise from 17.5 to 30 percent. This result implies that if we set the saving rate equal to the share going to capital (30 percent), we will achieve the Golden Rule steady state. 4. a. In the steady state, we know that sy = (δ + n + g)k. This implies that k/y = s/(δ + n + g). Since s, δ, n, and g are constant, this means that the ratio k/y is also constant. Since k/y = [K/(LE)]/[Y/(LE)] = K/Y, we can conclude that in the steady state, the capital–output ratio is constant. b. We know that capital’s share of income = MPK  (K/Y). In the steady state, we know from part (a) that the capital–output ratio K/Y is constant. We also know from the hint that the MPK is a function of k, which is constant in the steady state; therefore the MPK itself must be constant. Thus, capital’s share of income is constant. Labor’s share of income is 1 – [Capital’s Share]. Hence, if capital’s share is constant, we see that labor’s share of income is also constant. c. We know that in the steady state, total income grows at n + g, defined as the rate of population growth plus the rate of technological change. In part (b) we showed that labor’s and capital’s share of income is constant. If the shares are constant, and total income grows at the rate n + g, then labor income and capital income must also grow at the rate n + g. d. Define the real rental price of capital R as R = Total Capital Income/Capital Stock = (MPK  K)/K = MPK. We know that in the steady state, the MPK is constant because capital per effective worker k is constant. Therefore, we can conclude that the real rental price of capital is constant in the steady state. To show that the real wage w grows at the rate of technological progress g, define TLI = Total Labor Income L = Labor Force Using the hint that the real wage equals total labor income divided by the labor force: w = TLI/L. Equivalently, wL = TLI. In terms of percentage changes, we can write this as Δw/w + ΔL/L = ΔTLI/TLI. This equation says that the growth rate of the real wage plus the growth rate of the labor force equals the growth rate of total labor income. We know that the labor force grows at rate n, and, from part (c), we know that total labor income grows at rate n + g. We, therefore, conclude that the real wage grows at rate g. 5. a. The per worker production function is F(K, L)/L = AKα L1–α/L = A(K/L)α = Akα b. In the steady state, Δk = sf(k) – (δ + n + g)k = 0. Hence, sAkα = (δ + n + g)k, or, after rearranging: a Ø sA ø Ł1-ał k*=Œ œ . Œºd+n+gœß Plugging into the per-worker production function from part (a) gives a y*= AŁ1-aał ŒØ s øœ Ł1-ał . ºŒd+n+gœß Thus, the ratio of steady-state income per worker in Richland to Poorland is a Ø (y*Richland / y*Poorland ) =ŒŒºd+nRichland +g d+nPoorland +gœœß a Ø =Œ œ Œº 0.05+0.01+0.02 0.05+0.03+0.02œß c. If α equals 1/3, then Richland should be 41/2, or two times, richer than Poorland. a d. If 4Ł1-ał = 16, then it must be the case that a , which in turn requires that α equals 2/3. Ł 1-ał Hence, if the Cobb–Douglas production function puts 2/3 of the weight on capital and only 1/3 on labor, then we can explain a 16-fold difference in levels of income per worker. One way to justify this might be to think about capital more broadly to include human capital—which must also be accumulated through investment, much in the way one accumulates physical capital. 6. How do differences in education across countries affect the Solow model? Education is one factor affecting the efficiency of labor, which we denoted by E. (Other factors affecting the efficiency of labor include levels of health, skill, and knowledge.) Since country 1 has a more highly educated labor force than country 2, each worker in country 1 is more efficient. That is, E1 > E2. We will assume that both countries are in steady state. a. In the Solow growth model, the rate of growth of total income is equal to n + g, which is independent of the work force’s level of education. The two countries will, thus, have the same rate of growth of total income because they have the same rate of population growth and the same rate of technological progress. b. Because both countries have the same saving rate, the same population growth rate, and the same rate of technological progress, we know that the two countries will converge to the same steadystate level of capital per effective worker k*. This is shown in Figure 9-1. Hence, output per effective worker in the steady state, which is y* = f(k*), is the same in both countries. But y* = Y/(L  E) or Y/L = y* E. We know that y* will be the same in both countries, but that E1 > E2. Therefore, y*E1 > y*E2. This implies that (Y/L)1 > (Y/L)2. Thus, the level of income per worker will be higher in the country with the more educated labor force. c. We know that the real rental price of capital R equals the marginal product of capital (MPK). But the MPK depends on the capital stock per efficiency unit of labor. In the steady state, both countries have k*1 = k*2 = k* because both countries have the same saving rate, the same population growth rate, and the same rate of technological progress. Therefore, it must be true that R1 = R2 = MPK. Thus, the real rental price of capital is identical in both countries. d. Output is divided between capital income and labor income. Therefore, the wage per effective worker can be expressed as w = f(k) – MPK • k. As discussed in parts (b) and (c), both countries have the same steady-state capital stock k and the same MPK. Therefore, the wage per effective worker in the two countries is equal. Workers, however, care about the wage per unit of labor, not the wage per effective worker. Also, we can observe the wage per unit of labor but not the wage per effective worker. The wage per unit of labor is related to the wage per effective worker by the equation Wage per Unit of L = wE. Thus, the wage per unit of labor is higher in the country with the more educated labor force. 7. a. In the two-sector endogenous growth model in the text, the production function for manufactured goods is Y = F [K,(1 – u) EL]. We assumed in this model that this function has constant returns to scale. As in Section 3-1, constant returns means that for any positive number z, zY = F(zK, z(1 – u) EL). Setting z = 1/EL, we obtain Y K = F ,(1-u) . EL Ł EL ł Using our standard definitions of y as output per effective worker and k as capital per effective worker, we can write this as y = F[k,(1 – u)] b. To begin, note that from the production function in research universities, the growth rate of labor efficiency, ΔE/E, equals g(u). We can now follow the logic of Section 9-1, substituting the function g(u) for the constant growth rate g. In order to keep capital per effective worker (K/EL) constant, break-even investment includes three terms: δk is needed to replace depreciating capital, nk is needed to provide capital for new workers, and g(u) is needed to provide capital for the greater stock of knowledge E created by research universities. That is, break-even investment is [δ + n + g(u)]k. c. Again following the logic of Section 9-1, the growth of capital per effective worker is the difference between saving per effective worker and break-even investment per effective worker. We now substitute the per-effective-worker production function from part (a) and the function g(u) for the constant growth rate g, to obtain Δk = sF [k,(1 – u)] – [δ + n + g(u)]k In the steady state, Δk = 0, so we can rewrite the equation above as sF [k,(1 – u)] = [δ + n + g(u)]k. As in our analysis of the Solow model, for a given value of u, we can plot the left and right sides of this equation The steady state is given by the intersection of the two curves. d. The steady state has constant capital per effective worker k as given by Figure 9-2 above. We also assume that in the steady state, there is a constant share of time spent in research universities, so u is constant. (After all, if u were not constant, it wouldn’t be a “steady” state!). Hence, output per effective worker y is also constant. Output per worker equals yE, and E grows at rate g(u). Therefore, output per worker grows at rate g(u). The saving rate does not affect this growth rate. However, the amount of time spent in research universities does affect this rate: as more time is spent in research universities, the steady-state growth rate rises. e. An increase in u shifts both lines in our figure. Output per effective worker falls for any given level of capital per effective worker, since less of each worker’s time is spent producing manufactured goods. This is the immediate effect of the change, since at the time u rises, the capital stock K and the efficiency of each worker E are constant. Since output per effective worker falls, the curve showing saving per effective worker shifts down. At the same time, the increase in time spent in research universities increases the growth rate of labor efficiency g(u). Hence, break-even investment [which we found above in part (b)] rises at any given level of k, so the line showing breakeven investment also shifts up. Figure 9-3 shows these shifts. In the new steady state, capital per effective worker falls from k1 to k2. Output per effective worker also falls. f. In the short run, the increase in u unambiguously decreases consumption. After all, we argued in part (e) that the immediate effect is to decrease output, since workers spend less time producing manufacturing goods and more time in research universities expanding the stock of knowledge. For a given saving rate, the decrease in output implies a decrease in consumption. The long-run steady-state effect is more subtle. We found in part (e) that output per effective worker falls in the steady state. But welfare depends on output (and consumption) per worker, not per effective worker. The increase in time spent in research universities implies that E grows faster. That is, output per worker equals yE. Although steady-state y falls, in the long run the faster growth rate of E necessarily dominates. That is, in the long run, consumption unambiguously rises. Nevertheless, because of the initial decline in consumption, the increase in u is not unambiguously a good thing. That is, a policymaker who cares more about current generations than about future generations may decide not to pursue a policy of increasing u. (This is analogous to the question considered in Chapter 8 of whether a policymaker should try to reach the Golden Rule level of capital per effective worker if k is currently below the Golden Rule level.) 8. On the World Bank Web site (www.worldbank.org), click on the data tab and then the indicators tab. This brings up a large list of data indicators that allows you to compare the level of growth and development across countries. To explain differences in income per person across countries, you might look at gross saving as a percentage of GDP, gross capital formation as a percentage of GDP, literacy rate, life expectancy, and population growth rate. From the Solow model, we learned that (all else the same) a higher rate of saving will lead to higher income per person, a lower population growth rate will lead to higher income per person, a higher level of capital per worker will lead to a higher level of income per person, and more efficient or productive labor will lead to higher income per person. The selected data indicators offer explanations as to why one country might have a higher level of income per person. However, although we might speculate about which factor is most responsible for the difference in income per person across countries, it is not possible to say for certain given the large number of other variables that also affect income per person. For example, some countries may have more developed capital markets, less government corruption, and better access to foreign direct investment. The Solow model allows us to understand some of the reasons why income per person differs across countries, but given it is a simplified model, it cannot explain all of the reasons why income per person may differ. More Problems and Applications to Chapter 9 1. a. The growth in total output (Y) depends on the growth rates of labor (L), capital (K), and total factor productivity (A), as summarized by the equation ΔY/Y = αΔK/K + (1 – α)ΔL/L + ΔA/A, where α is capital’s share of output. We can look at the effect on output of a 5-percent increase in labor by setting ΔK/K = ΔA/A = 0. Since α = 2/3, this gives us ΔY/Y = (1/3)(5%) = 1.67%. A 5-percent increase in labor input increases output by 1.67 percent. Labor productivity is Y/L. We can write the growth rate in labor productivity as DY D(Y / L) DL = - . Y Y / L L Substituting for the growth in output and the growth in labor, we find Δ(Y/L)/(Y/L) = 1.67% – 5.0% = –3.34%. Labor productivity falls by 3.34 percent. To find the change in total factor productivity, we use the equation ΔA/A = ΔY/Y – αΔK/K – (1 – α)ΔL/L. For this problem, we find ΔA/A = 1.67% – 0 – (1/3)(5%) = 0. Total factor productivity is the amount of output growth that remains after we have accounted for the determinants of growth that we can measure. In this case, there is no change in technology, so all of the output growth is attributable to measured input growth. That is, total factor productivity growth is zero, as expected. b. Between years 1 and 2, the capital stock grows by 1/6, labor input grows by 1/3, and output grows by 1/6. We know that the growth in total factor productivity is given by ΔA/A = ΔY/Y – αΔK/K – (1 – α)ΔL/L. Substituting the numbers above, and setting α = 2/3, we find ΔA/A = (1/6) – (2/3)(1/6) – (1/3)(1/3) = 3/18 – 2/18 – 2/18 = – 1/18 = –0.056. Total factor productivity falls by 1/18, or approximately 5.6 percent. 2. By definition, output Y equals labor productivity Y/L multiplied by the labor force L: Y = (Y/L)L. Using the mathematical trick in the hint, we can rewrite this as DY D(Y / L) DL = + . Y Y / L L We can rearrange this as DY DY DL = - . Y Y L Substituting for ΔY/Y from the text, we find Using the same trick we used above, we can express the term in brackets as ΔK/K – ΔL/L = Δ(K/L)/(K/L) Making this substitution in the equation for labor productivity growth, we conclude that D(Y / L) DA aD(K / L) = + . Y / L A K / L 3. We know the following: ΔY/Y = n + g = 3.6% ΔK/K = n + g = 3.6% ΔL/L = n = 1.8% Capital’s Share = α = 1/3 Labor’s Share = 1 – α = 2/3 Using these facts, we can easily find the contributions of each of the factors, and then find the contribution of total factor productivity growth, using the following equations: Output = Capital’s + Labor’s + Total Factor Growth Contribution Contribution Productivity DY aDK (1-a)DL = + Y K L + DA A 3.6% = (1/3)(3.6%) + (2/3)(1.8%) We can easily solve this for ΔA/A, to find that + ΔA/A. 3.6% = 1.2% + 1.2% + 1.2% We conclude that the contribution of capital is 1.2 percent per year, the contribution of labor is 1.2 percent per year, and the contribution of total factor productivity growth is 1.2 percent per year. These numbers match the ones in Table 9-3 in the text for the United States from 1948–2002. IN THIS CHAPTER, YOU WILL LEARN: ▪ how to incorporate technological progress in the Solow model ▪ about policies to promote growth ▪ about growth empirics: confronting the theory with facts ▪ two simple models in which the rate of technological progress is endogenous Introduction In the Solow model of Chapter 8, ▪ the production technology is held constant. ▪ income per capita is constant in the steady state. Neither point is true in the real world: ▪ 1900–2013: U.S. real GDP per person grew by a factor of 8.3, or 1.9% per year. ▪ examples of technological progress abound (see next slide). Examples of technological progress ▪ U.S. farm sector productivity nearly tripled from 1950 to 2012. ▪ The real price of computer power has fallen an average of 30% per year over the past three decades. ▪ 2000: 361 million Internet users, 740 million cell phone users 2015: 3.1 billion Internet users, 4.9 billion cell phone users ▪ 2001: iPod capacity = 5gb, 1000 songs. Not capable of playing episodes of Game of Thrones. 2015: iPod touch capacity = 64gb, 16,000 songs. Can play episodes of Game of Thrones. ▪ A new variable: E = labor efficiency ▪ Assume: Technological progress is labor-augmenting: it increases labor efficiency at the exogenous rate g: E g= E ▪ We now write the production function as: Y FKLE= ( ,  ) ▪ where L × E = the number of effective workers. ▪ Increases in labor efficiency have the same effect on output as increases in the labor force. ▪ Notation: y = Y / LE = output per effective worker k = K / LE = capital per effective worker ▪ Production function per effective worker: y = f(k) ▪ Saving and investment per effective worker: s y = s f(k) (δ + n + g) k = break-even investment: the amount of investment necessary to keep k constant. Consists of: ▪ δ k to replace depreciating capital ▪ n k to provide capital for new workers ▪ g k to provide capital for the new “effective” workers created by technological progress Steady-state growth rates in the Solow model with tech. progress Variable Symbol Steady-state growth rate Capital per effective worker k = K / (L × E ) 0 Output per effective worker y = Y / (L × E ) 0 Output per worker (Y/ L) = y × E g Total output Y = y × E × L n + g The Golden Rule with technological progress To find the Golden Rule capital stock, express c* in terms of k*: c* = y* − i* = f (k* ) − (δ + n + g) k* c* is maximized when MPK = δ + n + g or equivalently, MPK − δ = n + g In the Golden Rule steady state, the marginal product of capital net of depreciation equals the pop. growth rate plus the rate of tech progress. Growth empirics: Balanced growth ▪ Solow model’s steady state exhibits balanced growth—many variables grow at the same rate. ▪ Solow model predicts Y/L and K/L grow at the same rate (g), so K/Y should be constant. This is true in the real world. ▪ Solow model predicts real wage grows at same rate as Y/L, while real rental price is constant. Also true in the real world. ▪ Solow model predicts that, other things equal, poor countries (with lower Y/L and K/L) should grow faster than rich ones. ▪ If true, then the income gap between rich & poor countries would shrink over time, causing living standards to converge. ▪ In real world, many poor countries do NOT grow faster than rich ones. Does this mean the Solow model fails? ▪ Solow model predicts that, other things equal, poor countries (with lower Y/L and K/L) should grow faster than rich ones. ▪ No, because “other things” aren’t equal: ▪ In samples of countries with similar savings & pop. growth rates, income gaps shrink about 2% per year. ▪ In larger samples, after controlling for differences in saving, pop. growth, and human capital, incomes converge by about 2% per year. ▪ What the Solow model really predicts is conditional convergence—countries converge to their own steady states, which are determined by saving, population growth, and education. ▪ This prediction comes true in the real world. Growth empirics: Factor accumulation vs. production efficiency ▪ Differences in income per capita among countries can be due to differences in: 1. capital—physical or human—per worker 2. the efficiency of production (the height of the production function) ▪ Studies: ▪ Both factors are important. ▪ The two factors are correlated: countries with higher physical or human capital per worker also tend to have higher production efficiency. Growth empirics: Factor accumulation vs. production efficiency ▪ Possible explanations for the correlation between capital per worker and production efficiency: ▪ Production efficiency encourages capital accumulation. ▪ Capital accumulation has externalities that raise efficiency. ▪ A third, unknown variable causes capital accumulation and efficiency to be higher in some countries than others. Policy issues ▪ Are we saving enough? Too much? ▪ What policies might change the saving rate? ▪ How should we allocate our investment between privately owned physical capital, public infrastructure, and human capital? ▪ How do a country’s institutions affect production efficiency and capital accumulation? ▪ What policies might encourage faster technological progress? ▪ Use the Golden Rule to determine whether the U.S. saving rate and capital stock are too high, too low, or about right. ▪ If (MPK − δ) > (n + g ), U.S. economy is below the Golden Rule steady state and should increase s. ▪ If (MPK − δ) 0.03 = n + g ▪Conclusion: The U.S. is below the Golden Rule steady state: Increasing the U.S. saving rate would increase consumption per capita in the long run. How to increase the saving rate ▪ Reduce the government budget deficit (or increase the budget surplus). ▪ Increase incentives for private saving: ▪ Reduce capital gains tax, corporate income tax, estate tax, as they discourage saving. ▪ Replace federal income tax with a consumption tax. ▪ Expand tax incentives for IRAs (individual retirement accounts) and other retirement savings accounts. Allocating the economy’s investment ▪ In the Solow model, there’s one type of capital. ▪ In the real world, there are many types, which we can divide into three categories: ▪ private capital stock ▪ public infrastructure ▪ human capital: the knowledge and skills that workers acquire through education ▪ How should we allocate investment among these types? Allocating the economy’s investment Two viewpoints: 1. Equalize tax treatment of all types of capital in all industries, then let the market allocate investment to the type with the highest marginal product. 2. Industrial policy: Govt should actively encourage investment in capital of certain types or in certain industries, because they may have positive externalities that private investors don’t consider. Possible problems with industrial policy ▪ The govt may not have the ability to “pick winners” (choose industries with the highest return to capital or biggest externalities). ▪ Politics (e.g., campaign contributions) rather than economics may influence which industries get preferential treatment. Establishing the right institutions ▪ Creating the right institutions is important for ensuring that resources are allocated to their best use. Examples: ▪ Legal institutions, to protect property rights. ▪ Capital markets, to help financial capital flow to the best investment projects. ▪ A corruption-free government, to promote competition, enforce contracts, etc. Establishing the right institutions: North vs. South Korea After WW2, Korea split into: ▪ North Korea with institutions based on authoritarian communism ▪ South Korea with Western-style democratic capitalism Today, GDP per capita is over 10x higher in S. Korea than N. Korea Encouraging tech. progress ▪ Patent laws: encourage innovation by granting temporary monopolies to inventors of new products. ▪ Tax incentives for R&D ▪ Grants to fund basic research at universities ▪ Industrial policy: encourages specific industries that are key for rapid tech. progress (subject to the preceding concerns). CASE STUDY: Is free trade good for economic growth? ▪ Since Adam Smith, economists have argued that free trade can increase production efficiency and living standards. ▪ Research by Sachs & Warner: Average annual growth rates, 1970–89 open closed developed nations 2.3% 0.7% developing nations 4.5% 0.7% CASE STUDY: Is free trade good for economic growth? ▪ To determine causation, Frankel and Romer exploit geographic differences among countries: ▪ Some nations trade less because they are farther from other nations, or landlocked. ▪ Such geographical differences are correlated with trade but not with other determinants of income. ▪ Hence, they can be used to isolate the impact of trade on income. ▪ Findings: increasing trade/GDP by 2% causes GDP per capita to rise 1%, other things equal. Endogenous growth theory ▪ Solow model: ▪ sustained growth in living standards is due to tech progress. ▪ the rate of tech progress is exogenous. ▪ Endogenous growth theory: ▪ a set of models in which the growth rate of productivity and living standards is endogenous. The basic model ▪ Production function: Y = A K where A is the amount of output for each unit of capital (A is exogenous & constant) ▪ Key difference between this model & Solow: MPK is constant here, diminishes in Solow ▪ Investment: sY ▪ Depreciation: δK ▪ Equation of motion for total capital: ΔK = sY − δK The basic model ΔK = sY − δK ▪ Divide through by K and use Y = A K to get: Y K = = sA− Y K ▪ If s A > δ, then income will grow forever, and investment is the “engine of growth.” ▪ Here, the permanent growth rate depends on s. In Solow model, it does not. Does capital have diminishing returns or not? ▪ Depends on definition of capital. ▪ If capital is narrowly defined (only plant & equipment), then yes. ▪ Advocates of endogenous growth theory argue that knowledge is a type of capital. ▪ If so, then constant returns to capital is more plausible, and this model may be a good description of economic growth. A two-sector model ▪ Two sectors: ▪ manufacturing firms produce goods. ▪ research universities produce knowledge that increases labor efficiency in manufacturing. ▪ u = fraction of labor in research (u is exogenous) ▪ Mfg prod func: Y = F [K, (1 − u )E L] ▪ Res prod func: ΔE = g (u)E ▪ Cap accumulation: ΔK = s Y − δK A two-sector model ▪ In the steady state, mfg output per worker and the standard of living grow at rate ΔE / E = g (u ). ▪ Key variables: s: affects the level of income, but not its growth rate (same as in Solow model) u: affects level and growth rate of income Facts about R&D 1. Much research is done by firms seeking profits. 2. Firms profit from research: ▪ Patents create a stream of monopoly profits. ▪ Extra profit from being first on the market with a new product. 3. Innovation produces externalities that reduce the cost of subsequent innovation. Much of the new endogenous growth theory attempts to incorporate these facts into models to better understand technological progress. Is the private sector doing enough R&D? ▪ The existence of positive externalities in the creation of knowledge suggests that the private sector is not doing enough R&D. ▪ But, there is much duplication of R&D effort among competing firms. ▪ Estimates: Social return to R&D ≥ 40% per year. ▪ Thus, many believe govt should encourage R&D. Economic growth as “creative destruction” ▪ Schumpeter (1942) coined term “creative destruction” to describe displacements resulting from technological progress: ▪ the introduction of a new product is good for consumers but often bad for incumbent producers, who may be forced out of the market. ▪ Examples: ▪ Luddites (1811–12) destroyed machines that displaced skilled knitting workers in England. ▪ Walmart displaces many mom-and-pop stores. C H A P T E R S U M M A R Y 1. Key results from Solow model with tech progress: ▪ Steady-state growth rate of income per person depends solely on the exogenous rate of tech progress ▪ The U.S. has much less capital than the Golden Rule steady state 2. Ways to increase the saving rate ▪ Increase public saving (reduce budget deficit) ▪ Tax incentives for private saving C H A P T E R S U M M A R Y 3. Empirical studies ▪ Solow model explains balanced growth, conditional convergence. ▪ Cross-country variation in living standards is due to differences in cap. accumulation and in production efficiency. 4. Endogenous growth theory: Models that ▪ examine the determinants of the rate of tech. progress, which Solow takes as given. ▪ explain decisions that determine the creation of knowledge through R&D. Solution Manual for Macroeconomics Gregory N. Mankiw 9781464182891, 9781319106058