Budgeting

In an attempt to illustrate math concepts and to help math students understand how math is used in the real world, I would like to show how exponents are used to represent really HUGE numbers. As an example, I will use the Proposed 2011 U.S. Federal Government Budget and the projected annual deficit it will leave in its wake.

Let's start with a definition of the U.S. Budget Deficit. (Not to be confuse with the U.S. Trade Deficit.) The U.S. Budget Deficit can be represented by a simple formula or equation, as follows:

REVENUES minus OUTLAYS = Budget SURPLUS or Budget DEFICIT.

When this formula is equal to zero, that is when "Revenues" = "Outlays", then the budget is said to be "Balanced". The Fiscal Commission has been put in charge to do this by 2015. When this formula is positive, meaning when "Revenues" are greater than "Outlays", the result is a Budget Surplus. However, when this equation is negative, that is, when government "OUTLAYS" are more than its "REVENUES", then this creates a Budget Deficit. Each year, it is a very difficult task for the current administration to "Balance the Budget". The current Fiscal Commission under the Obama Administration has been charged with the task of providing a Balance Budget by 2015. It remains to be seen, whether the Fiscal Commission will be able to accomplish this directive. Already, disclaimers are being issued as to the unlikelihood of this event actually coming to pass, due to our current economic condition.

To understand this concept of a "Budget Deficit" a bit more, let's look at the terms "Revenues" and "Outlays". Every year, the U.S. federal government publishes its projected Revenues (money to be received) compared to its proposed Outlays (money to be spent on government goods and services) for the upcoming fiscal year. "Revenues" are the monies coming into the Treasury from various sources such as income taxes, other various taxes, borrowing and other financing techniques.

"Outlays" are the government expenditures which pay for all the government programs such as defense, education, highways, economic recovery, social security benefits, job creation programs, the new health care program and many, many more goods and services as well as interest payments on previous years' government debt. Two of the most contested issues among politicians are (1) "Just how much should our federal government require us (its citizens) to pay in the form of taxes especially Federal Income Taxes?" and (2) "Just how big should our federal government be?" The former question is generally thought to be related to the "REVENUES" side of the formula while the latter question is usually related to the "OUTLAYS" term of the equation.

Below are the specifics underlying the Proposed 2011 U.S. Budget:

2011 Budgeted REVENUES are $2.5 Trillion
Less
2011 Budgeted OUTLAYS are $3.8 Trillion
Equals
Budget Deficit ( $1.3 Trillion).

Written as a number (without decimals and the word "TRILLION"), it looks like this:
$1,300,000,000,000!

Just how BIG is 1.3 Trillion dollars?

Consider this:
$1 - one dollar has no zeros.
$10 - Ten dollars has one zero.
$100 - One hundred dollars has two zeros.

$1 Thousand has 3 zeros, written as $1,000.
$1 Million has 6 zeros, written as $1,000,000
$1 Billion has 9 zeros, written as $1,000,000,000
$1 Trillion has 12 zeros, written as $1,000,000,000,000

Oh by the way, the number after the decimal, ".3", is not insignificant either, it is
equal to $300 Billion dollars, more than one thousand times the amount that Oprah Winfrey made in 2008, which was approximately $260 Million!

Using exponents
1 Thousand = 1,000 = 10^3 (where "^" is the exponent sign on most computer keyboards)
1 Million = 1,000,000 = 10^6
1 Billion = 1,000,000,000 = 10^9
1 Trillion = 1,000,000,000,000 = 10^12

Another way to conceptualize this is shown below:
1 Million is 1,000 thousands
1 Billion is 1,000 millions
1 Trillion is 1000 billions.

So if you could find one-thousand billionaires willing to pay 1.3 billion dollars ($1,300,000,000) each... That would pay off ONLY the 2011 deficit. It does not address the previous years' deficit and/or the current national debt that the federal government has amassed since 1789!!!

Can't find 1,000 billionaires? How many billionaires like Bill Gates do you know, anyway?...probably not a thousand!

Then let's look for Millionaires. It would take only one-million millionaires to pay 1.3 million dollars ($1,300,000) each, in order to pay off the planned 2011 budget deficit!

Let's pause for a quick math help tip here.
Note: 1 trillion = 1 million times 1 million = 1 million squared!
Or 1,000,000,000,000 = 1,000,000 x 1,000,000 = 1,000,000^2
Or 10^12 = 10^6 x 10^6 = (10^6)^2
All that is being said here is that a trillion is a million millions! And yet the projected U.S. Budget Deficit for 2011 is even LARGER!!! 30% larger or 1.3 Trillion Dollars!

Can't find 1,000,000 Millionaires? How many millionaires like Oprah do you know, anyway?... probably not a million of them!

How about each and every U.S. citizen, which is approximately 300 million people (300,000,000) of us? If you and every one of us, I mean everyone regardless of age or income level, could pay an extra $4,333.33 more than we already pay in various taxes, then the budget would be balanced (Money In = Money Out). Can you afford an extra $4,333? Most people can't!

The intention here is to help online math students understand the complexity and the enormity of the U.S. Budget Deficit, not just from a mathematical viewpoint but from social, economical and political aspects as well.