Economists often assert that, on average (but not necessarily in
any given year), GDP growth is the sum of population growth and the
growth of productivity.  However, we all know that businesses and
individuals borrow every year and increasing amounts every year. 
Borrowing is, by definition, always from the future.  That is to say
that the borrower will be able to consume less in the future because
he will have to repay today's borrowing.  It would seem, therefore,
that borrowing should add to GDP growth.  However, the population
growth + productivity growth formula certainly seems to roughly equal
GDP growth over time.  How can this be explained?

The argument in favour of using GDP is not that it is a good indicator
of standard of living, but rather that (all other things being equal)
standard of living tends to increase when GDP per capita increases.
This makes GDP a proxy for standard of living, rather than a direct
measure of it.

GDP is not 'the sum of population growth and the growth of
productivity', it is: the total value of final goods and services
produced within a country's borders in a year and does not measure
population growth (unless you take the next step and divide it by
population).

Borrowing does not add to GDP because it is merely a transfer within
the system between individuals in the system.  It is nuetral. These
interest charges would be part of GDP if using the income approach.

Can you point to examples of "However, the population
growth + productivity growth formula certainly seems to roughly equal
GDP growth over time." so we can get a clearer picture of the
phenomenon you are talking about.

Sue, 
As Canadian pointed out, GDP is not directly influenced by borrowing. 
Borrowing does not produce nor does it hinder production by itself. 
However, borrowing may (and probably does) stimulate people to
purchase more... which in turn stimulates producers to produce more,
this extra production is an increase in GDP (Gross Domestic Product)
since there is more Product being created.

Using this same logic, when people pay back their loans more than they
are borrowing, this will stimulate them to purchase less and therefore
producers will be stimulated to produce less.  This lower production
will decrease GDP.

So, although borrowing doesn't directly affect GDP, you can see how it
does have some influence indirectly.


Canadian,
"However, the population growth + productivity growth formula
certainly seems to roughly equal GDP growth over time."
This is simply what is the case assuming that Sue is referring to per
capita growth (which i think is a fine assumption).

An example (as requested):
100 people in the population
GDP $1000
If the population growth rate is 2% per year then in 10 years the
population will be 122.
If GDP in 10 years has risen to $1500, then you can see that $220 of
that was due to the increased population (GDP per capita would be the
same as before if GDP had only risen $220).  This leaves $280 as the
productivity growth over that 10 years.  This equates to about a 2.5%
annual growth rate per capita.

Another note, the borrowing does not have to be internal the the
economy... it could be (and very often is) a temporary money transfer
outside of the country.

GDP is the total value of all the goods and services produced with in
a country in a particular year.  Population only affects GDP numbers
in the sense that more people normally means more production and
consumption.

National Income in a country is often measured in the simplest form by:

C + I + G + (X-M)

C=consumer spending, I= Investment, G= Government Spending, X=Exports, M (Imports)


National Income per Capita (which is what seems that you are
interested in) is the same formula as above divided by the national
population.

If the economy doesn't grow "faster" than the rate of population
growth then effectively GDP per capita or National Income per capita
is decreasing, or the standard of living is decreasing.

Going into debt to finance spending in the longer term often affects
"I"as less savings are available in the future to be converted into
Investment.

I missed my final point.  When you borrow in the short term, the money
doesn't disappear out of the economy. If the borrower used that money
to invest instead of spend, and the investment was successful, it
doesn't mean the busines will spend less over time.


If you borrow and pay interest, the person or company that is earning
the interest earns that interest as income, and he either spends it or
saves it. Income is not counted in the formula I presented above
(because the model I used was the expenditure model).  The spending or
investment of that borrowed money is counted as an increase to the
GDP.

Now obviously this whole model assumes that the borrowed money is an
injection into the economy from "unproductive" sources like savings
accounts or investment funds.

Population Growth and Productivity Growth are things that both add to
the net National Income.  By more people being born, doesn't make the
economy more productive.  Here you will need to clarify what you mean
by your last sentence