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Ch7%20Cowen%20Tabarrok - Growth Capital Accumulation and...

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Unformatted text preview: Growth, Capital Accumulation, and the Economics of Ideas: Catching Up vs. the Cutting Edge heChlneseecnomyasbeeng owinglatentastonishingu rate. In 2006, GDP per capita in China grew by 10 percent. In the same year, GDP per capita in the United States grew by just 2.3 percent. in its entire history, the US. economy has never grown as fast as the Chinese economy is growing today. If these rates continue, China wiil be richer than the United States in less than 25 years, How can this make sense? Is there something wrong with the US. economy? Do the Chinese have a magical potion for economic growth? Remember, in the last chapter we explained that among the key institutions promoting economic growth were property rights, honest government, political stability, at dependabie legai system, and competitive and open markets. But for each and every one of these institutions, the United States ranks higher than China, dew spite China’s having made remarkabie improvements in recent decades. So why is China growing so much more rapidly than the United States? To answer this Question, we must distinguish between two types of growth, catching up and cutting edge. Countries that are catching up have some enorw mous advantages.To become rich, 3 poor country does not have to invent new ideas, technologies, or methods of management. All it has to do is adopt the ideas already deveioped in the rich countriesAs we will see, catch—up coun— tries like China grow primarily through capital accumulation and the adoption of some simple ideas that massively improve productivity. I The United States is the world’s ieading economy~—it is on the cutting edge. Growth on the cutting edge is primarily about developing new ideas. But de~ veloping new ideas is more difficult than adopting ideas already in existence. Calculus isn’t easy but it doesn’t take a genius to understand calculus; it does take a genius to invent caiculus. Countries on the cutting edge grow primarily through idea generation. "11.5 when the capita}. stock stops growing, output stops growing as well.Thus, the iron logic of diminishing returns tells us that capital alone cannot be the key to economic growth. Let’s explain this in more detail. , Figure 7.4 focuses attention on the two key functions, the investment func— tion from Figure 7.2 and the depreciation function from Figure 7.3. .- Depreciation = 0.02 X K investment = 0.3 X all? The steady state K stock is found where investment = {Depreciation Capital increases or Decreases until investment Equals Depreciation When investment is greater than depreciation, the capital stock grows. When investment is less than depreciation, the capital stock shrinks. When investment equals depreciation, the capitai stock stays the same. __.._____._.._i Consider first a case where the capital stock grows larger. For instance, when K = 100, 3 units of output are invested in new capital and 2 units of capital depreciate. Investment exceeds depreciation so in the next period both the capitai stock and output will be larger. Thus, when investment is greater than depreciation (Investment > Depreciation) we have 'economiclgrowth. Investment increases as the capital stock gets larger, but because of the iron logic, investment increases at a diminishing rate. Depreciation, however, inw creases with the capital stock at a linear (constant) rate. Thus, at some point in" vestment equals depreciation (Investment = Depreciation). At this point, every unit of investment is being used to replace depreciated capitai, so the amount ofnet or new investment (investment after depreciation) is zero.We call this the steady state ievel of capital. At the steady state ievei of capitai, there is no new (net) investment and economic growth stops.We can summarize as follows: Investment > Depreciation—«the capitai stock grows and output next period is bigger Investment < Depreciation—the capital stock shrinks and output next period is smaller Investment 3 Depreciation—the capital stock and output are constant (the steady state) Growth, Capital Accumulation and the Economics of ideas: Catching Up vs. the Cutting Edge m CHAPTER 7 9 121 Check the Math W’henK: 100, Y E V 100 "—= 10, ofthese 10 units-0.3 >< i0 = 3 , units areinvested in new capitai. Depreciation is 0.02 X 100 w 2 units so Investment (3) > Deprecim tier: (2) and the capital stock and output grow. At the steady state the capital stock is neither increasing nor decreasing. Check the Math As Figure 7.4 is drawn the steady state occurs when K 5 225 because: Investment 5 0.3 X V225 2 4.5 Depreciation L” 0.02 X 225 = 4.5 thus when K = 225 Investment = Depreciation 322 ° PART 2 9 Economchrowth GDP per capita, reel U.S. dollars {2000) $40,009 France United States. 30,000 20,000 $9,000- Average years of schooling GDP- per Capita is Higher in Countries with More Human Capital (2000) Source: Penn World Tables and Barro and Lee, 2000 We learn, from our “capital only” model that long—run economiggrowth cannot be due to capital accumulationThe logic of diminishing returns means that eventually capital and output will cease growing. Economic growth, how— ever, does not seem to be slowing. So what else could drive long—run economic growth? Let’s return to the other factors of production that we discussed in Chapter 6-human capital and technological knowledge. Can increases in human capital drive long—run economic growth? Human capital is an important contributor to the wealth of nations. Figure 7.5 shows that GDP per capita is higher in countries with more homan capital, as mea—~ sured by average years of schooling. But human capital is just like physical capital in that it has diminishing re» turns and it deoreciates. In other words, an economic principles class is prohaw biy the most important economics class that you will take and all the human capital in the world today will be gone in a hundred years. (Why will all the human capital in the world today be gone in a hundred years? Hint:Where will your human canital be in a hundred years?) Thus, Within the Solow model, the logic of diminishing returns apoiies to human capital just as much as to physi- cal capital and neither can drive iongmrun economic growth. Better Ideas Drive Long-Run Economic Growth Can better ideas maintain long—run economic growth? Better ideas let us pro~ duc‘e more output from the same inputs of physical and human capital. A per— sonal computer today has about the same amount of silicon and labor ingot as a computer produced 20 years ago but today’s computer is much bettermthe difference is ideas. Recall our simple production function: Y=VT< :0 as Growth, Capital Accumulation and the Economics of Ideas: Catching Up vs. the Cutting Edge “9 C HAPTE R 7 9 123 We can think of hotter ideas as a way of getting more output from the same Put So remembering that we let A stand for ideas that increase productivity, ts now Write our production function as: Y=Axff€ :Notice that an increase in better ideas or technological knowledgewwas rep— sentcd by [emincreases output even while holding K constant, that is, an crease in A represents an increase in productivity. Figure 7.6 graphs two prom fiction functionsThe first is when A “J 1, the production function that we ave been working with all along. The second is when A = 2. Notice that hen K 5 16, output is 4 when A = 1, but it’s 8 when A * 2.Technologicai " owledge means that we can get more output frorn the same input. 1516 20 25 Capital, K n increase in A Increases Output Holding K Constant An ncrease in A represents an increase in productivity. lfA =_ ’lhthen a epital stock of 16 can produce 4 units of oUtput. If A = 2, 1then the same capital stock can produce twice as much output. ' m..~..._...._..~._.........__-._._........_”mean“...Mummwgwm.mmm.wyw.wmmwnum~_mu So long as we can develop better ideas that shift the production function . upwards then economic growth will continue. In a way, it should be obvious _ that better ideas are the key to longmrnn economic growth. How much ecom» nomic growth would there have been without the discovery of electricity or .' DNA or the development of the internal combustion engine, the computer chip, or the polymerase chain reaction? It’s just not enough to throw more ef— " fort at a problem; we have to actually know what we are doing and that boils dowu to ideas. ‘ Solow himself tried to estimate how much of US. economic prosperity was due to capital and labor and how much was due to ideas. He came up with the figure that hetter ideas are responsible for about three—fourths of the US. stan— dard of living. Many economists have subsequently debated the exact number, but no one contests the central importance of ideas and technological progress _ for human well—being. usemmmwrmeenm ': fit??? 124- 0: PART 2 *3 Economic'Growth {g fifi‘hwjfimgfifi So to understand economic growth we must move from capitai accumulation to take a closer look at the economics of ideasTo do that head to the section below titled “Growing on the Cutting EdgezThe Economics of Ideas.” Alternate tively, more lessons can be learned from a cioser inspection of the Soiow model. We deive into these further lessons in the next (optional) section. > What happens to the margina'i product of capital as more cap— itai is added? > Why does capitai depreciate? What happens to the totai amount of capital depreciation as the cepitei stock increases? """""" g" The Soiow Modeiwfleteils and Further Lessons (thionai Section) Let’s return to Figure 7.4, which we also reprint here as Figure 7.7. Depreciation = 0.92 x K 6 _____________________ I . investment : 0.3 X \i-K— I I=D24.5 ------------- 4 3 wwwwww ' ' , The steady state K stock is found where investment a Depreciation When investment is greater than depreciation the capitei stock grows When investment :5 less than depreciation the capital stock shrinks When investment equai s depreciation the capital stock stays the same ‘ Capital Increases or Decreases until investment Equals Depreciation We know that if Investment > Depreciation the capital stock increases and if Investment = Depreciation we are at the steady state ievel of capital, the ievel of capital such that the capital stock neither increases nor decreases. it’s also true that if Investment < Depreciation then the capital stock and output shrink Remember that Y3 W so If we know K we know Y And if K15 grow~ ing, then Yis growingwe can see this relationship a littie better in Figure 7.8, which plots investment, depreciation, and output in the same graph. That figure may look compiicated, but don’t get thrown off the basic idea, which is simply that the capital stock drives output, Y. For exampie, if K is at the steady state level (K i 225, in this case), then Ywill aiso be at a steady state Zevel of output, in this cese 15.We take the 225 off the horizontal axis and bounce it off the Y = WE curve to get to GDP = 15 on the vertical axis. Sim” flatly, since K drives Y, whenever K is growing then so is YThus, Figure 7.8 Growth, Capital Accumulation and the Economics of ideas: Catching Up vs. the Cutting Edge @ C HAPT E R 7 II i253 W...“..............w_.r-.-m.mwmm.__._W.qwmwm.m._._m-~m Output = W 20 Steady state output, Y z 15 20 Depreciation = {102 X K " investment In 0.3 X J? 100 200 225 300 400 + Capital, K Steady state When Capital Is in the Steady State, Output: Is in the Steady State The capital stock drives output. At Km 225, output is V225 = 15. At K m 225 investment equals depreciation; so the capital stock is neitherr growing nor shrinking and thus output is neither growing nor shrinking. i l i i i i I i i E E ca pita! stock 1 i i i 3 w‘M”MiiEmi'i’ffi'sTtrEires in shun more‘dEEailihan"we“h€d’l3€f6ié”Eliat our ihéorviof carpi: tal growth is also a theory of economic growth. I i In Figure 7.8 Q‘ ______ I i > What happens when the The Soiow Model and an increase in the invessment Rate What, happens in the Solow model "if “y, the fraction of output that is saved and invested, increases? It is simple: a greater investment rate means more capital, which 'means more output.An increase in the investment rate therefore increases a country’s steady state level of GDP. The result just shows that investment in— creases the number of “tractors” per worker which raises GDP per worker. In Figure 7.9 on the next page, we show this intuition in the graph by piet— ting two investment functions: Investment m 0.3%, which means that: 3 units 0f every 10 units of output are saved and invested (y = 0.3, as it was in Figure 7.8}, and also Investment a": (MM/K which means that 4 units of every 10 units of output are saved and invested {y = 0.4}. Notice that when 3/ = 0.4, the new sseady state capital stock increases to K = 400 and output increases to 20. Thus, the Soiow modei predicts that countries with higher rates of invest— ment wili he wealthier. Is this prediction of the Solow model consistent with the evidence? Yes. Figure 7.10, also on the next page, shows that GDP per Capital is higher in countries that have higher investment rates. This makes intuitive sense. More savings mean that more capitai goods can be produced and consumers can enjoy a higher standard ofiiving. How wealthy Wouid a country be if it spent all of its resources on partying? The Solow model says that an increase in the investment rate will increase Steady state output. But in the Solow mode}, the iron logic of diminishing ertUrns cannot be forever avoided.When the investment rate increases we have i capital stock is 400? g > What is investment? i > What is depreciation? l g > What happens to output? I I" aimerzsaratz‘éfié' rear-animatcoimmamnaefi fia‘ksmmflcmufinfi‘é mmwmesewsm-fismra to rditmrwtm‘ W m-fwasom‘maum. at.“ '4 136 9 PART 2 ‘3 Economic Growth In this chapter, we will do two things. First, we will develop a model of eco— nomic growth based on capital accumulationThe model wiil help us under— stand some puzzles suchras‘ why China is growing so much faster right now than theUnited States and why the countries that lost World War II, Germany , and japan, grew much faster in the postwar decades than did the winner, the United States.We will also discuss how poor and rich countries can converge in income over time. Our model of economic growth based on capital accumulation does a good job of explaining catch—up growth but it doesn’t help much to explain growth on the cutting edge. If we think about growth in the United States, for exam" ple, we probably do not think first about more tractors, buildings, and facto— ries—the sorts of things that characterize growth in China. Instead, we think about iPhones, the Internet, and genetic engineering, that is, new products, new processes, and new ideas.’l‘hus, in the second half of the chapter we turn to cuttingmedge growth and the economics of ideasThe economics of ideas explains why growth in the United States is siower than in China, but also why growth in China will slow down. It also suggests, however, that US. and worldwide economic growth may become faster in the decades ahead than it has been in the past.To put it bluntly (but regretfully for us), many of you will see more progress in your lifetimes than we will have seen in ours. The Solow Model and Catch-Up Growth . Let’s begin with a model of the wealth of nations and economic growth called the I gSOlOWTnOClCl(aftérNébElPrlze—mnmng economistAKothtlsolfii-yjfThe 3616‘? model begins with a production functionfl production function expresses a rela— tionship between output and the factors of production, namely the exact way in which more inputs will produce more outputs. For simplicity, we assume that there is only one output, Y, which We can think of as GDP, and the three factors of production that we discussed in the last chapter: physical capital written K; huw man capital, which we write as eL, and can understand as education, e, times La— bor; and ideas that increase the productivity of capital and labor, which we write as A.Thus, we can write that output, Y, is a function, P, of the inputs A, K, and 6L: Y = F(A, K, at) (I) That looks abstract but it represents a simple economic truth. If we look at a typical production process, say an automobile factory, output depends on capi— tal (the machines, K), labor (the workers, L, adjusted for their level of skill, so eL), and the whole factory is based on ideas (A), namely the invention of the auto and all the machines that help make it. We also can think of the entire economy as relying on capital, labor, and ideas on a larger scaie.We will focus on the Solow production function as a description of an entire economy because we are looking at the causes and consequences of overall economic growth. For our first look at the Solow model, we will temporarily ignore changes in ideas, education, and labor. If we assume that A, e, and L are constant, then we can simplify our expression for output as Y x F(K). Notice that because L is constant an increase in K always implies an increase in the amount of capi— tal per worker, K/ L, and an increase inY is also always an increase in output per worker, Y/L. .31, Production and Diminishing Returns "ice 2 quick sketch of what our production function, P{K),shou1d 100k ' Eire K should produce more Yhut at a diminishing rate. 0:; a farm, for :fié, the first tractor is very productiveThe second tractor is stili useful, but much as the first tractor.The third tractor is driven only when one of the {actors breaks down (remember that the amount of ia‘oor is constant). this means is that increases in capital, K, produce less output, Y, the more fiiready have-“"50 we should have a eroduction function where output in- "with more K but at a decreasing rate. Foliowing this logic, Figure 7.1 :hutput, Y, on the vertical axis against capitai, K, on the horizontai axis, ‘ i ‘ I l I ' I i I i I ‘ 1 ‘ 1 ‘ I ' I 4 ‘ ' I l I ‘ I t l ' I ' i I i . I l I I I ‘ | ‘ I I i J_ L... L. L_.| um. _L_i L__l _l_l 6 8 10 ’12 14%?6 18 20 22 2425 "3*- Capita!,K run Logic of Diminishing Returns More capitai, K, creates more output {:1 diminishing rate. The first unit of capital adds one unit to output but the it of capital adds just 0.13 units to output. ' / WMW-WHHW.Wm—ww-_ P1321 is diminishing. t' can sometimes help to look at a specific grociuction function. In Figure .71, 363d the production function Y m F(K] m VIZ", which means that output .6 square root of the capitai input.To see how this works in more detail, 138 in some numbers. IfK E 4, then Y = W x 2. If K increases to 16, then V13 w—w' 4 anti so forth. I. Growth: Capital Accumulation and the Economics of ideas: Catching Up vs. the Cutting Edge 0 C H APT E R 7 m 117 The marginal product of capital is the increase in output caused by the adéition of one more unit of capitalffhe marginal proéuct of capital diminishes as more and more capital is added. 118 9 PART 2 '9 EconomicGrowth As we said, the reason the marginai product of capital diminishes is that the first unit of capital (the first tractor) is appiied where it is most productive, the second unit is applied to slightly less productive tasics because the first unit is aiready performing the most productive tasks, the third unit is applied to even iess productive tasks, and so on. Growth in China and the United States The iron iogic of diminishing rem turns explains quite a bit about why China is now growing so much more rapidly than the United States. Imagine, for example, that a country labors unm tier poor institutions—like a lack of competitive and open markets—mo that the incentives to invest in capita} are low. Now suppose that new institutions are put into place, perhaps new leaders with better ideas repiace the old guardThe new institutions increase the incentives to invest and the capital} stock grows, But in a country without a lot of...
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