This is a question and answer post about the economics of GDP calculation
based on the following question:

The
values key macroeconomic variables for the U.S. economy in 2011 were: C =
$9,484, I = $1,870, G = $2,480, X = $1,804 and M = 2,208. All figures are in
billions of 2005 dollars.

Use
the information above to find:

Real
GDP

Total Income

NT + S (where NT stands for net taxes and S represents savings)

Total Income

NT + S (where NT stands for net taxes and S represents savings)

In order to do this problem we need to remember the GDP (gross
domestic product) equation:

Y = C + I + G + NX

Where:

Y is GDP

C is consumption

I is investment

G is government spending

NX is net exports or exports minus imports (X – M)

We can use the information above to calculate real GDP (we know it
is real GDP because it was given to us in 2005 dollars, which is apparently the
base year for this amount). So we add:

9,484+1,870+2,480+1,804-2,208 which gives us a real GDP equal to:

$13,430 (in billions of 2005 dollars).

To get total income we have to know the relationship between GDP
and income. Since a relationship is not
specified in the question, we can assume that total income is going to be equal
to GDP. If this is the case the answer
to total income is going to be the same as the answer to real GDP. The reason that total income can be the same
as real GDP is because of how GDP is measured.
GDP is the value of every final good or service produced within a
country during a specified time period.
Since all of these goods and services must be purchased, the money has
to go somewhere and it generally goes to the owners of the factors of
production. This means that the owners
of the capital, labor, land, and entrepreneurship get paid (have an income) the
same amount as is recorded for GDP.

Finally we need to calculate the sum of NT and S or net taxes and
savings. To do this we need to remember
that total economy wide savings is equal to private savings plus public
savings. Net taxes is calculated as the
difference between taxes paid to the government minus transfers received from
the government or (T-TR). Since none of
this information is available to us we have to do some guessing.

First, we need to assume that we have a closed economy with
respect to savings and investment and this will make S = I or savings equal to
investment.

Second, if we assume that the government is operating under a
balanced budget, then net taxes are equal to government spending. So NT = G.
we can now add G and I to get NT + S which will be:

1,870+2,480=4,350

Now it is possible that the assumptions above do not hold, but
based on the question I cannot be sure.
Please leave a comment if you have more information or believe the
assumptions I made are not accurate, thanks!