Modern Principles: Macroeconomics Tyler Cowen and Alex Tabarrok Chapter 7 Growth, Capital Accumulation, and the Economics of Ideas: Catching Up vs. the Cutting Edge Copyright © 2010 Worth Publishers • Modern Principles: Macroeconomics • Cowen/Tabarrok
Introduction • In 2006: § China: GDP per capita grew by 10% § United States: GDP per capita grew by 2. 3% • United States has never grown as fast as • the Chinese economy is growing today. Why is China growing more rapidly than the U. S. ? § Is there something wrong with the U. S. economy? § Do the Chinese have a magical potion for growth? Slide of 73
Introduction • There are two types of growth § Catch-up growth • Takes advantage of ideas, technologies, or methods of management already in existence § Cutting-edge growth • Primarily about developing new ideas • China is growing much faster than the U. S. because: § The U. S. economy is on the cutting edge. § The Chinese economy is catching up. 12. Slide of 73
Introduction • What do we learn in this chapter? § A model based on capital accumulation. • Explains catch-up growth. • Allows us to answer the following questions: § Why China is growing faster than the U. S. § Why the losers of WWII grew much faster than the winner. • How poor and rich countries can converge in income over time. § About cutting-edge growth and the economics of ideas. 12. Slide of 73
The Solow Model and Catch-Up Growth • Robert Solow – Nobel Prize in Economics • Total Output, Y, of an economy depends on: § Physical capital: K § Human capital: education x Labor = e. L § Ideas: A • This can be expressed as the following “production function”: 12. 5 Slide 5 of 73
The Solow Model and Catch-Up Growth • For now, ignore changes in ideas, education, and labor so that A, e, and L are constant. The production function becomes: • MPK: marginal product of capital • We draw a particular production function in the next slide where: § The additional output resulting from using an additional unit of capital. § As more capital is accumulated, the MPK gets smaller and smaller. Slide 6 of 73
The Solow Model and Catch-Up Growth • The “Iron Logic” of Diminishing Returns Output, Y 3. 2 3 1 Conclusion: as more capital is added, MPK declines. 0 1 2 3 4 5 6 7 8 9 10 11 12 12. 7 Capital, K Slide 7 of 73
The Solow Model and Catch-Up Growth • Growth in China and the United States § The “iron logic of diminishing returns” largely explains why… • The Chinese economy is able to grow so rapidly. § It turned toward markets which increased incentives. § The capital stock was low § The MPK was high. • China will not be able to achieve these high growth rates indefinitely. 12. Slide of 73
The Solow Model and Catch-Up Growth • Why Bombing a Country Can Raise Its • Growth Rate. Also explained by the “iron law”… § Much of the capital stock was destroyed during WWII. Therefore the MPK was high. § Following the war, both Germany and Japan were able to achieve much higher growth rates than the U. S. as they “caught up”. • Check out the following table. 12. Slide of 73
The Solow Model and Catch-Up Growth Conclusions: 1. Catch-up growth (Germany, Japan) is much greater than cutting-edge growth (U. S. ) 2. Eventually the catch-up growth slows down. Slide of 73
The Solow Model and Catch-Up Growth • Capital Growth Equals Investment Minus • Depreciation § Capital is output that is saved and invested. § Let g be the fraction of output that is invested in new capital. The next figure shows how output is divided between consumption and investment when g = 0. 3. 12. Slide of 73
The Solow Model and Catch-Up Growth • Capital Growth Equals Investment Minus Depreciation Output, Y 20 When K = 100, Output = 10 15 10 Consumption = (1 - 0. 3) x 10 = 7 5 Investment = 0. 3∙Y 3 2 0 Investment = (0. 3) x 10 = 3 0 100 200 300 400 12. Capital, K Slide of 73
The Solow Model and Catch-Up Growth • Capital Growth Equals Investment Minus Depreciation (cont. ). § Depreciation: amount of capital that wears out each period § Let d be the fraction of capital that wears out each period. This is called the depreciation rate so that: § The next diagram shows that the amount of depreciation depends on the capital stock. 12. 13 Slide 13 of 73
The Solow Model and Catch-Up Growth • Capital Depreciation Depends on the Amount of Capital Depreciation 8 Depreciation = 0. 02∙K 6 4 2 0 0 100 200 300 400 12. Capital, K Slide of 73
The Solow Model and Catch-Up Growth • Capital Alone Cannot be the Key to Economic Growth § Again, the “iron logic of diminishing returns” explains this insight. Let’s see how this works. § As capital increases, • depreciation increases at a constant rate = d. • output increases at a diminishing rate. • Because investment is a constant fraction of output, at some point depreciation will equal investment. § The capital stock will stop growing. § Output will stop growing. 12. Slide of 73
The Solow Model and Catch-Up Growth • Capital Increases or Decreases Until Investment = Depreciation GDP, Y 8 Depreciation = 0. 02∙K At K = 400, Inv. < Dep. → ↓ K 6 Investment = 0. 3∙Y 4. 5 4 At K = 100, Inv. > Dep. →↑K 3 2 0 0 100 225 300 Result: equilibrium at K = 225 Y = 4. 5 inv. = dep. =4. 5 400 Capital, K 12. Slide of 73
The Solow Model and Catch-Up Growth • Capital Increases or Decreases Until Investment = Depreciation Check the Math • At K = 100, Y =√ 100 = 10 • Depreciation = 0. 02 x 100 = 2 • Investment = 0. 3 x 10 = 3 • Investment > Depreciation Result: K and Y grow. Check the Math • At K = 400, Y =√ 400 = 20 • Depreciation = 0. 02 x 400 = 8 • Investment = 0. 3 x 20 = 6 • Investment < Depreciation Result: K and Y decrease. Check the Math • At K = 225, Y =√ 225 =15 • Depreciation = 0. 02 x 225 = 4. 5 • Investment = 0. 3 x 15 = 4. 5 • Investment = Depreciation Result: 1. Investment = Depreciation 2. K and Y are constant. This is a steady state. 12. Slide of 73
The Solow Model and Catch-Up Growth • Capital Alone Cannot be the Key to Economic Growth (cont. ) § The logic of diminishing returns means that eventually capital and output will cease growing. § Therefore, other factors must be responsible for long-run economic growth. § Consider: • Human capital: knowledge, skills, experience • Technological knowledge: better ideas 12. Slide of 73
The Solow Model and Catch-Up Growth 12. Slide of 73
The Solow Model and Catch-Up Growth • Better Ideas Drive Long-Run Economic Growth § Human Capital • Like capital, it is subject to diminishing returns and it depreciates. • Logic of diminishing returns also applies to human capital. • Conclusion: Human capital also cannot drive long-run economic growth. § What about technological knowledge? 12. Slide of 73
The Solow Model and Catch-Up Growth • Better Ideas Drive Long-Run Economic Growth (cont. ) § Technological knowledge • A way of getting more output from the same input (an increase in productivity). • We can include technological knowledge in our model by letting A stand for ideas that increase productivity. Therefore, let the production function be: 12. 21 Slide 21 of 73
The Solow Model and Catch-Up Growth 12. 22 Slide 22 of 73
The Solow Model and Catch-Up Growth • An Increase in A Increases Output Holding K Constant (cont. ) § Conclusion: • Technological knowledge or more generally better ideas are the key to long-run economic growth. • Solow estimated that better ideas are responsible for ¾ of our increased standard of living. 12. Slide of 73
Ø What happens to the marginal product of capital as more capital is added? Ø Why does capital depreciate? What happens to the total amount of capital depreciation as the capital stock increases? 12. 24 Slide 24 of 73
The Solow Model – Details and Further Lessons • Let’s review what we know now: § If Investment > Depreciation → K and Y grow. § If Investment < Depreciation → K and Y fall. § If Investment = Depreciation → K and Y are constant. • Two important conclusions § Steady state equilibrium occurs when investment equals depreciation. § When K is in steady state equilibrium, Y is in steady state equilibrium. § These results are illustrated in the next two diagrams. 12. Slide of 73
The Solow Model – Details and Further Lessons • When in steady state equilibrium, Y When K is in steady state equilibrium, Y is in steady state equilibrium. Output, Y 8 Depreciation = 0. 02∙K 6 Investment = 0. 3∙Y 4. 5 4 The Steady State K is found where investment = Depreciation 3 2 0 0 100 225 300 400 12. Capital, K Slide of 73
The Solow Model – Details and Further Lessons • When K is in steady state equilibrium, Y is in steady state equilibrium. Output, Y 20 Steady state output 15 Depreciation = 0. 02∙K 10 5 Steady state capital stock 0 100 225 300 400 Capital, K 12. Slide of 73
Ø What happens when the capital stock is 400? Ø What is investment? Ø What is depreciation? Ø What happens to output? 12. 28 Slide 28 of 73
The Solow Model – Details and Further Lessons • Solow Model and an Increase in the Investment Rate § What happens when g, the fraction of output that is saved and invested increases? • ↑g ↑K ↑Y § Conclusion: an increase in the investment rate increases a country’s steady state level of GDP. § We show this result in the next diagram. 12. Slide of 73
The Solow Model – Details and Further Lessons • An Increase in the Investment Rate Increases Steady State Output, Y 20 15 Depreciation = 0. 02∙K 10 5 0 100 225 300 400 Capital, K Slide of 73
The Solow Model – Details and Further Lessons • An Increase in the Investment Rate Increases Steady State Output (cont. ) § The results presented in the previous diagram predict that: • An increase in investment rate, g, causes output to increase. • Because labor is held constant, output per capita also increases. § An important test of our model: • Are its predictions consistent with real world data? • The next figure suggests that they are. 12. Slide of 73
The Solow Model – Details and Further Lessons Slide of 73
The Solow Model – Details and Further Lessons • An Increase in the Investment Rate Increases Steady State Output (cont. ) § An Important Idea • An increase in the investment rate = ↑ steady state level of output. • As the economy moves from the lower to the higher steady state output = ↑ growth rate of output • This higher growth rate is temporary. § Conclusion: ↑investment rate = ↑ steady state level of output but not its long-run growth rate. § These points are illustrated in following case study of South Korea. 12. Slide of 73
The Solow Model – Details and Further Lessons • The Case of South Korea § In 1950, South Korea was poorer than Nigeria. § 1950 s: the investment rate was < 10%. § 1970 s: Investment rate more than doubled. § 1990 s: Investment rate increased to over 35%. § South Korea’s GDP increased rapidly. § As GDP reached Western levels, the 12. growth rate has slowed. Slide of 73
The Solow Model – Details and Further Lessons • What Determines High Investment Rates? § Incentives which include • Low real interest rates • Low marginal tax rates § Institutions which include • Honest government • Secure property rights § One of the reasons that the investment rate increased in South Korea is that capitalists believed that their investments would be protected. • Effective financial intermediaries 12. Slide of 73
The Solow Model – Details and Further Lessons • The Solow Model and Conditional Convergence § Conditional Convergence: Among countries with similar steady state levels of output, poorer countries grow faster than richer countries. § The Solow model predicts that a country will grow faster the farther its capital stock is below its steady state value. • Conclusion: Conditional convergence is a prediction of the Solow model. § The next figure presents evidence of convergence. Slide of 73
The Solow Model – Details and Further Lessons 12. Slide of 73
The Solow Model – Details and Further Lessons • From Catching Up to Cutting Edge • • § Several predictions of Solow model are consistent with the evidence. • Countries with higher investment rates have higher GDP per capita. • Countries grow faster the farther their capital stock is from the steady state level. One prediction is NOT consistent with the evidence: § Steady state: Long-run growth = 0 What explains the observed long-run growth? § Answer: Better ideas 12. Slide of 73
The Solow Model – Details and Further Lessons • Solow and the Economics of Ideas in One diagram § Generation of ideas results in long-run economic growth. § Let’s see how this works: • We begin at steady state equilibrium. • New ideas → ↑A → ↑Output at every level of K • ↑ Output → ↑Investment → Investment > Depreciation →↑ K→ ↑ Output (movement along new production function). • As ideas continue to grow, output continues to grow. 12. 39 Slide 39 of 73
The Solow Model – Details and Further Lessons • Solow and the Economics of Ideas in One diagram (cont. ) Output, Y Effect of ↑A from 1 to 1. 5 c 33. 7 Output ↑ b Better Ideas 15 a 225 lation u Capital Accum Depreciation = 0. 02∙K 506 Capital, K Slide 40 of 73
ØWhat happens to investment and depreciation at the steady state level of capital? ØIn Figure 7. 9, how much is consumed in the old steady state? How much is consumed in the new steady state? ØDo countries grow faster if they are far below their steady state or if they are close? ØDo countries with higher investment rates have a lower or higher GDP per capita? 12. 41 Slide 41 of 73
Growing on the Cutting Edge: The Economics of Ideas • The United States and other developed regions such as Japan and Western Europe are on the cutting edge of economic growth. • In order to keep on growing these countries must develop new ideas to increase the productivity of capital and labor. • Conclusion: The economics of ideas becomes the key to growth on the cutting edge. 12. Slide of 73
Growing on the Cutting Edge: The Economics of Ideas • The Economics of Ideas 1. Ideas for increasing output are primarily researched, developed, and implemented by profit-seeking firms. 2. Spillovers mean that ideas are underprovided. 3. Government has a role in improving the production of ideas. 4. The larger the market, the greater the incentive to research and develop new ideas. 12. Slide of 73
Growing on the Cutting Edge: The Economics of Ideas 1. Research and Development Is Investment for Profit. § keys to increasing technological knowledge: • Incentives • Institutions that encourage investment in physical and human capital and R&D. § 70% of scientists and engineers in the U. S. work for private firms. § Profits provide incentive to invest in R&D • Implication: Property rights, honest government, political stability, a dependable legal system, and competitive open markets help drive the generation of technological knowledge. Slide of 73
Growing on the Cutting Edge: The Economics of Ideas 1. Research and Development Is Investment for Profit (cont. ). § Not just the number of scientists and engineers that are important • All kinds of people come up with new ideas. • Business culture and institutions are also important. § Institutions that are especially important: • Commercial settings that help innovators to connect with capitalists • Intellectual property rights • A high-quality education system 12. Slide of 73
Growing on the Cutting Edge: The Economics of Ideas 1. Research and Development is Investment for Profit (cont. ). § A commercial setting that helps innovators connect with capitalists. • Ideas without financial backers are sterile. • The U. S. is good at connecting innovators with businessmen and venture capitalists. • American culture supports entrepreneurs: § People like Apple CEO Steve Jobs are lauded in the popular media. § Contrast this to the treatment of 18 th century British entrepreneur John Kay. Slide of 73
Growing on the Cutting Edge: The Economics of Ideas John Kay (1704 -1780) invented the “flying shuttle” used in cotton weaving, the single most important invention launching the industrial revolution. Kay, however, was not rewarded for his efforts. His house was destroyed by “machine breakers, ” who were afraid that his invention would put them out of a job. Kay was forced to flee to France where he died a poor man. 12. Slide of 73
Growing on the Cutting Edge: The Economics of Ideas • Institutions that are especially important § Intellectual property rights • New processes, products, and methods can be copied by competitors. § World’s first MP 3 player was the Eiger Labs MPMan introduced in 1998. § Copied by other firms and Eiger Labs lost out in the competition. § Patents • Grant temporary monopoly. • Can slow down spread of technology. • Trade-off between creating incentives to research and develop new products and avoiding too much monopoly power = one of 12. trickiest in economic policy Slide of 73
Growing on the Cutting Edge: The Economics of Ideas • Institutions that are especially important (cont. ) § A high-quality education system • Important at all levels of education. • Creates necessary talent. • Universities generate basic and applied research. 12. Slide of 73
Growing on the Cutting Edge: The Economics of Ideas 2. Spillovers, and Why There Aren’t Enough Good Ideas § Ideas are non-rivalrous. § Ideas can be used simultaneously. • Use of an idea by one individual does not mean less of the idea available to someone else. § The spillover or diffusion of new ideas generates widespread economic growth. § Implication: Spillovers mean that the generator of the idea doesn’t get all of the benefits. • Result: Too few ideas are produced. • Let’s see why. Slide of 73
Growing on the Cutting Edge: The Economics of Ideas 2. Spillovers, and Why There Aren’t Enough Good Ideas (cont. ) § Optimal social investment in R&D occurs where: § § § MSB = MSC Optimal private investment occurs where: MPB = MPC With spillover benefits: MSB = MPB + spillovers and MSC = MSB Conclusion: Optimal Private Investment in R&D < Optimal Social Investment in R&D § Implication: Spillovers result in too little investment in research and development. 12. Slide of 73
Growing on the Cutting Edge: The Economics of Ideas • Spillovers Mean Too Little Investment in Research and Development $ Spillover benefits IP = optimal private investment in R&D IS =optimal social investment in R&D MPB = MPC MSB = MSC MPC = MSC MSB Assumes there are no spillover costs MPB IP IS Quantity of R&D Slide of 73
Growing on the Cutting Edge: The Economics of Ideas 3. Government’s Role in the Production of New Ideas § Ideas in mathematics, physics, and molecular biology have many applications so spillovers can be large. • Problem: Even if the social benefits are large, the private benefits can be small. • Solution: Subsidize the production of new ideas or give tax breaks for R&D expenditures. § Both shift the MC of R&D curve down → ↑ R&D investment. 12. Slide of 73
Growing on the Cutting Edge: The Economics of Ideas 3. Government’s Role in the Production of New Ideas (cont. ) § Large spillovers to basic science suggest a role for government subsidies to universities. • Especially those parts of the universities that produce innovations and the basic science behind those innovations. • Universities produce scientists § Most of the 1. 3 million scientists were trained in government subsidized universities. 12. Slide of 73
Growing on the Cutting Edge: The Economics of Ideas 4. Market Size and Research and Development § Innovations like pharmaceuticals, new computer chips, software, and chemicals require large R&D expenditures. § Companies will avoid investing in innovations with small potential markets. § Larger markets mean increased rewards (thus incentives) for R&D. § As the world market grows companies will increase their R&D investments. 12. Slide of 73
Ø What would happen to the incentive to produce new ideas if all countries imposed high tax rates on imports? Ø What are spillovers and how do they affect the production of ideas? Ø Some economists have proposed that the government offer large cash prizes for the discovery of cures for diseases like malaria that affect people in developing countries. What economic reasons might there be to support a prize for malaria research rather than, say, cancer research? 12. 56 Slide 56 of 73
The Future of Economic Growth • Over the last 10, 000 years per capita world GDP has been growing. § § Dawn of civilization to about 1500: growth = 0% AD 1500 – 1760: growth = 0. 08% Growth doubled in next 100 years. Increased even further during the 19 th and 20 th centuries. § Today: world wide growth of per capita GDP = 2. 2% 12. Slide of 73
The Future of Economic Growth • Economic growth can be even faster. How? § The following framework helps us think about this. A (ideas) = Population x Incentives x Ideas/Hour § Population • ↑population → ↑ number of people with new ideas § Much of the world is poor; thousands of potentially great scientists are laboring in menial jobs. § As the world gets richer → ↑ production of ideas → everyone benefits 12. Slide of 73
The Future of Economic Growth • Economic growth can be even faster. How? (cont. ) • A (ideas) = Population x Incentives x Ideas/Hour § Incentives • Appear to be increasing § Consumers are richer § Markets are expanding due to trade § World wide improvement in institutions § Property rights § Honest government § Political stability 12. § Dependable legal system Slide of 73
The Future of Economic Growth • Economic growth can be even faster. How? (cont. ) • A (ideas) = Population x Incentives x Ideas/Hour § Ideas per Hour • New ideas do not experience diminishing returns. • Two reasons why this is so. 1. Many ideas make creating new ideas easier. 2. The field of ideas that can be explored is so large that diminishing returns may not set in for a very long time. 12. Slide of 73
The Future of Economic Growth • Recap: Economic growth might be even faster in the future than it has been in the past. § There are more scientists and engineers in the world than ever before, and their numbers are also increasing as a percentage of the population. § Incentives are increasing due to growing markets resulting from • Increasing trade • Increasing wealth in developing countries § Better institutions and more secure property rights are spreading throughout the world. 12. Slide of 73
q. Takeaway • As K accumulates, the MPK declines until investment = depreciation, and growth stops. • The Solow model tells us three things about economic growth: § Countries that have higher investment rates will be wealthier. § Growth will be faster the further away a country’s capital stock is from its steady state value. § Capital accumulation cannot explain long-run economic growth. 12. Slide of 73
q. Takeaway • New ideas are the driving force behind long-run economic growth. § Ideas are non-rivalrous which means there are spillover benefits. § Spillover benefits means that the originator of the new idea will not receive all of the benefits. § In order to achieve the optimal number of ideas government can support production of new ideas… • By protecting intellectual property. • By subsidizing production of new ideas. 12. Slide of 73
q. Takeaway • There is a trade-off between providing appropriate incentives to produce new ideas and providing appropriate incentives to share new ideas. • The larger the size of the market, the greater the incentive to invest in R&D. • More people and wealthier countries increase the number of people devoted to the production of new ideas. • The increased wealth of many developing nations, the move to freer trade, and the spread of better institutions all encourage the future of economic growth. 12. Slide of 73
Modern Principles: Macroeconomics Tyler Cowen and Alex Tabarrok Chapter 7 Appendix: Excellent Growth Copyright © 2010 Worth Publishers • Modern Principles: Macroeconomics • Cowen/Tabbarrok
Appendix • Excellent Growth § Using a spreadsheet, you can easily explore the Solow model and duplicate all the graphs. First, calculate the increasing capital stock using the formula in A 3 and let the spreadsheet do the rest. Note: Clicking on the lower right corner of a cell and dragging it down will duplicate the formula in the lower cells. 12. 66 Slide 66 of 73
Appendix • Excellent Growth (cont. ) Second, calculate output, Y, using the formula: 12. 67 Slide 67 of 73
Appendix • Excellent Growth (cont. ) Third, graphs can be created using the data generated 12. 68 In the steps one through three. Slide 68 of 73
Appendix • Excellent Growth (cont. ) Lastly, you can experiment with different investment shares in E 2 or the depreciation rates in F 2. 12. 69 Slide 69 of 73
Appendix • The Mathematics of Economic Growth • • along the Transition Path Objective: To see how economic growth varies along the transition path to a new steady state equilibrium. We will do two things: § Outline the mathematics. § Use a spreadsheet to visualize our results. 12. 70 Slide 70 of 73
Appendix • The Mathematics By plotting these two expressions separately on a graph, we can see how the steady state changes with the values of the investment rate and depreciation rate. 12. 71 Slide 71 of 73
Appendix • The Mathematics d, g/K 1/2 0. 08 0. 07 0. 06 Difference is the growth rate of the capital stock. The bigger the difference the faster K grows. 0. 05 0. 04 0. 03 0. 02 d = 0. 02 0. 01 0. 4/K 1/2 400 Capital, K 12. 72 Slide 72 of 73
Appendix • The Spreadsheet Plotting Y against time shows the transition to steady 12. 73 state Slide 73 of 73
Appendix • The Spreadsheet Result: The transition to steady state proceeds at a decreasing rate. As K approaches 400 growth slows down. Slide 74 of 73
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