Economic Growth
by vivek ambastha Indian Istitute OF Management,Ahmedabad 
Compound Rates of Growth
In the modern version of an old legend, an investment 
banker asks to be paid by
placing one penny on the first square of a chess board, two 
pennies on the second
square, four on the third, etc. If the banker had asked 
that only the white squares be
used, the initial penny would have doubled in value thirty-
one times, leaving $21.5
million on the last square. Using both the black and the 
white squares would have
made the penny grow to $92,000,000 billion.
People are reasonably good at forming estimates based on 
addition, but for
operations such as compounding that depend on repeated 
multiplication, we
systematically underestimate how quickly things grow. As a 
result, we often lose
sight of how important the average rate of growth is for an 
economy. For an
investment banker, the choice between a payment that 
doubles with every square on
the chess board and one that doubles with every other 
square is more important
than any other part of the contract. Who cares whether the 
payment is in pennies,
pounds, or pesos? For a nation, the choices that determine 
whether income doubles
with every generation, or instead with every other 
generation, dwarf all other
economic policy concerns.
Growth in Income Per Capita
You can figure out how long it takes for something to 
double by dividing the growth
rate into the number 72. In the 25 years between 1950 and 
1975, income per capita
in India grew at the rate of 1.8% per year. At this rate, 
income doubles every 40
years because 72 divided by 1.8 equals 40. In the 25 years 
between 1975 and 2000,
income per capita in China grew at almost 6% per year. At 
this rate, income doubles
every 12 years.
These differences in doubling times have huge effects for a 
nation, just as they do
for our banker. In the same 40-year timespan that it would 
take the Indian economy
to double at its slower growth rate, income would double 
three times, to eight times
its initial level, at China's faster growth rate.
From 1950 to 2000, growth in income per capita in the 
United States lay between
these two extremes, averaging 2.3% per year. From 1950 to 
1975, India, which
started at a level of income per capita that was less than 
7% of that in the United
States, was falling even farther behind. Between 1975 and 
2000, China, which
started at an even lower level, was catching up.
China grew so quickly partly because it started from so far 
behind. Rapid growth
could be achieved in large part by letting firms bring in 
ideas about how to create
value that were already in use in the rest of the world. 
The interesting question is
why India couldn't manage the same trick, at least between 
1950 and 1975.
From The Concise Encyclopedia of Economics, David R. 
Henderson, ed. Liberty Fund,
2007. Reprinted by permission of the copyright holder.
Growth and Recipes
Economic growth occurs whenever people take resources and 
rearrange them in
ways that are more valuable. A useful metaphor for 
production in an economy comes
from the kitchen. To create valuable final products, we mix 
inexpensive ingredients
together according to a recipe. The cooking one can do is 
limited by the supply of
ingredients, and most cooking in the economy produces 
undesirable side effects. If
economic growth could be achieved only by doing more and 
more of the same kind
of cooking, we would eventually run out of raw materials 
and suffer from
unacceptable levels of pollution and nuisance. Human 
history teaches us, however,
that economic growth springs from better recipes, not just 
from more cooking. New
recipes generally produce fewer unpleasant side effects and 
generate more economic
value per unit of raw material.
Take one small example. In most coffee shops, you can now 
use the same size lid
for small, medium, and large cups of coffee. That wasn’t 
true as recently as 1995.
That small change in the geometry of the cups means that a 
coffee shop can serve
customers at lower cost. Store owners need to manage the 
inventory for only one
type of lid. Employees can replenish supplies more quickly 
throughout the day.
Customers can get their coffee just a bit faster. Such big 
discoveries as the
transistor, antibiotics, and the electric motor attract 
most of the attention, but it
takes millions of little discoveries like the new design 
for the cup and lid to double
average income in a nation.
Every generation has perceived the limits to growth that 
finite resources and
undesirable side effects would pose if no new recipes or 
ideas were discovered. And
every generation has underestimated the potential for 
finding new recipes and ideas.
We consistently fail to grasp how many ideas remain to be 
discovered. The difficulty
is the same one we have with compounding: possibilities do 
not merely add up; they
multiply.
In a branch of physical chemistry known as exploratory 
synthesis, chemists try
mixing selected elements together at different temperatures 
and pressures to see
what comes out. About a decade ago, one of the hundreds of 
compounds discovered
this way—a mixture of copper, yttrium, barium, and oxygen—
was found to be a
superconductor at temperatures far higher than anyone had 
previously thought
possible. This discovery may ultimately have far-reaching 
implications for the storage
and transmission of electrical energy.
To get some sense of how much scope there is for more such 
discoveries, we can
calculate as follows. The periodic table contains about a 
hundred different types of
atoms, which means that the number of combinations made up 
of four different
elements is about 100 × 99 × 98 × 97 = 94,000,000. A list 
of numbers like 6, 2, 1,
7 can represent the proportions for using the four elements 
in a recipe. To keep
things simple, assume that the numbers in the list must lie 
between 1 and 10, that
no fractions are allowed, and that the smallest number must 
always be 1. Then there
are about 3,500 different sets of proportions for each 
choice of four elements, and
3,500 × 94,000,000 (or 330 billion) different recipes in 
total. If laboratories around
the world evaluated 1,000 recipes each day, it would take 
nearly a million years to
go through them all. (If you like these combinatorial 
calculations, try to figure out
From The Concise Encyclopedia of Economics, David R. 
Henderson, ed. Liberty Fund,
2007. Reprinted by permission of the copyright holder.
how many different coffee drinks it is possible to order at 
your local shop. Instead of
moving around stacks of cup lids, baristas now spend their 
time tailoring drinks to
each individual palate.)
In fact, the previous calculation vastly underestimates the 
amount of exploration
that remains to be done because mixtures can be made of 
more than four elements,
fractional proportions can be selected, and a wide variety 
of pressures and
temperatures can be used during mixing.
Even after correcting for these additional factors, this 
kind of calculation only begins
to suggest the range of possibilities. Instead of just 
mixing elements together in a
disorganized fashion, we can use chemical reactions to 
combine elements such as
hydrogen and carbon into ordered structures like polymers 
or proteins. To see how
far this kind of process can take us, imagine the ideal 
chemical refinery. It would
convert abundant, renewable resources into a product that 
humans value. It would
be smaller than a car, mobile so that it could search out 
its own inputs, capable of
maintaining the temperature necessary for its reactions 
within narrow bounds, and
able to automatically heal most system failures. It would 
build replicas of itself for
use after it wears out, and it would do all of this with 
little human supervision. All we
would have to do is get it to stay still periodically so 
that we could hook up some
pipes and drain off the final product.
This refinery already exists. It is the milk cow. And if 
nature can produce this
structured collection of hydrogen, carbon, and 
miscellaneous other atoms by
meandering along one particular evolutionary path of trial 
and error (albeit one that
took hundreds of millions of years), there must be an 
unimaginably large number of
valuable structures and recipes for combining atoms that we 
have yet to discover.
Objects and Ideas
Thinking about ideas and recipes changes how one thinks 
about economic policy
(and cows). A traditional explanation for the persistent 
poverty of many less
developed countries is that they lack objects such as 
natural resources or capital
goods. But Taiwan stared with little of either and still 
grew rapidly. Something else
must be involved. Increasingly, emphasis is shifting to the 
notion that it is ideas, not
objects, that poor countries lack. The knowledge needed to 
provide citizens of the
poorest countries with a vastly improved standard of living 
already exists in the
advanced countries. If a poor nation invests in education 
and does not destroy the
incentives for its citizens to acquire ideas from the rest 
of the world, it can rapidly
take advantage of the publicly available part of the 
worldwide stock of knowledge. If,
in addition, it offers incentives for privately held ideas 
to be put to use within its
borders—for example, by protecting foreign patents, 
copyrights, and licenses, by
permitting direct investment by foreign firms, by 
protecting property rights, and by
avoiding heavy regulation and high marginal tax rates—its 
citizens can soon work in
state-of-the-art productive activities.
Some ideas such as insights about public health are rapidly 
adopted by less
developed countries. As a result, life expectancy in poor 
countries is catching up with
the leaders faster than income per capita. Yet governments 
in poor countries
continue to impede the flow of many other kinds of ideas, 
especially those with
commercial value. Automobile producers in North America 
clearly recognize that they
can learn from ideas developed in the rest of the world. 
But for decades, car firms in
From The Concise Encyclopedia of Economics, David R. 
Henderson, ed. Liberty Fund,
2007. Reprinted by permission of the copyright holder.
India operated in a government-created protective time 
warp. The Hillman and
Austin cars produced in England in the 1950s continued to 
roll off production lines in
India through the 1980s. After independence, India's 
commitment to closing itself off
and striving for self-sufficiency was as strong as Taiwan's 
commitment to acquiring
foreign ideas and participating fully in world markets. The 
outcomes—grinding
poverty in India and opulence in Taiwan—could hardly be 
more disparate.
For a poor country like India, enormous increases in 
standards of living can be
achieved merely by letting in the ideas held by companies 
from industrialized
nations. With a series of economic reforms that started in 
the early 1990s, India has
begun to open itself up to these opportunities. For some of 
its citizens such as the
software developers who now work for firms located in the 
rest of the world, these
improvements in standards of living have become a reality. 
This same type of
opening up is causing a spectacular transformation of life 
in China. Its growth in the
last 25 years of the twentieth century was driven to a very 
large extent by foreign
investment by multinational firms.
Leading countries like the United States, Canada, and the 
members of the European
Union cannot stay ahead merely by adopting ideas developed 
elsewhere. They must
offer strong incentives for discovering new ideas at home, 
and this is not easy to do.
The same characteristic that makes an idea so valuable—
everybody can use it at the
same time—also means that it is hard to earn an appropriate 
rate of return on
investments in ideas. The many people who benefit from a 
new idea can too easily
free-ride on the efforts of others.
After the transistor was invented at Bell Labs, many 
applied ideas had to be
developed before this basic science discovery yielded any 
commercial value. By now,
private firms have developed improved recipes that have 
brought the cost of a
transistor down to less than a millionth of its former 
level. Yet most of the benefits
from those discoveries have been reaped not by the 
innovating firms, but by the
users of the transistors. In 1985, I paid a thousand 
dollars per million transistors for
memory in my computer. In 2005, I paid less than ten 
dollars per million, and yet I
did nothing to deserve or help pay for this windfall. If 
the government confiscated
most of the oil from major discoveries and gave it to 
consumers, oil companies
would do much less exploration. Some oil would still be 
found serendipitously, but
many promising opportunities for exploration would be 
bypassed. Both oil companies
and consumers would be worse off. The leakage of benefits 
such as those from
improvements in the transistor acts just like this kind of 
confiscatory tax and has the
same effect on incentives for exploration. For this reason, 
most economists support
government funding for basic scientific research. They also 
recognize, however, that
basic research grants by themselves will not provide the 
incentives to discover the
many small applied ideas needed to transform basic ideas 
such as the transistor or
web search into valuable products and services.
It takes more than scientists in universities to generate 
progress and growth. Such
seemingly mundane forms of discovery as product and process 
engineering or the
development of new business models can have huge benefits 
for society as a whole.
There are, to be sure, some benefits for the firms that 
make these discoveries, but
not enough to generate innovation at the ideal rate. Giving 
firms tighter patents and
copyrights over new ideas would increase the incentives to 
make a new discovery,
but might also make it much more expensive to build on 
previous discoveries.
From The Concise Encyclopedia of Economics, David R. 
Henderson, ed. Liberty Fund,
2007. Reprinted by permission of the copyright holder.
Tighter intellectual property rights could therefore be 
counter-productive and slow
growth down.
The one safe measure that governments have used to great 
advantage has been to
use subsidies for education to increase the supply of 
talented young scientists and
engineers. They are the basic input into the discovery 
process, the fuel that fires the
innovation engine. No one can know where newly trained 
young people will end up
working, but nations that are willing to educate more of 
them and let them follow
their instincts can be confident that they will accomplish 
amazing things.
Meta-Ideas
Perhaps the most important ideas of all are meta-ideas. 
These are ideas about how
to support the production and transmission of other ideas. 
The British invented
patents and copyrights in the seventeenth century. North 
Americans invented the
modern research university and the agricultural extension 
service in the nineteenth
century, and peer-reviewed competitive grants for basic 
research in the twentieth
century. The challenge now facing all of the industrialized 
countries is to invent new
institutions that encourage a higher level of applied, 
commercially relevant research
and development in the private sector.
As national markets for talent and education merge into 
unified global markets,
opportunities for important policy innovation will surely 
emerge. In basic research,
the United States is still the undisputed leader, but in 
key areas of education, other
countries are surging ahead. Many of them have already 
discovered how to train a
larger fraction of their young people as scientists and 
engineers.
We do not know what the next major idea about how to 
support ideas will be. Nor do
we know where it will emerge. There are, however, two safe 
predictions. First, the
country that takes the lead in the twenty-first century 
will be the one that
implements an innovation that more effectively supports the 
production of new ideas
in the private sector. Second, new meta-ideas of this kind 
will be found.
Only a failure of imagination—the same one that leads the 
man on the street to
suppose that everything has already been invented—leads us 
to believe that all of
the relevant institutions have been designed and that all 
of the policy levers have
been found. For social scientists, every bit as much as for 
physical scientists, there
are vast regions to explore and wonderful surprises to 
discover.

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