Math in Society: Mathematics for liberal arts majors

Federal income comes from our individual income taxes and business income taxes. Income is also borrowed by selling savings bonds, notes and Treasury bills (United States Government, 2019). The government has to pay interest on the national debt. After that, there are two types of spending, mandatory and discretionary. Mandatory spending includes Social Security payments, Medicare and other items required by law. Discretionary spending is the amount that Congress budgets annually to fund programs and agencies. Here is a pie chart showing the percentage of spending for each type in 2019. The data comes from the Congressional Budget Office (Congressional Budget Office, 2020).

The Federal Budget is like a home budget, with income and expenses. The U.S. Government’s fiscal year goes from October 1st of one year to September 30th of the next year. Work on the budget begins about a year and a half before the budget is finalized.

First, departments and agencies submit their proposals to the White House. Then the President submits their budget plan to Congress. Each chamber of Congress analyzes the proposal and makes their own budget resolution. Then a conference committee of House and Senate members resolves the differences between the two plans and makes a final version that each chamber votes on.

After the budget is passed, the Senate and House Appropriations committees distribute the discretionary part of the funding among 12 subcommittees that oversee different groups of agencies. As before, conference committees meet to merge the two versions of the appropriations bills. All 12 bills must be passed by both the Senate and the House and then signed by the President to enact the new budget.

If any appropriations bill is not signed by September 30th, there is no budget for the new fiscal year. In this case, Congress must pass a continuing resolution to temporarily fund the government. If they do not, or if the president does not sign it, the governement will shut down. The last government shutdown went from December 22, 2018 to January 25, 2019. This was the longest shudown in U.S. history and left over 800,000 federal workers either working without pay or being furloughed at home (Robert, 2020).

If the government spends less than it collects in income, there will be a budget surplus for that year. If it spends more than it collects, there will be a deficit for that year. It is also possible to have a balanced budget where the spending equals the income. The federal deficit refers to the budget shortfall in a single time period, like a quarter or a year. For example, in the Fiscal Year 2018, the U.S. deficit was $779 billion. The graph below shows the federal deficit or surplus each year since 1974 using data from the Congressional Budget Office (Congressional Budget Office, 2014).

It is hard to find graphs with a vertical axis in dollars becase the value of the dollar changes over time. One dollar in 1974 could buy a lot more than it can today. In the graph above, each dollar amount is converted to the equivalent of 2013 dollars to account for that. The vertical scale is in billions of 2013 dollars. The largest deficits in 2009 to 2012 were from spending and corporate bailouts to recover from the Great Recession of 2008.

On the graph above, $1 on the vertical scale represents one billion dollars or $1,000,000,000. The highest deficits go down to about -$1,500 billion, which we would write as -$1,500,000,000,000. Here is a chart that shows large numbers and how many zeros they have.

Instead of writing all the zeros, we can abreviate large numbers using decimals. For example, 1,200,000 can be written as 1.2 million. We can write 900,000 as 0.9 million. We can also translate the other way and write 4.567 trillion as 4,567,000,000,000. Note there can be more than one way to write a number. We could write 400,000,000 as either 400 million or 0.4 billion. It is convenient that we put the decimal where the comma goes and vice versa.

A more common way to measure the deficit is as a percentage of the gross domestic product. The gross domestic product, or GDP, is the total value of all the finished goods and services produced within a county’s borders in a specific period of time. The GDP is a measure of the size of an economy. The growth rate of the GDP is one measure of a nation’s economic health (Bureau of Economic Analysis, 2019). The GDP of the United States in 2019 was $21.73 trillion but due to the COVID-19 pandemic, there was a drop in the second quarter of 2020 to $19.74 trillion. (Bureau of Economic Analysis, 2020).

Now we can look at more graphs that are written in terms of the percent of GDP. Here is a graph of federal spending and revenues as a percentage of the GDP

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“Federal Revenue and Spending, 1985-2050” is copyrighted by Peter G. Peterson Foundation and used under the permissions granted for educational use.

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For each year, if we take the revenue and subtract the spending, we get the budget surplus or deficit. If the result is negative it is a deficit. And here is a graph of the deficits in terms of percentage of GDP

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“Updated Budget Projections: 2019 to 2029” by Congressional Budget Office is in the Public Domain.

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The words deficit and debt are easily confused because they have similar meanings. The deficit is the yearly shortfall, and the national debt is the total cumulative amount of debt held by the government.

As you can see from the previous graphs, most years had a budget deficit. If we add all of those up over time, this is what the national debt looks like

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“Federal Debt: 1791-2019” is copyrighted by Peter G. Peterson Foundation and used under the permissions granted for educational use.

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Just like we pay interest on our personal debt, the U.S. pays interest on the national debt. The interest on the debt is expected to keep increasing as shown in this graph

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“Net Interest Cost” is copyrighted by Peter G. Peterson Foundation and used under the permissions granted for educational use.

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There are several websites that keep a running total of the national debt. One of them is USDebtClock.org

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usdebtclock.org

. This one also shows the population, debt per citizen and debt per taxpayer. It shows the spending and deficit with counters that are constantly moving. At the bottom you can also see the debt to GDP ratio compared with previous ratios. The rest of the website shows statistics like the GDP, income tax revenue, median income, unemployment and much more. You can also see statistics for other states and countries.

Now let’s do some calculations with these large numbers in the next example.

For more comparisons, here is a graph showing the debt to GDP ratios around the world in 2020

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“Public Debt Percent GDP World Map” by Wikimedia Commons Contributors, Wikimedia Commons, the free media repository.

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We can also do calculations with large numbers that involve percentages. We will look at some pie charts related to government income and spending.

In this chapter, we have looked at many important quantitative aspects of government: apportionment, voting methods, how the president is chosen, gerrymandering and the federal budget. Filling out the census, being informed and voting are extremely important for the U.S. democracy. Please make up your own mind and vote if you are eligible.