The Facts of Growth

The Facts of Growth
O
ur perceptions of how the economy is doing are often dominated by year-to-year fluctuations in economic activity. A recession leads to gloom, an expansion to optimism. But if we step back to get a look at activity over longer periods—say. over many decades—the picture changes. Fluctuations fade. Growth—the steady increase in aggregate output over time—dominates the picture.
Figure 10.1 shows the evolution of Australian GDP (in 1966 dollars to 1973. and chain volume since) from 1901.The years from 1929 to 1932 correspond to the large decrease in output during the Great Depression.and the years 1981 -83 correspond to the largest postwar recession. Note how small these two episodes appear compared with the steady increase in output over the last 100 years.
Figure 10.1 Australian real GDP since 1900

100,000
10.000-
Australian GDP
£ X
я M
0
The scale used to ► measure GDP on the vertical axis in Figure 10.1 is called a logarithmic scale. The characteristic cf a logarithmic scale is that the same proportional increase in a variable is represented by the same distance on the vertical axis. For more discussion, see Appendix 2 at the end of the book..
a. Q
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я ti a:
1.000
I i i I I I il i
1991 2001
I i i I ) i
1921 1931 1941
1961 1971
1901 1911
1951
1981



Aggregate Australian output has increased by a factor of 28 since 1900.
SOURCES: M. Butlin.'A Preliminary Annual Database 1900/01 1973.74 . RBA Discussion Paper 7701. May 1977. RBA Table GI0.
With this in mind, we now shift our focus from fluctuations to growth. Put another way, we turn from the study of the determination of output in the short and medium run—where fluctuations dominate— to the determination of output in the long run—where growth dominates.
• Section 10.1 looks at growth in Australia and other rich countries over the last sixty years.
• Section 10.2 takes a broader look, across both time and space.
• Section 10.3 gives a primer on growth and introduces the framework to be developed in the next three chapters.
10.1 GROWTH IN RICH COUNTRIES SINCE 1950
Tabic 10.1 gives thc evolution of output per capita (CDP divided by population) lor Australia, Prance, Germany, lapan the United Kingdom and the United States since 1950. We have chosen these six countries not only because they include the worlds major economic powers but because what has happened to them is broadly representative of what has happened in other advanced countries over the last half-centurv or so.
There are two reasons for looking at the numbers tor output per capita rather than the numbers tor total output. The evolution of the standard of living is given by the evolution of output per capita, not a country's total output. And. when comparing countries with different populations, output numbers must be adjusted to lake account ot these differences in population size. This is exactly what output per capita does.
Before discussing the table we must look into how the output numbers are constructed. Often, in constructing output numbers tor countries other than the United States, we use the straightforward method ol taking that country's GDP expressed in that country's currency, then multiplying it by the current exchange rate to express it in terms of US dollars. But as we discussed in Chapter 1, this simple calculation won't do here lor two reasons.
4 Output'. GDP. Output per capita: GDP divided by population.
• f irst exchange rates can vary a lot I more on this in Chapters 18-21 . The US dollar appreciated and then depreciated in the 1980s by roughly 50 per cent vis-a-vis thc currencies ol its trading partners. But, surely the standard of living in the United States didn't increase by 50 per cent and then decrease by 50 per cent compared with the standard ol living ol its trading partners in the l')80s. Yet this is the conclusion we would reach il we compared GDP per capita using current exchange rales.
Table 10.1 The evolution of output per capita in six rich countries from 1950 to 2004
Annual growth rate output per capita 1950-73 1974-2004 1950 Real output per capita (chain volumes) 2004 2004/1950
Australia 2.3% 2.0% 9.302 27.994 3.0
France 4.1% 1.7% 5,921 26,168 4.4
Germany 4.8% 1.8% 4,642 25,606 5.5
Japan 7.9% 2.1% 2.188 24,661 11.3
United Kingdom 2.6% 2.1% 8.082 26.762 3.3
United States 2.4% 2.1% 11,233 36.098 3.2
Average 4.0% 2.0% 6,895 27.882 5.1
1 1
SOURCES' Penn World Tables, constructed by Alan Heston. Robert Summers and Bcttina Aten. Penn World Table Version 6.2, Centre for International Comparisons at the University of Pennsylvania (CICUP). October 2006 (http://pwtecon.upenn.edu). German data 1950-73 are from the OECD Economic Outlook, and population growth rates from the IMF International Financial Statistics (IFSl.The averages in thc last line are simple (unweighted) averages.
 
• The second reason goes beyond fluctuations in exchange rates. In 2003. GDP per capita in India, using the current exchange rate was US$560, compared with US$37,300 in the United States Surely nobody could live on US$560 a year in the United States. But people live on it—admittedly not very well—in India, where the prices ol basic goods, those goods needed lor subsistence, arc- much lower than in the United States. The level ot consumption ol the average person in India who consumes mostly basic goods, isn't sixty-six 37.300 divided by 560 times smaller than that of the average person in the United Stales. This pattern applies lo other countries besides the United States and India. In general, the lower a country's output per capita, the lower the prices of food and basic services in thai country.
numbers
The bottom line: when ► comparing standard of living across countries, use PPP numbers.These can be obtained from the Penn World Tables for most countries from 1950 to 2004. The OECD produces PPP figures on an ongoing basis for OECD
Policy measures with such magic results have proven difficult to discover! ►
So. when our focus is on comparing standards ol living, either across time or across countries, we gel more meaningful comparisons by correcting lor the effects just discussed—variations in exchange rates, and systematic differences in prices across countries. The numbers in Table 10.1 are obtained by making these corrections. The details ol construction are complicated, bin the principle is simple: the numbers lor GDP in Table 10.1 are constructed using a common set ol prices lor all countries. Such adjusted real GDP numbers, which you can think ol as measures of purchasing power across time or across countries, are called purchasing power parity 'PPP numbers. Further discussion is given in the
locus box The construction ol PPP
The dillerences between PPP numbers and the numbers based on current exchange rales can be substantial. Return to our comparison between India and the United Slates. Wc saw that, at current exchange rates the ratio ol G.DP per capita in the United Slates ю GDP per capita in India was 66 in 2003. Using PPP numbers Irom the Penn World Tables (available for India only up lo 2003), the ratio is only 37,300/3,212 = 11,6,- while this is still a large difference, il is much smaller than the ratio obtained using current exchange rales.
Or take comparisons among rich countries Based on the type ol numbers we saw in Chapter I— numbers constructed using current exchange rates GDP per capita in Australia in June 2008 was equal to 1 10 per cent (50,700/46.300) of the GDP per capita in the United States. But based on the PPP numbers produced by the OF.CD. GDP per capita in Australia was in lact equal to 8') per cent (4 1,300/46,300) ol GDP per capita in the United States in 2008.
More generally, PPP numbers suggest thai the United States still has the highest GDP per capita among the worlds major countries. Interestingly, Australia was ranked second lo the United States among these six rich countries in 2004 The clfect ol the PPP adjustment makes a big difference to the ranking. II Australia's relatively weak exchange rate in late 2008 was used, Australia would fall in the rankings, yet its comparative standard ot living has not changed much:
We can now return to Table 10.1 You should draw three main conclusions from the table:
I. The standard of living has increased significantly since 1950. Growth from 1950 to 2004 has increased real output per capita by a factor ol 3.0 in Australia, 3.2 in the United States. 5.5 in Germany and 11.3 in lapan.
These numbers show what is sometimes called the force of compounding. In a different context you probably have heard how saving even a little while you are young will build to a large amount by the time you retire. For example, il ihe interest rate is 4.9 per ccnt a year an investment of $1 with the proceeds reinvested every year will have grown to about $11 within liflv years [I + 0.049]5" - 10.93 dollars). The same logic applies to growth rales. The average annual growth rate in lapan over the period 1950—2004 was equal to 4.6 per cent ([7.9% p a. times 23 years • 2.1 % p.a. times 31 years], divided by 54 years). This high growth rate has led to an eleven-fold increase in real output per capita over the period.
Clearly, a better understanding of growth, il it leads to the design ot policies that stimulate growth, can have a very large effect on the standard ol living. Suppose we could lind a policy measure that increased the growth rale permanently by I percent. This would lead, alicr lorty years, to a standard of living 50 per ccnt higher than it would have been without the policy, a substantial difference. 
THE CONSTRUCTION OF PPP NUMBERS
Consider two countries—say. the United States and Russia—but without attempting to fit the characteristics of these two countries ve-y closely.
Suppose that in the United States annual consumption per capita equals US$20,000. Individuals buy two goods: every year they buy a new car for US$10,000 and spend the rest on food.The price of a yearly bundle of food is US$10,000.
In Russia.annual consumption per capita equals 60.000 rubles. People keep their cars for fifteen years.The price of a car is 300,000 rubles, so individuals spend on average 20.000 rubles—300,000/15—a year on cars. They buy the same yearly bundle of food as their US counterparts, at a price of 40,000 rubles.
Russian and US cars are of identical quality, and so is Russian and US food. (You may dispute the realism of these assumptions. Whether a car in country X is the same as a car in country Y is very much the type of problem confronting economists constructing PPP measures.) The exchange rate is such that one US dollar is equal to 30 rubles. What is consumption per capita in Russia relative to consumption per capita in the United States?
One way to answer is by taking consumption per capita in Russia and converting it into US dollars using the exchange rate. Using that method. Russian consumption per capita in US dollars is $2,000 (60.000 rubles divided by the exchange rate, 30 rubles to the US dollar). According to these numbers, consumption per capita in Russia is only 10 per cent of US consumption per capita.
Does this answer make sense? True. Russians are poorer, but food is much cheaper in Russia. A US consumer spending all of his US$20,000 on food would buy two bundles of food (US$20.000/US$ 10.000). A Russian consumer spending all of his 60.000 rubles on food would buy 1.5 bundles of food (60.000 rubles/40.000 rubles). In terms of food bundles, the difference looks much smaller between US and Russian consumption per capita. And given that one-half of consumption in the United States and two-thirds of consumption in Russia goes to spending on food, this seems like a relevant calculation.
Can we improve on our initial answer? Yes. One way is to use the same set of prices for both countries and then measure the quantities of each good consumed in each country using this common set of prices. Suppose we use US prices. In terms of US prices, annual consumption per capita in the United States is obviously still US$20,000. What is it in Russia? Every year, the average Russian buys approximately 0.07 cars (one car every fifteen years) and one bundle of food. Using US prices—specifically, US$10,000 for a car and US$10,000 for a bundle of food—gives Russian consumption per capita as [(0.07 x US$10,000) + (I x US$10,000)] = (US$700 + US$10,000) = US$10,700. So. using US prices to calculate consumption in both countries puts annual Russian consumption per capita at US$I0.700/US$20,000 = 53.5 per cent of annual US consumption per capita, a better estimate of relative standards of living than we obtained using our first method (which gave only 10 per cent).
FOCUS T BOX
This type of calculation—namely, the construction of variables across countries using a common set of prices—underlies PPP estmates. Rather than using US dollar prices as in our example (why use US rather than Russian or, for that matter, French prices?), these estimates use average prices across countries: these prices are called'international dollar prices'.The estimates we use in Table 10.1 and elsewhere in this chapter are the result of an ambitious project known as the Penn World Tables'. ('Penn' is for the University of Pennsylvania, where the project is located.) Led by three economists—Irving Kravis, Robert Summers and Alan Heston—over more than twenty years, this project has constructed PPP series not only for consumption (as we just did in our example) but more generally for GDP and its components, going back to 1950. for most countries in the world. Other agencies, such as the OECD and the World Bank, have since been stimulated to try to improve on the construction of PPP-adjusted macro series.
For more on the construction of PPP numbers, go to the website listed under Table 10.1.
2. Growth rata of output per capita have decreased since the mid-1970s. The lirst two columns ol Table 10.1 show growth rates of output per capita lor both pre- and post-1973. Pinpointing the exact date ol the decrease in growth is difficult,- 197.3, the date used to split the sample in the table, is as good as any date in the mid-1970s. It was about when oil prices shot up 
Growth has decreased in all six countries. The decrease has been stronger in the countries that were growing last pre-1973, such as France, Germany and especially Japan, with the result that the differences in growth rates across countries are smaller post-1973 than they were pre-1973
If it continues this decline in growth will have profound implications lor the evolution of the standard ol living in the future. At a growth rate ol 4 per ccnt per year—the average growth rate across our six countries Irom 1950 to 1973—it takes only eighteen years tor the standard of living to double.
At a growth rate of 2.0 per cent per year—the average Irom 1974 to 2004—it takes thirty-five years, about twice as long. Expectations ol last growth in individual income that had developed in the 1950s and 1960s have had to confront the reality ol lower growth since 1973 In this context it is easy to sec why the increase in productivity growth in Australia and the United States from the second half of the 1990s that we saw in Chapter I is potentially big news. Provided the global slowdown in 2008-09 turns out to be short-lived, it may be the sign that we are poised lor a return to the high pre-1973 growth rates. We will return to the issue in Chapter 12.
3. Levels of output per capita across the six countries have converged Ibecome closer) over time. Put another way, those countries that were behind have grown lasier reducing the gap between them and the United States.
In 1950 output per capita in the United States was around twicc the level ol output per capita in France and (iermany, and about five times the level ol output per capita in Japan. From the perspectives of Japan and Europe, the United States looked like the land ol plenty, where everything was bigger and better. Today these perceptions have faded, and the numbers explain why Using PPP numbers US output per capita is still the highest, but in 2004 it was only 38 per cent above the average output per capita in the other live countries, a much smaller difference than in the 1950s (86 per cent).
This convergence of levels of output per capita across countries is not specific to the six countries we are looking at but extends to the set of OECD countries. This is shown in Figure 10.2, which plots the average annual growth rate of output per capita Irom 1950 to 2000 against the initial level ol output per capita in 1950 lor the countries that are members ol the OECD today. There is a clear negative relation between the initial level ol output per capita and the growth rate since 1950—countries that were behind in 1950 have typically grown faster. The relation isn't perfect: Turkey which had roughly the same low level of output per capita as Japan and South Korea in 1950, has had a growth rate equal to only about hall that ol Japan. Tiny Luxembourg stands out as a rich state that managed to grow really well to be the richest in 2000, largely by exporting tax-sheltered financial services. And New Zealand has managed the lowest average growth to move from fourth-richest to eleventh in 2000. But the negative relation lor these OECD countries is clearly there. In terms ol real GDP per capita, Australia was ranked lourth in 1950. hut dropped to ninth in 2000. Wc can now understand why Australia had such a low average real GDP growth per capita ol about 2 per ccnt over filtv years—it was a relatively rich country in 1950. However, Australia's drop in the rankings is a cause for concern.
Some economists have pointed to a problem in graphs like Figure 10.2. By looking at the set of countries that are members ol the OECD today, what we have done in effect is to look at a club of economic winners. Although OECD membership isn't officially based on economic success, economic success is surely an important determinant ot membership. But when you look at a club whose membership is based on economic success, you will lind that those who came from behind had the lastest growth. This is precisely why they made it to the club. Thus, the finding of convergence could come in part from the way we sclcctcd the countries in the lirst place.
The 'rule of 70': if a ► variable grows at x per cent a /ear, it will take approximately 70/ years for the variable to double. If * = 4. it will take about 18 (70 divided by 4) years for the variable to double. If x = 1.9. it will take about 39 (70 divided by 1.9) years.
From the focus box in У Chapter I: the OECD (which stands for Organisation for Economic Cooperation and Development) is an international organisation that includes most of the world's rich economies. The complete list is given in Chapter I.
So, a belter way ol looking at convergence is to define the set of countries we look at not on ihe basis ol where they are today—as we did in Figure 10.2 by taking today's OECD members—but on the basis ol where they were in say, 1950. For example, we can look at all countries that had an output per capita of at least 30 percent ol LIS output per capita in 1950, then look for convergence within that group. Il turns out that most ol the countries in that group have indeed converged, and therefore convergence isn't solely an OECD phenomenon. However, a few countries—notably Uruguay,
Figure 10.2 Growth rate of real GDP per capita from 1950 to 2004 versus real GDP per capita in 1950; OECD countries
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Mexico
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Australia
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Switzerland New Zealand
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4,000 6.000 8.000
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12,000
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Real GDP per capita in 1950 (chain, 1996 US$)


Countries that had о lower level of output per capita in 1950 have typically grown faster.
SOURCE. PWT 6.2. see Table 10.1. Czecn Republic. Slovakia. Poland. Greece aid Hungary are not included because of missing data. Germany is excluded because of the consolidation of West and East Germany in 1991 .The starting date for Greece is extrapolated back from 1951. and South Korea from 1953.
Argentina and Venezuela among them—haven't converged. A most striking case is Argentina. In 1950, output per capita in Argentina was $6,941 (in 1996 US dollars), about 17 per cent higher than the output per capita in France. In 2004. it stood at $10,939 in 1996 US dollars), a meagre average annual growth rate ol 0.8 per cent over lihy years—lar below the 2001 French level of $26,168.
10.2 A BROADER LOOK ACROSS TIME AND SPACE
look lurther hack in lime. Economic historians are able to piece together various sources of information to produce a rough sketch. Figure 10.3 presents data Irom Angus Maddisons research on real GDP per person in the world over the last 2,000 years. What is remarkable is how much progress was made in the second half of the twentieth century in Western countries. Asia dominated by China and India, only began to make progress in the late twentieth century. Africa hasn't made significant improvements even in the twentieth century, unfortunately declining in recent years. Despite the difficulty in constructing reliable data, there is agreement among economic historians about the main evolutions over the last 2,000 years.
• From the end ol the Roman Empire to roughly 1500, there was essentially no growth ol output per capita in Europe—most workers were employed in agriculture, in which there was little technological progress. Because agriculture's share ol output was so large, inventions with applications outside agriculture could contribute little lo overall production and output. While there was some output growth, a roughly proportional increase in population led to roughly constant output per capita.
• From about 1500 to 1700, growth of output per capita turned positive but small, around 0.1 per ccnt per year, increasing to 0.2 percent per year Irom 1700 to 1820.
• Even during the Industrial Revolution, growth rales weren't high by current standards. The growth rate of output per capita from 1820 to 1450 in the United States was only 1.5 per ccnt per year.
This period of stagnation of output per capita is often called the Malthusian era. Thomas Robert lialthus.
an English economist writing at the end of the 18th century, argued that this proportional increase in output and population wasn't a coincidence.Any increase in output, he argued, would lead to a decrease in mortality. * which would in turn lead to an increase in population until output per capita was back at its initial level. Europe was in a trap, unable to increase its output per capita. Eventually. Europe was able to escape that trap. But the issue remains very relevant in many poor countries.
• On the scale ol human history, therefore, growth of output per capita is a recent phenomenon. In light of the growth record of the last 200 years or so. what appears unusual is the high growth rate ach eved in the 1950s and the 1960s, rather than the lower growth rate since 1973.

Western
Tin phenomenal development during the twentieth century isn't only evident from output per capita data. The World Bank 'www.worldbank.org) produces information on a variety of development indicators. Some prominent examples are:

Figure 10.3 Real GDP per person from 0 to 1998
After minimal progress for 1,900 years, significant gains were made in the twentieth century, particularly in Western countries (Europe. US, Japan, Australia, etc.).
1 I I I I I I I
1700 1820 1870 1913 1950 1973 1998
World
Asia (not Japan) Africa

SOURCE Angus Maddison. The Wo rid Economy. A Millennium Perspective (OECD. 2001). 
• At the beginning of the twentieth century, the world's population was 1 billion people. Now it
supports 6.4 billion.
• I rom the beginning to the end ol the century, average life expectancy increased dramatically, from
forty years to sixty-seven years.
• In 1400, 25 per cent ol babies died in their first year of life,- now less than 6 per cent die.
• l he proportion ot adults that can read and write has increased from 25 per cent lo nearly 80 per cent.
Overall there has been remarkable global growth in the last 100 years. However, that doesn't mean
that everyone is better oil. For example the number of people in poverty has changed little in 100 years. Using PPP-adjusted data. Xavicr Sala-i-Martin has shown that the number ol people living on less than US$2 in 1085 prices! per day at the end of the twentieth century was almost one billion, which was the size ol the entire world population in 14(H)! And in 1900 most ol the world's population would have been living on less than US$2 per day. Therefore, over the twentieth century the total number living at that level ol poverty changed little—though, ol course, thc proportion ol the population living at that level has fallen dramatically. The vast majority ol these poor people today live- in Africa. Fortunately, the global trend in the standard ot living has been moving in thc right direction in the last twenty years, mainly due to the rapid growth in China and, to a lesser extent, India. You shouldn't conclude that output growth could do little lor the number ol people in poverty in the twentieth century—rather, growth is likely to be one ol the best cures, or at least necessary to prevent an increase in poverty. A lack ol economic growth will olten set the scene lor a vicious cycle of population explosion, war, disease and more poverty.
Our focus on the growth ol CDP per capita as the measure ol a country's well-being does override many interesting teatures ol development. The focus box Growth and happiness' discusses the relationship between the growth ol GDP per capita and the happiness that people express.
History puts into context the convergence ol OFCD countries to the level ot LIS output per capita since 1950. Thc United States wasn't always the world's economic leader. History looks more like a long-distance race in which one country assumes leadership lor some time, only lo lose it lo another and return to the pack or disappear Irom sight For much of the first millennium, and until the fifteenth century, China probably had the world's highest level ot output per capita. For a couple of centuries, leadership moved lo the cities of northern Italy. Leadership was then assumed by the Netherlands until around 1820, and then by the United Kingdom Irom 182.0 lo around 1870. Since then, the United Stales has been mainly in the lead, though economic historians rank Australia number one for a very brief interlude at the beginning ol the twentieth century, and right now tiny Luxembourg dominates. Ignoring very small countries, the Llnited States is now the outright leader. Seen in this light, history looks more like leapfrogging iin which countries get close to the leader and then overtake il than convergence (in which the race becomes closer and closer). If history is any guide, the Llnited States may not remain in thc lead forever.
Looking across countries
We have seen how output per capita has converged among OliCD countries. But what about the other countries? Are the poorest countries also growing faster? Are ihey converging towards the United Slates, even il they are still tar behind?
A first answer is given in Figure 10.4 which plots the annual growth rate ol output per capita Irom I960 to 2000 against output per capita lor the year I960, for I 10 countries. The striking feature of Figure 10.4 is that there is no clear pattern. Il is not lhe case thai, in general, countries thai were behind in I960 have grown faster. Some have, hut many have not.
The numbers for 1950 are missing for too many countries to use 1950 as the initial year, as we did in Figure 10.2. Also there are data available for many more countries in 2000 than in 2004. Figure 10.3 includes all 4 the countries for which PPP estimates of GDP per capita exist for both I960 and 2000.There are some notable absences, such as a number of Eastern European countries, for which the numbers for 1960 are not available.
The cloud ol points in Figure 10.4 hides, however, several interesting sub-patterns, which appear when we put countries into different groups. In figure 10.5 we identity live groups. Thc diamonds represent thc OFCD countries we looked at earlier (excluding Japan and South Korea). The squares represent Alrican countries The triangles represent Fast and Southeast Asian countries. The + symbols arc for Southwest Asia and the Middle Last, and thc x symbols represent Latin America. Together, these live groups account lor I 10 countries.
Figure 10.4 Growth rate of real GDP per capita from 1960 to 2004 versus real GDP per capita in 1960: 110 countries
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4,000 6,000 8.000 10.000 12.000 Real GDP per capita (chain index, 1996 US$)


There is no clear relation between the growth rate of output since 1960 and the level of output in 1960. SOURCE- See Table 10.1.


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Figure 10.5 Growth rate of real GDP per capita from 1960 to 2004 versus real GDP per capita in 1960; I 10 countries from five regions
п Africa Ш Latin America А Е & SE Asia SF1 SWAsia & Middle East о OECD (non-Asia)


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4.000 6.000 8.000 10.000 12.000 14,000 16,000 Real GDP per capita (chain index, 1996 US$)
East and Southwest Asian countries are converging to OECD levels. There is no evidence of convergence for almost all the African countries. SOURCE: Sec Table 10.1.
2.000
The figure yields three main conclusions: I. The picture for the OECD countries (the rich countries) is much the same as in Figure 10.2, which looked at a slightly different period of time (from 1950 to 2004, rather than from I960 to 2004). Nearly all start at high levels of output per capita (say, at least one-third ol the LIS level in 1960), and there is clear evidence ol convergence. 
2. Convergence is also visible lor most Asian countries. While Japan (represented as a triangle here) was thc lirst ot the Asian countries to grow rapidly and now has thc highest level ol output per capita in Asia, a number of other Asian countries are trailing it closely. The lour triangles in the top left corner of the figure correspond to Singapore, Taiwan, Hong Kong and South Korea—four countries sometimes called the four tigers. All tour have had average annual growth rates of CDP per capita in excess of 5.5 per cent over the last forty years. In I960 their average output per capita was about 17 per cent ol US output,- hy 200-1 it had increased to 68 per cent of US output.
3. The picture is very different, however, lor African countries. Convergence is certainly not thc rule in Africa. Most African countries were very poor in I960, and many have had negative growth of output per capita—an absolute decline in their standard of living—since then. War-ravaged countries (the three lowest squares in the figure) suffered the most: output in Democratic Republic of Congo declined 3.2 per cent per year, Angola and thc Central African Republic by 2 per cent. P.ven in thc absence of major wars, output per capita has declined at about I per cent a year in Chad and Madagascar since I960,- as a result, output per capita in these two countries stands at about 70 per cent ot its I960 level. Why so many African countries aren't growing is one of the main questions lacing development economists today.
We will not lake on the wider challenges raised by the lacts presented in this section. Doing so would take us too lar into economic history and development economics. But they put in perspective the three basic facts discussed earlier for the OECD:
• Growth isn't a historical necessity. There was little growth for most of human history, and in many countries today growth remains elusive. Theories that explain growth in the OECD today must also be able to explain the absence of growth in the past, and its absence in much of Africa today.
• Convergence ol output per capita in many OECD countries towards thc level of the United States may well be the prelude to leapfrogging, a stage when output per capita in one or more countries increases above output per capita in thc United States. Theories that explain convergence must therefore also allow lor the possibility that convergence will be lollowed by leapfrogging and the appearance of a new economic leader.
• Finally, in a longer historical perspective, it isn't so much thc lower growth since 1973 in thc OECD that is unusual. More unusual is the earlier period of exceptionally fast growth. Finding the explanation tor lower growth today may come from understanding what lactors contributed to fast growth after World War II, and whether these factors have disappeared.
GROWTH AND HAPPINESS
Economists take for granted that higher output per capita means higher utility and increased happiness. The evidence on direct measures of happiness, however, points to a more complex picture.
Looking across countries
Figure I shows the results of a study of happiness in eighty-one countries in the late 1990s. In each country, a sample of people was asked two questions.The first was:'Taking all things together, would you say you are very happy, quite happy, not very happy, not at all happy?'The second was:'All things considered, how satisfied are you with your life as a whole these days?' Answers were rated on a scale ranging from I (dissatisfied) to 10 (satisfied). The measure on the vertical axis is constructed as the average of the percentage of people declaring themselves very happy or happy in answer to the first question, and the percentage of people answering six or more to the second question.The measure of output per capita on the horizontal axis is the level of output per capita, measured at PPP prices, in 1999 dollars. (The levels of output per capita in the figure are constructed by the World Bank and are somewhat different from the numbers from the Penn World Tables used in the rest of the chapter.) The figure suggests three conclusions.
4 The distinction between g'owth theory and development economics is fuzzy. A rough distinction is that growth theory takes many institutions (for example, the legal system, the form of government) as given. Development economics asks what institutions are needed to sustain growth.
FOCUS 'BOX
First, most of the countries with very low happiness levels are the Eastern European countries, which in the 1990s were suffering from the collapse of the communist regimes and the difficult transition to capitalism. 
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60 -
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Ь^и' .Uraguv .SWW
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Luanda bdu «Penj Estona «Slovake
■ •Jordan" aLihufta
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Bai^gbdeah ■Mtocdoofe
J**™ Utvu «Albania „ ■ ввсЬт» Goorgui • Bulgaria
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Figure I Happiness and output per capita across countries
100-,
-n
8 90 e
80 -
5.000 10,000 15,000 20.000 25,000 30.000 35.000 Income per person (US$ per year)


SOURCE. Work) Values Survey. 1999-2000 Wave.
Second, and leaving those countries aside, there appears to be a positive relation between happiness and the level of output per capita. Happiness is lower in poor countries than in rich ones.
Third, looking at rich countries—the countries with PPP output per capita above US$20.000 (in 1999 dollars), there appears to be no relation between the level of output per capita and happiness. (To see that, cover the left side of the figure and just look at the right side.) For this set of countries, higher output per capita does not seem to yield greater happiness.
What do happiness surveys have to say about life in Australia? People living in Australia have consistently reported high levels of life satisfaction in a variety of surveys since the 1940s. These results, including the World Values Survey from Figure I, have been summarised by Andrew Leigh and Justin Wolfers. They find that happiness data, GDP per capita data and the human development index data (produced by the United Nations) yield fairly similar conclusions about the well-being of people living in Australia. In fact, they claim that 'Australians are slightly happier than one might expect based on their nation's economic performance'.
Looking over time
One may reasonably argue that comparing happiness across countries is difficult. Different cultures may have different notions of what happiness is. Some countries may be chronically happier or unhappier than others. For this reason, it may be more informative to look at what happens to happiness over time in a given country.
In the United States, the Genera/ Social Survey has asked the following question since the early 1970s:'Taken all together, how would you say things are these days—would you say you are very happy, pretty happy, or not too happy?' Table I gives the proportion of answers in each category given in 1975 and in 1996.


Table 1 Distribution of happiness United States over time (%) in the
1975 1996
Very happy 32 31
Pretty happy 55 58
Not too happy 13 II
1 1

Table 2 Distribution of happiness in the United States across income groups (%)
Income level Top quarter Bottom quarter
Very happy 37 16
Pretty happy 57 53
Not too happy 6 31
1 1

The numbers in the table are striking. During those twenty-one years, output per capita increased by more than 60 per cent, but there was basically no change in the distribution of happiness. In other words, a higher standard of living was not associated with an increase in self-reported happiness. Evidence from Gallup polls over the last sixty years confirms the finding. The proportion of people defining themselves as 'very happy' is the same as it was in the early 1950s.
Looking over individuals
Does this mean that 'money' (more properly 'income') does not bring happiness? The answer is 'no'. If one looks across individuals at any point in time, rich people are likely to report themselves as happier than poor people.This is shown in Table 2, which is again constructed using the answers to the General Social Survey and gives the distribution of happiness for different income groups in the United States in 1998.
The results are again striking. The proportion of'very happy' people is much higher among the rich (the people in the top quarter of the income distribution) than among the poor (the people in the bottom quarter of the income distribution). And the reverse holds for the proportion of 'not too happy' people. The proportion is much lower among the rich than among the poor.
What conclusions can we draw from all this evidence? At low levels of output per capita, say up to US$ 15.000 or about half of the current US level, increases in output per capita lead to increases in happiness. At higher levels, however, the relation appears much weaker. Happiness appears to depend more on people's relative incomes. If this is ndeed the case, this has important implications for economic policy, at least in rich countries. Growth, and therefore policies that stimulate growth, may not be the key to happiness. SOURCES:This box is based on the bonel Robbins Метопа/ Lectures on 'Happiness. Has Social Science a Que?', gh-en by Richard Layard. April 2003 lhttp:llcep.lse.ac.ukleventsllccwresl layardl RL030303.pdfi. (These three fascinating lectures review t/ie psychological and medical research on the topic; they present more facts and discuss the implications for economy policy./
contribution to the theory of economic growth', appeared n the Quarterly Journal of Economics. February 1956. pp. 65-94. Solow received the Nobel Prize for economics in 1987 for his work on growth.
Note that we are using the same symbol, F. for the function that relates unemployment to wages in the wage-setting relation of Chapter 6 and for the production
The results on Australia can be fburd in 'Happiness and the Human Development Index:Australia Is Not a Paradox', by Andrew Leigh and Justin Wolfers.January 2006. NBER Work-ng Paper Senes.Working Paper II925. .
10.3 THINKING ABOUT GROWTH: A PRIMER
How do we go about explaining the lacts we have seen in Sections 10.1 and 10.2? What determines growth? What is the role ol capital accumulation? What is the role ot technological progress? To think about and answer these questions, economists use a framework originally developed by Robert Solow, i Solows article, A from the Massachusetts Institute of Technology, in the late 1950s. Almost simultaneously, a similar framework was presented bv Trevor Swan of the Australian National Llniversity. Sometimes it is called the Solow—Swan model and sometimes the Solow model. The framework has proven sturdy and useful, and we will use it here. This section provides an introduction. Chapters 11 and 12 provide a more detailed analysis of the roles of capital accumulation and technological progress in the process ol growth.
The aggregate production function
The starting point ol any theory ol growth must be an aggregate production function a specification of the relation between aggregate output and the inputs in production.
The aggregate production function introduced in Chapter 6 to study thc determination of output in the short run and the medium am took a particularly simple form. Output was simply proportional to the amount ol labour used by firms—more specifically, proportional to thc number ot workers employed by firms (equation [6.2J). As long as our focus was on fluctuations in output and employment, the assumption was acceptable. But, now that our focus shifts to growth, that assumption will no longer do: it implies that output per worker is constant, ailing out growth (or at least growth of output per worker) altogether. It is time to relax it. Prom now on. we will assume that there arc two inputs, capital and labour and that the relation between aggregate output and the two inputs is given by 4 function here.They are
NOT the same. Do not У - F(K.N) (10.1) confuse them. 
As before, V is aggregate output. К is capita! the sum of all the machines, plants and office buildings in the economy. N is labour—the number of workers in the economy. The function Г, which tells us how much output is produced for given quantities ol capital and labour, is the aggregate production function.
This way of thinking about aggregate production is an improvement on our treatment in Chapter 6. But it should be clear that it is still a drastic simplification of reality. Surely machines and ollice buildings play very different roles in production, and should be treated as separate inputs. Surely workers with PhDs are different from workers who didn't finish high school. Yet, by constructing the labour input as simply equal to the number of workers in the economy, we treat all workers as identical. Wc will relax some of these simplifications later. For the time being, equation 1 10.1), which emphasises the role of both labour and capital in production, will do.
The next step must be to think about where the aggregate production function, Г, which relates output to the two inputs, comes from. In other words what determines how much output can be produced lor given quantities of capital and labour? The answer: The state of technology. A country with a more advanced technology will produce more output Irom the same quantities of capital and labour than will an economy with only a primitive technology.
How should we define the state of technology? As the set ol blueprints defining both the range of products that can be produced in the economy as well as the techniques available to produce them? Or as not only the set ol blueprints but also the organisation of firms the organisation and sophistication ot markets, the system of laws and the quality ol their enforcement, the political system, and so on? For most of the next two chapters, we will think ot the state ol technology according to the narrow definition the set ot blueprints. At the end ol Chapter 12 and in Chapter 13, however we will consider the broader definition, and return to the role ol the other (actors, from legal institutions lo the quality of government.
Returns to scale and returns to factors
Now that we have introduced ihe aggregate production function, what restrictions can wc reasonably impose on this function? Consider first a thought experiment in which wc double both ihe number ot workers and the amount ol capital in the economy. What do you expect will happen to output? A reasonable answer is that output will double as well. In eltect we have cloned the original economy, and the clone economy can produce output in the same way as the original economy. This property is called constant returns to scale II ihe scale ol operation is doubled—that is, if the quantities of capital and labour arc doubled—then output will also double.
2 У = F(2K,2N)
Or, more generally, for any number .v (this will be useful below),
xY = F(xK.xN) (10.2)
We have looked at what happens to production when both capital and labour are increased. Let's now ask a dillerent question: What should we expect to happen il only one ol the two inputs in the economy—say, capital—is increased?
Surely output will increase. 1 hat part is clear. But it is reasonable to assume that the same increase in capital will lead to smaller and smaller increases in output as the level of capital increases. In other words, if there is little capital lo siart with, a little more capital will help a lot. II there is a lot of capital to start with, a little more capital may make little difference. Why? Think, for example, of a secretarial pool, composed of a given number of secretaries. Think ol capital as computers.
The aggregate ►
production function is
r = ад.
Aggregate output (V) depends on the aggregate capital stock (K) and aggregate employment \N).
The function F depends on the state of technology. The higher the sate of technology, the higher F(K.N) for а > given К and a given N.
Following up on growth ►
theory versus development economics: think of growth theory as focusing on the role of technology in the narrow sense, and development economics as focusing on the role of technology in the broader sense.
Constant returns to scale: F(xK.xN) = xY. Or F(xKjrN) = ifiY where p = 1. If p > 1, there would be increasing returns to scale; if p < 1. there would be decreasing returns to scale. We will introduce models with increasing returns at the enc of the next chapter.
Output here is secretarial services. The two inputs are secretaries and computers. The production function ' relates secretarial services to the number of secretaries and the number of computers.
The introduction of the lirst computer will substantially increase the pool's production, because some of the more time-consuming tasks can now be done automatically by the computer. As the number of computers increases and more secretaries in the pool get their own computer, production will further increase, although perhaps by less per additional computer than was the case when the first one was introduced. Once each and every secretary has a PC, increasing the number ot computers luriher is
unlikely to increase production very much, if at all. Additional computers may simply remain unused and lei I in their shipping boxes, and lead to no increase in output whatsoever.
We will refer to the property that increases in capital, for a given labour input, lead to smaller and smaller increases in output as the level ot capital increases as decreasing returns to capital (a property that will be familiar to those who have taken a course in microeconomics). Sometimes, it is called the diminishing marginal productivity of capital'. A similar property holds for the other input, labour: increases in labour, given capital, lead to smaller and smaller increases in output as the level of labour increases, i Return to our example, and think ol what happens as you increase the number of secretaries tor a given number of computers.) There arc decreasing returns to labour as well.
Output and capital per worker
The production function we have written down, together with thc two properties we have just introduced, implies a simple relation between output per worker and capital per worker.
(10.3)
Make sure you understand what is behind the algebra.
^ Suppose capital and the number of workers both double.What happens to output per worker?
Increases in capita per worker lead to smaller and smaller increases in output per worker as
4 the level of capital per worker increases.

Increases in capital per worker lead to smaller and smaller increases in output per worker.
Figure 10.6 Output and capital per worker
Constant returns to scale implies that we can rewrite equation (10.1) as a relation between output per worker and capital per worker. To get this result algebraically, remember that x can take on any value, so let x = l/N in equation i 10.2), so that
N \ N N N
Note that Y/N is output per worker and K/N is capital per worker. So, equation (10.3) says lhat the amount of output per worker depends on the amount of capital per worker. This relation between output per worker and capital per worker is drawn in Figure 10.6.
Even under constant returns to scale, there are decreasing returns to each factor, keeping the other factor constant
• Given labour, there are decreasing returns to capital: increases in
I capital lead to smaller and smaller increases in output as the level of capital increases.
• Given capital, there are decreasing returns to labour: increases in labour lead to smaller and smaller increases in output as the level of labour increases.
Output per worker (Y/N) is measured on the vertical axis, capital per worker (K/N) on the horizontal axis. The relation between the two is given by the upward-sloping curve. As capital per worker increases, so does output per worker. Note that the curve is drawn so that increases in capital lead to smaller and smaller increases in output. This follows from the property that there are decreasing returns to capital. At point A, where capital per worker is low. an increase in capital per worker, represented by the horizontal distance AB, leads to an increase in output per worker equal to the vertical distance A'B'. At point C, where capital per worker is larger, the same increase in capital per worker, represented by the horizontal distance CD (where thc distance CD is equal to the distance AB),
leads to a much smaller increase in output per worker, only CD'. This is just as in our example of thc secretarial pool, where additional computers led to less and less effect on total output.
The sources of growth
We are now ready to return to our basic question: Where does growth come from? Why does output per worker—or output per capita, if we assume that the ratio of workers to the population as a whole remains roughly constant over time—go up over time? Equation (10.3) gives a lirst answer:
• Increases in output per worker (Y/N) can come from increases in capital per worker (K/N). This is the relation we just looked at in figure 10.6. As (K/N) increases—as we move to the right on the horizontal axis—(Y/N) increases.
• Or they can come Irom improvements in the state of technology, which shift the production function, F, and so lead to more output per worker given capital per worker. This is shown in Figure 10.7. An improvement in thc state ol technology shifts the production function up, Irom F(K/N,\) to F(K/N, 1)'. For a given level of capital per worker, the improvement in technology leads to an increase in output per worker. For example, for the level ol capital per worker corresponding to point A, output per worker increases from A' to B'. (To return to our secretarial pool example, a reallocation ol tasks within the pool may lead to better division ol labour and an increase in the output per secretary.)
Hence, we can think of growth as coming from capital accumulation and from technological progress—thc improvement in the state ol technology. We will see, however, that these two factors play very different roles in the growth process:
• Capital accumulation by itself cannot sustain growth. A lormal argument will have to wait until Chapter I I. But you can already get the intuition for this answer from Figure 10.6. Because of decreasing returns to capital, sustaining a steady increase in output per worker would require larger and larger increases in the level of capital per worker. At some stage, the economy won't be willing or able to save and invest enough to lurther increase capital. At that stage, output per worker will slop growing.
Increases in capital per ► worker: movements along the production function.
Improvements in the ► state of technology: shifts of the production function.
Does this mean that an economy's saving rate—the proportion of income that is saved—is irrelevant? N't). Il is true that a higher saving rate cannot permanently increase the growth rale of output. But a higher saving rate can sustain a higher level of output. Let us state this in a slightly dillerent way. Take two economies that differ only in their saving rate. The two economies will grow
Figure 10.7 The effects of an improvement in the state of technology

F(K/N,1)
F(K/N, 1)
Capital per worker, KIN
г
>-
0 J h. a a.
z
О



An improvement in technology shifts the production function up, leading to an increase in output per worker for a given level of capital per worker. 
at the same rate,- hut, at any point in time, the economy with the higher saving rate will have a higher level ol output per capita than the other. How and how much the saving rate affects the level ol output, and whether a country such as Australia (which has a very low saving rate> should try to increase its saving rate, will be one ot the topics ol Chapter 1 I.
• Sustained growth requires sustained technological progress. This really follows from the first proposition. Given that the two lactors that can lead to an increase in output arc capital accumulation and technological progress, if capital accumulation cannot sustain growth forever then technological progress must be key. And it is. We will see in Chapter 12 that the economy's rate ol growth ol output per capita is eventually determined by the economy's rate of technological progress.
This has a strong implication. In the long run, an economy that sustains a higher rate of tech¬nological progress will eventually overtake all other economies. This raises the question ol what determines the rate ol technological progress. What wc know about the determinants of techno¬logical progress—from the role ol spending on fundamental and applied research to the role ol patent laws, to the role of education and training—will be one of the topics ol Chapter 12.
SUMMARY
• Over long periods, lluctuations in output are dwarfed by growth, the steady increase of aggregate output over time.
• Looking at growth in six rich countries ( Australia, France, Germany, Japan, the United Kingdom and the United States» since 1950, three main tacts emerge:
I All six countries have experienced strong growth and a large increase in the standard ot living. Growth Irom 1950 lo 2004 increased real output per capita by a factor of 3.0 in Australia, 3.2 in the United States, 5 5 in Germany and I 1.3 in lapan.
2. Growth has decreased since the mid-1970s. The average growth rate of output per capita ol the six countries went from 4.0 per cent per year Irom 1950 to 1973 to 2.0 per cent from 1974 to 2004.
3. The levels ol output per capita across the six countries have converged over time. Put another way. those countries that were behind grew faster from 1950 to 1973, reducing the gap between them and the world economic leader, the United States. From 1974 to 2004, the European countries and Australia maintained their position, but Japan continued the convergence process.
• Looking at the evidence across a broader set of countries and a longer period, the following facts emerge:
1. On the scale of human history, sustained output growth is a recent phenomenon. From the end ol the Roman Empire to roughly the year 1500. there was essentially no growth ol output per capita in Europe. Even during the Industrial Revolution, growth rates weren't high by current standards. The growth rate of output per capita Irom 1820 to 1950 in the Llnited States was 1.5 per ccnt.
2. Convergence of levels ol output per capita isn't a worldwide phenomenon. Many Asian countries are rapidly catching up, but most African countries have very low levels of output per capita and low growth rates.
3. Australia and New Zealand were highly ranked among OF.( I) countries in terms ot output per capita in 1950, but had relatively low growth rates in the next fifty or so years.
• To think about growth, economists start Irom an aggregate production function relating aggregate output to two lactors of production, capital and labour. How much output is produced given these inputs depends on the state of technology.
• Llndcr the assumption of constant returns, the aggregate production function implies that increases in output per worker can come Irom either increases in capital per worker or improvements in the state of technology.
• Capital accumulation by itself cannot permanently sustain growth of output per capita. Nevertheless, how much a country saves is very important because the saving rate determines the level of output per capita, il not its growth rate.
• Sustained growth ol output per capita is ultimately due to technological progress. Perhaps the most important question in growth theory is what determines technological progress.
KEYTERMS
growth, 232 four tigers, 241
logarithmic scale, 232 aggregate production function, 243
output per capita 233 state of technology, 244
standard of living, 233 constant returns to scale. 211
purchasing power, 234 decreasing returns to capital. 245
purchasing power parity (PPP), 2.34 decreasing returns lo labour, 245
convergence, 236 capital accumulation, 246
Malthusian era, 238 technological progress, 246
poverty, 239 saving rate, 246
leapfrogging, 239
QUESTIONS AND PROBLEMS
Quick check
1. Using the information in this chapter, label each of the following statements 'true', 'false' or

'uncertain'. Explain briefly.
a. Despite the Great Depression, Australian output was higher in 1940 than in 1929.
b. On a logarithmic scale, a variable that increases at 5 per cent a year will move along an upward- sloping line, with a slope ol 0.05.
c. The price of food is higher in poor countries than in rich countries.
d. Output per capita (persons in most countries in the world is converging to the level ol output per capita in the United States.
e. For about 1,000 years alter the lall ol the Roman Empire, there was essentially no growth in output per person in Europe, because any increase in output led to a proportional increase in population.
f. Capital accumulation doesn't affect the level of output in thc long run. Only technological progress does that.
g. The aggregate production function is a relation between output on the one hand and labour and capital on the other.
h. Evidence suggests that happiness in rich countries increases with output per person.
2. Use Table 70.7 to answer the following questions:
a. Calculate what output per capita would have been in 2004 for each of the six countries il the growth rate during 1974-2004 tor each country' had remained the same as during 1950-73.
b. What would have been the ratio ol output per capita in lapan relative to output per capita in the United States?
c. Did convergence continue during the growth slowdown Irom 1974 to 2004?
3. Assume lhat the average consumer in Papua New Guinea IPNG) ami Australia buys the quantities
ami pays the prices indicated in the following table: 

Papua New Guinea Australia
5 kina A$ I
400 1,000
20 kina A$2
200 2,000
 
('.rtract the database file fa very large xls file). If yon know how. use filters in your spreadsheet program.
a. Find the chain index GDP per capita for France, Belgium Italy and the United States for 1950-2004.
b. Define lor each country lor each year the ratio ol its real GDP to that of the United Stales lor that year (so that this ratio will be equal to one (or thc United Stales lor all years .
c. Graph the ratios lor France, Belgium and Italy over the period for which you have data, 1950-2004 (all in the same graph). Does your graph support the notion of convergence among the lour countries listed in part a)?
d. Repeat the same exercise lor Argentina, Venezuela, Chad, Madagascar and the United Stales. Does your new graph support the notion ol convergence among this group ol countries?
8. Growth successes and failures
Go to the website containing the latest Penn World Table (http://pwt.econ.upenn.edu) and collect data on real GDI' per capita lchained series/ for 1970 for all available countries. Do the same for a recent year of data, say one year before the most recent year available in the Penn World Table. Iff you choose the most recent year available, the Penn World Table may not have the data for some countries relevant lo this question.)
a. Rank the countries according to GDP per person in 1970. List thc countries with lhe ten highest
levels ol GDI1 per person in 1970. Are there any surprises? h. Carry out the analysis in part (a) lor the more recent year for which you collected data. Has the composition ol the ten richest countries changed since 1970?
c. l or each ol the ten countries you listed in part (b), divide the recent level of GDP per capita hy the level in 1970. Which of these countries has had thc greatest proportional increase in GDP per capita since 1970?
d. Carry out the exercise in part (c lor all thc countries lor which you have data. Which country has had the highest proportional increase in GDP per capita since 1970? Which country has had the smallest proportional increase? What fraction of countries have had negative growth since 1970?
e. Do a brief Internet search on either the country Irom part (c) with the greatest increase in GDP per capita or the country Irom part (d) with the smallest increase. Can you ascertain any reasons lor the economic success, or lack of it, for this country?
We invite you to visit the Blanchard-Sheen page on the Pearson Australia website at
www.pearson.com.au/highered/blanchardsheen3e
for many World Wide Web exercises relating to issues similar to those in this chapter.
FURTHER READINGS
CHAPTER ф
Saving, Capital Accumulation and Output
S
ince I960, Australia and, particularly, the United States have had relatively low (and declining) saving rates—24 per cent and 18 per cent, on average, respectively—compared with, for example. Japan (32 per cent). Can this explain why the US growth rates have been lower than in most OECD countries in the last fifty years? Would increasing their saving rates lead to sustained higher growth in the future?
We have already given the basic answer to these questions at the end of Chapter 10, and the answer is 'no'. Over long periods—an important qualification to which we will return—an economy's growth rate doesn't depend on its saving rate.The relatively low US growth rate in the last fifty years cannot be explained by the saving rate.The Australian saving rate declined after 1974 and has since been close to the OECD average.Though it increased in the 1990s to reach 23 per cent in 2008. we shouldn't expect this increase in the saving rate to lead to sustained higher Australian growth.
This conclusion doesn't imply, however, that we shouldn't be concerned about the low Australian and the particularly low US saving rates of 23 per cent and 13 per cent respectively in 2008. Even if the saving rate doesn't permanently affect the growth rate, it does affect the level of output and the standard of living. In this chapter, we will show that an increase in the saving rate would lead to higher investment, and thus growth, for some time and eventually to a higher standard of living.
The effects of the saving rate on capital and output per capita are the topics of this chapter.
• Sections I I.I and I 1.2 look at the interactions between output and capital accumulation, and the effects of the saving rate.
• Section 11.3 plugs in numbers to give a better sense of the magnitudes involved.
• Section 11.4 extends our discussion to take into account not only physical capital but also human capital.
I I. I INTERACTIONS BETWEEN OUTPUT AND CAPITAL 
Change in the capital stock
The effects of capital on output
We started discussing the first of these two relations, the ellect of capital on output, in Section 10.3. There we introduced the aggregate production function and you saw that, under the assumption of constant returns to scale, we can write the following relation between output per worker and capital per worker:
N \N '
Output per worker (Y/N) is an increasing function of capital per worker (K/N). Under the assumption of decreasing returns to capital, the larger the initial ratio ol capital per worker, the smaller the effects of an increase in capital per worker. When capital per worker is already very high, further increases in capital per worker have only a small ellect on output per worker.
To simplify notation, we will rewrite this relation between output and capital per worker simply as
X = tl -
N ! \ N
Suppose, for example. ► the function F has the 'double square root' form, so У = F(K,N) = \ K\ N. Divide both sides by N: Y VKVN N = N
T
N
So. in this case, the function f giving the relation between output per worker and capital per worker is simply the square root function:
where the function f represents the same relation between output and capital per worker as the function F.


In this chapter, we will make two further assumptions:
The lirst is that the size of the population, the participation rate and the unemployment rate arc all constant. This implies that employment. N, is also constant. To see why go back to the relations we saw in Chapter 1, and again in Chapter 6. between population, the labour force, unemployment and employment.
- The labour force is equal to population times the participation rate. So, if the size of the population is constant, and the participation rate is constant, the labour force is also constant.
- Employment, in turn, is equal to the labour force times I minus the unemployment rate. It, for example, the size of the labour torcc is 10 million, and the unemployment rate is 5 per cent, then employment is equal to 9.5 million (10 million times [l - 0.05]). So, it the labour lorce is constant, and the unemployment rate is constant, employment is also constant.
Under these assumptions, output per worker (output divided by employment), output per capita (output divided by population i and output itself all move proportionately. Although we will usually refer to movements in output or capital per worker, to lighten the text we will sometimes just talk about movements in output or capital, leaving out the per worker' or per capita' qualification.
Saving/investment
Figure I I. I Capital, output and saving/ investment
Capital stock
The reason for assuming that N is constant is to make it easier to focus on the role ol capital accumulation in growth: if N is constant, the only factor of production that changes over time is capital. The assumption isn t very realistic, however, and wc will relax it in the next two chapters. 
In Chapter 12 we will allow for steady population and employment growth And in Chapter 13 we will see how we can integrate our analysis of thc long run—which ignores fluctuations in employment—with our earlier analysis ot the short and medium run—which focused precisely on these fluctuations in employment and the fluctuations in output and unemployment But both steps arc better left to later.
• Thc second assumption is that there is no technological progress, so the production function • or, equivalently, F) doesn't change over time.
Again, the reason for making this assumption—which is obviously contrary to lact is to focus just on the role of capital accumulation. In Chapter 12 we will introduce technological progress and see that thc basic conclusions derived here about the role of capital in growth also hold when there is technological progress. Again this step is better left to later.

From the production side: the level ot capital per worker determines
* the level of output per worker.
As you will see in Chapter 19. saving and investment need not be equal in an open economy. A country may save more than it invescs. and lend the difference to the rest of the world. Japan, for example, has been running a large trade • * and current account surplus for a long time, lending part of its saving to the rest of the world. In contrast. Australia has been running deficits for most of its recent history.
You have now seen two specifications of saving behaviour (equivalently. consumption behaviour): one for the short run in Chapter 3, and one for the long run in this chapter.You may wonder how the two specifications relate to each other, and whether
* they are consistent.The answer to the last part is 'yes'. A full discussion is given in Chapter 16.
To summarise: With these two assumptions, our first relation between output and capital per worker, from the production side, can be written as
(II.
where we have introduced time indexes for output and capital but not lor labour, N, which we assume to be constant and so doesn't need a time index. (In other words, we could write labour in equation I 1.1 ; with a time index—that is, as N,. But our assumption lhat it is constant implies that N, N.1 In words: Higher capital per worker leads to higher output per worker.
The effects of output on capital accumulation
To derive the second relation, between output and capital accumulation, we proceed in two steps. First, we derive the relation between output and investment. Then we derive the relation between investment and capital accumulation.
Output and investment
To derive the relation between output and investment, we make three assumptions:
• We continue to assume that the economy is closed. As we saw in Chapter 3 (equation [3.10]), this implies that investment 1. is equal to saving—thc sum of private saving, 5, and public saving, T G
1 = S + (T - G)
• To focus on the behaviour of private saving we ignore both taxes and government spending, so T - С and by implication public saving, the difference between taxes and government spending, T - G = 0. We will relax this assumption later on when we discuss thc implications ol fiscal policy on growth.' With this assumption, thc previous equation becomes.-
1 = S
Investment is equal to private saving.
• We assume that private saving is proportional to income, so,
5 = sY
The parameter s is the saving rate, and has a value between zero and I. This assumption captures two basic facts about saving: 1 1 the saving rate doesn't appear to systematically increase or decrease as a country becomes richer,- and (2) richer countries don't appear to have systematically higher or lower saving rates than poorer ones.
Combining these two relations, and introducing time indexes, gives:
SAVING, CAFTTAI ACCUMUL ATION AND Ot JTPl Jl
chapter 11
I, = «У, 
Investment is proportional to output: the higher the output, the higher the saving and so the higher the investment.
Investment and capital accumulation
Ihe second step relates investment, which is a How 'the new machines produced and new plants built during a given period), to capital, which is a stock 1 the existing machines and plants in the economy at a point in time).
Think of time as measured in years, so / denotes year / . / + I denotes year t + 1. and so on. Think of the capital stock as being measured at the beginning of each year, so K, refers to the capital stock at the beginning ol year I. K,., to the capital slock ai the beginning of year < 1, and so on.
Assume that capital depreciates at rate 8 ithe lowercase Greek delta) per year: that iv from one year to the next a proportion 8 of the capital stock breaks down and becomes useless,- equivalently, a proportion I - r5i ol the capital stock remains intact trom one year to the next.
I he evolution ot the capital stock is then given by
Kl+] = (I - 8)K, + /,
The capital stock at the beginning ol year t + I, K,+ J is equal to the capital stock at the beginning of year f which is still intact in year t ■ I I 8)Kt, plus the new capital stock put in place during year I—that is, investment during year t, I,.
We can now combine the relation Irom output and investment and the relation from investment to capital accumulation to obtain the second relation that we need to think about growth: the relation trom output to capital accumulation.
Recall that flows are variables that have a time dimension (that is. they are defined per unit of time): stocks are variables that don't have a time dimension (Ciey are defined at a point in ► time). Output, saving and investment are flows. Employment and the capital stock are stocks.
In national accounts ► statistics, the depreciation of capital ЛК is called 'consumption of fixed capital'.
Replacing investment by saving in the previous equation, and dividing both sides by ,V (the number ol workers in the economy), gives.-
KM.
N
Xi
N
- (I 8)
N



In words: Capital per worker at the beginning of year t + 7 is equal to capital per worker at the beginning of year t. adjusted for depreciation, plus investment per worker during year t, itself equal to the saving rate times output per worker during year t.
V, K,
К
К N
- 8
- S'
N
N
From the saving side: the level of output per worker determines the change in the level of capital per worker over time. ►
Expanding the term (1 - 8)KJS to K,/N - 8K,/N, moving K,/N to the left, and reorganising the right side:
f+i
{11.2)
N
In words: The change in the capital stock per worker—represented by the difference between the two terms on the left—is equal to saving per worker—represented by the first term on the right—minus depreciation—represented by the second term on the right. This equation gives us the second relation between output and capital per worker.
I 1.2 IMPLICATIONS OF ALTERNATIVE SAVING RATES
5AVING. CAPITAL ACCUMULATION AND OUTPUT
chapter 11
Dynamics of capital and output
Replacing output per worker > Y,/N) in equation I 1.21 hy its expression in terms ot capital per worker Irom equation (I I. I > gives:
KM K, (K,\ K, (4-')
N ~ N ~ Sf\Uj ~ d~N
Change in capital Investment — Depreciation
Irom year t to t + I during year t during year f
This relation describes what happens to capital per worker. The change in capital per worker from this year to the next depends on the difference between two terms:
• Investment per worker the lirst term on the right. The level of capital per worker this year deter¬mines output per worker this year. Given the saving rate, output per worker determines the amount у ^ у of saving per worker and thus of investment per worker this year. 4 — -> ft ' )-> sf
N \ N I ' \ N
• Depreciation per worker the second term on the right. The capital stock per worker determines the , K amount of depreciation per worker this year. 4 — -> If investment per worker exceeds depreciation per worker, the change in capital per worker
is positive: capital per worker increases.
II investment per worker is less than depreciation per worker, the change in capital per worker is negative: capital per worker decreases.
Given capital per worker, output per worker is then given by equation III):
N r\N
Equations II 1.3) and (11.1 contain all the information we need to understand the dynamics of capital and output over time. Thc easiest way to interpret them is to use a graph. We do this in Figure I 1.2, where output per worker is measured on the vertical axis and capital per worker is measured on the horizontal axis.
In Figure 11.2. look first at the curve representing output per worker, f(K,/N), as a function of capital per worker. The relation is the same as in Figure 10.5: output per worker increases with capital per worker, but—because of decreasing returns to capital the ellect is smaller the higher the level ot capital per worker.
Now look at the two curves representing the two components on the right ot equation 111.3).
• The relation representing investment per worker, sf{K,/N), has the same shape as the production function, except that it is lower by a lactor > (the saving rate). Suppose thc level ot capital per worker is equal to Ku/K in Figure I 1.2. Output per worker is then given by the distance AB, and investment per worker is given hy ihe vertical distance AC, which is equal to s times the vertical distance AB. Thus, just as lor output per worker, investment per worker increases with capital per worker, but by less and less as capital per worker increases. When capital per worker is already very high, the effect ol a further increase in capital per worker on output per worker, and thus in turn on investment per
worker, is very small. 4 To make the graph
• The relation representing depreciation per worker, 8K,/N, is represented by a straight line. easier to read, we Depreciation per worker increases in proportion to capital per worker, so the relation is represented hnvc assllmed an by a straight line with slope equal to fi. At the level of capital per worker Ku/N, depreciation per гГш'сап'ус! tell worker is given by thc vertical distance AD. roughly whaTvalue we lhe change in capital per worker is given by thc difference between investment per worker and have assumed for >?
depreciation per worker. At K(,/N, the dilference is positive,- investment per worker exceeds What would be a depreciation per worker by an amount represented by the vertical distance CD = ЛС -AD; capital per plausible value for s>) worker increases. As we move to the right along thc horizontal axis and look at higher and higher levels
Depreciation per worker

Z
s
IT
| Y*IN
о
S
im
V
a
>и H<
(KglN) K*IN
Capital per worker, KIN
Output per worker
Investment per worker sf(K,IN)
Figure I 1.2 Capital and output dynamics
SAVING. CAF'I TAL ACCUMUI AI ON AND OUT PU1
II:< ■ »V
chapter 11
CAPITAL ACCUMULATION AND GROWTH IN FRANCE IN THE FOCI JS AFTERMATH OF WORLD WAR II
'BOX
When World War II ended in 1945, France had suffered some of the heaviest losses of all European countries. The losses in lives were large; more than 550.000 people had died, out of a population of 42 million.The losses in capital were much larger. Estimates are that the French capital stock in 1945 was about 30 per cent below its prewar value. A more vivid picture of the destruction of capital is provided by the numbers in Table I.
The model of growth we have just seen makes a clear prediction about what will happen to a country that loses a large part of its capital stock: the country will experience fast capital accumulation and output growth for some time. In terms of Figure I 1.2, a country with capital per worker initially far below K*IN will grow rapidly as it converges to К*/N and output per worker converges to Y*IN.
Tri.s prediction fares well in the case of postwar France.There is plenty of anecdotal evidence that small increases in capital led to large increases in output. Minor repairs to a major bridge would lead to the reopening of that bridge. Reopening the bridge would lead, in turn, to large reductions in the travel time between two cities, leading to a large reduction in transport costs. A large reduction in transport costs would then allow a plant to get much-needed inputs and increase production, and so on.
The more convincing evidence, however, comes directly from the numbers on growth of aggregate output itself. From 1946 to 1950, the annual growth rate of French real GDP was a very high 9.6 per cent per year, leading to an increase in real GDP of about 60 per cent over five years.
Was all the increase in French GDP due to capital accumulation? The answer is 'no'.There were other forces in addition to the mechanism in our model. Much of the remaining capital stock in 1945 was old. Investment had been low in the 1930s (a decade dominated by the Great Depression) and nearly non-existent during the war. Much of the postwar capital accumulation was associated with the introduction of more modern capital and the use of more modern production techniques. This was another reason for the high growth rates of the postwar period.
Table 1 Proportion of the French capital stock destroyed by the end of World War II
Railways (%) Tracks 6 Rivers (%) Waterways 86
Stations 38 Canal locks II
Engines 21 Barges 80
Hardware 60 Buildings (numbers)
Roads(%) Cars 31 Dwellings 1,229,000
Trucks 40 Industrial 246,000

SOURCE: G iles Saint-Paul.'Economic reconstruction in France. 1945-1958'. in Rudiger Dornbusch.Willem Nolling and Richard Layard (edsi. Poseur Economic Reconstruction and Lessons for the East Today (Cambridge. MA: MIT Press. 1993). pp. 83-114.
 
(11.5)
We now have all the elements we need to discuss the effccts ol the saving rate on output per worker both over time and in steady state.
The saving rate and output
Wc can now return to the question asked at the beginning of the chapter: What arc the effects of the
saving rate on the growth rate of output per worker? Our analysis leads to a three-part answer:
1. The saving rate has no effect on the long-run growth rate of output per worker, which is equal to zero.
This conclusion is rather obvious: we have seen that, eventually, the economy converges to a constant level of output per worker. In other words, in the long run the growth rate ot output is equal lo zero, whatever the value ol the saving rate.
There is, however, a way ol thinking about it that will be useful when we introduce technological progress in Chapter 12. Think ol what would be needed to sustain a constant positive growth rate of output per worker in the long run. Capital per worker would have to increase. Not only that, but, because of decreasing returns to capital, it would have to increase faster than output per worker. This implies that each year the economy would have to save a larger and larger fraction ol output and put it towards capital accumulation. At some point, the fraction of output it would need to save would be greater than one—something that is clearly impossible. This is why it is impossible to sustain a constant positive growth rate forever. In the long run, capital per worker must be constant and so must output per worker.
2. Nonetheless, the saving rate determines the level of output per worker in the long run. Other things being equal, countries with a higher saving rale will achieve higher output per worker in the long run.
XI
N
Some economists argue that the high output growth achieved by the Soviet Union from 19S0 to 1990 was the result of such a steady increase in the saving rate over time, and so could rot be sustained forever. Paul Krugman has used the term 'Stalinist growth' to denote this type of growth—growth resulting from a higher k and higher saving rate over time. Note that the first proposition is a statement about the growth rate of output per worker. The second proposition is a statement about the level of output per worker. ►
chapter I I
Figure 11.3 illustrates this point. Consider two countries with the same production function, the same level of employment and the same depreciation rate, but different saving rales—say, and S| > s„. Figure I 1.3 draws their common production function, f(K,/K , and the functions giving saving investment per worker as a function ot capital per worker tor each of the two countries, s^f(K,/N) and s,f\ K,/N). In the long run, the country with saving rate s0 will reach the level ol capital per worker, KJN. and output per worker. Y,JN. The country with saving rate s, will reach the higher levels K,/N and Y,/N.


Figure I 1.3 The effects of different saving
rates Z
i
щ Yi/N
L.
| y0/N
9 a
з a.
з
О


(Ko/N) (K,/N) Capital per worker, K/N
Output per worker f(KJN)
Investment per worker f(KJN)
Depreciation per worker
8KJN S
Investment per worker s0f(Kt/N)


A country with a higher saving rate achieves a higher level of output per worker in steady state.
SAVING. CAPITAL ACCUMULATION AND OUTPUT
chapter I I
3. An increase in lhe saving rate will lead to higher growth of output per worker for some time, but not forever.
This conclusion follows Irom the two propositions iust discussed. From the lirst, we know that an increase in the saving rate doesn't allect the long-run growth rate of output per worker, which remains equal to zero. From the second, we know that an increase in the saving rate leads to an increase in the long-run level of output per worker. It lollows that, as output per worker increases to its new higher level in response to the increase in the saving rale the economy will undergo a period of positive growth. This period of growth will end when the economy reaches its new steady state.
We can use Figure I 1.3 again to illustrate this point. Consider a country that has an initial saving rate of s0. Assume that capital per worker is initially equal to K,/.\ with associated output per worker Y„/i\ . Now consider the effects of an increase in the saving rate from su to s,. (You can think of this increase as coming from tax changes that make it more attractive to save or from reductions in thc budget deficit,- thc origin of the increase in thc saving rate doesn t matter here. The function giving saving/investment per worker as a Iunction ol capital per worker shifts upward from >,j{K,/l\ to sJ(K,/N).
At the initial level of capital per worker, K,JK. investment now exceeds depreciation, so capital per worker increases. As capital per worker increases, so does output per worker, and the economy undergoes a period of positive growth. When capital per worker eventually reaches investment is again equal to depreciation and growth ends. The economy remains Irom then on at К|/.\', with associated output per worker at Y|/\. The movement ol output per worker is plotted against time in Figure 11.4. Output per worker is initially constant at level Y()/N. Alter the increase in the saving rate, say. at time t, output per worker increases lor some time until it reaches the higher level ol output per worker, Yt/N, and the growth rate returns to zero.
We have derived these three results under the assumption ol no technological progress and thus no growth ol output per worker in the long run. But, as we will see in Chapter 12, thc three results extend directly to an economy in which there is technological progress. Let us briefly indicate how.

Time
An economy where there is technological progress has a positive growth rate ol output per worker even in the long mn. This long-run growth rate is independent ol the saving rate—the extension of the first result iust discussed. The saving rate affects, however, the level ol output per worker—the extension of the second result. So, an increase in the saving rate leads to growth greater than the steady-state growth rate for some time until the economy reaches its new higher path—the extension ol our third result.
Figure I 1.4
The effects of an increase in the saving rate on output per worker
An increase in the saving rate leads to a period of growth until output reaches its new. higher, steady-state level. 
These three results are illustrated in Figure 11.5. which extends Figure 1 1.4 by plotting the ellect of an increase in ihe saving rale in an economy with positive technological progress. The figure uses a logarithmic scale to measure output per worker, so that an economy where output per worker grows at a constant rate is represented by a line with slope equal to that growth rale. Ai the initial saving rate s,„ the economy moves along A A. If, at time t, the saving rale increases to >,, the economy experiences higher growth lor some time until it reaches its new higher path, BB. On path BB. the growth rate is again the same as before the increase in the saving rale (that is, the slope of BB is the same as the slope of A A).
The saving rate and consumption
Governments can use various instruments to alfeel the saving rate. Thev can nin budget delicits or surpluses. I hey can give tax breaks to savers, making it more attractive to save. They can make il mandatory for employers to contribute towards workers' superannuation. What saving rate should governments aim lor? To think about the answer, we must shift our locus Irom the behaviour of output to ihe behaviour ol consumption: what matters to people is not how much is produced but how much they consume.
Il is clear that an increase in saving must come initially ai the expense ol lower consumption. (Fxcept when we think it helpful, we will drop the per worker' in this subsection and iust refer lo consumption rather than consumption per worker, capital rather than capital per worker, and so on.1 A changc in the saving rate ibis year has no elleci on capital this year and so no effect on output and income this year. So, an increase in saving comes initially with an equal decrease in consumption.
Docs an increase in saving lead to an increase in consumption in ihe long am? Not necessarily. Consumption may decrease, not only initially but also in the long ain. You may find this surprising. Alter all, we know from Figure I 1.3 thai an increase in the saving rate always leads lo an increase in the level of output per worker. But output is not the same as consumption. To see why not consider what happens lor two extreme values ol the saving rate.
See the discussior of logarithmic scales in Appendix 2 at the end of the book. ► Investment this year doesn't affect the capital stock this year: I, affects
K,»|.notK,. ► Because we assume that employment is constant, we are ignoring the short-run effect of an increase in the saving rate on output we focused on in Chapter 3.
In the short run. not only does an increase in the saving rate reduce consumption given income, but it may also create a recession and decrease income further. We will return to a discussion of short-run and long-run effects of changes in saving at various points in die book. See, for example.
Chapter 27.
An economy in which the saving rate is land has always been) zero is an economy in which capital is equal to zero. In this case, output is also equal to zero, and so is consumption. A saving rate equal to zero implies zero consumption in the long run.
Figure 1 1.5 (With technological progress)
The effects of an
increase in the Associated В
saving rate on with saving
output per rate s, > s0
worker in an /
economy with z
technological i: /
progress с
V
J£ ^-v /
i ® is 6 •** /
u и Q. 01
3 /
a
3 f \
0 ^^ \
Associated with saving rate s0
A
1
t
Time
An increase in the saving rate leads to a period of higher growth until output reaches a new. higher path.
 
SAVING, CAPITAL ACCUMULATION AND OUTPUT
chapter I I
Now go to the opposite extreme and consider an economy in which the saving rate is equal to one: people save all their income. Thc level ol capital, and thus output, will be very high. Rut because people- save all of their income, consumption is equal to zero. What happens is that the economy is carrying an excessive amount of capital. Simply maintaining that level of output requires that all output be devoted to replacing depreciation! A saving rate equal to I also implies zero consumption in the long run.
These two extreme cases imply that there must be some value ol the saving rate between 0 and I that maximises the steady-state level of consumption. Increases in the saving rate below this value lead to a decrease in consumption initially but to an increase in consumption in thc long run. Increases in the saving rate beyond this value decrease consumption not only initially but also in the long ain. This happens because the increase in capital associated with the increase in the saving rate leads to only a small increase in output, ar increase that is too small to cover the increased depreciation-, the economy carries too much capital. The level of capital associated with the value ol the saving rate that yields the highest level ol consumption in steady state is known as the golden-rule level of capital Increases in capital beyond the golden-rule level reduce steady-state consumption.
This argument is illustrated in figure I 1.6. which plots consumption per worker in steady state (on the vertical axis) against the saving rate (on the horizontal axis). A saving rate equal to zero implies a capital stock per worker equal to zero a level of output per worker equal to zero and, by implication, a level ol consumption per worker equal to zero. For > between 0 and s(. i(.; lor golden ntle), higher values ol the saving rate imply higher values for capital per worker, output per worker and consumption per worker. For s larger than increases in the saving rate still lead to higher values ot capital per worker and output per worker,- but they lead to lower values ol consumption per worker. This is because the increase in output is more than offset by the increase in depreciation due to the larger capital stock. For s - I. consumption per worker is equal to zero. Capital per worker and output per worker are high, but all of output is used iust to replace depreciation, leaving nothing lor consumption.
Il an economy already has so much capital lhat ii is operating beyond the golden rule, then increasing saving further will decrease consumption not only in the short run but also in the long run. Is this a relevant worry? Do some countries actually have too much capital? The empirical evidence suggests that most OECD countries are actually lar below their golden-rule level ol capital. II they were to increase the saving rate it would lead to higher consumption in the future.
Maximum steady-state Figure 1 1.6
consumption per worker The effects of the
2 / saving rate on
С consumption per
iT 1 worker in steady
я 1» state
0 J к
V a
с
о

E
3
с
и f 1 \
0 SG 1
Saving rate, s
An increase in the saving rate leads to an increase, and then to a decrease, in consumption per worker in steady state.
 
This conclusion implies that, in practice, governments lace a trade-off: an increase in the saving rate implies lower consumption lor some time, higher consumption later. What should they do? How closc to the golden rule should governments try to get? That depends on how much weight they put on the welfare of current generations (who arc more likely to lose Irom policies aimed at increasing the saving rate) versus the welfare of future generations (who arc more likely to gain). Enter politics: future generations don't vote. This implies that governments are unlikely to ask current generations tor large sacriliccs, which in turn means that capital is likely to stay tar below its golden-rule level. These intergencrational issues are very much in evidence in the current debate on age pensions and superannuation reform,- this is explored in the focus box The ageing population: age pensions, super¬annuation and savings'.