In a recent Cabinet meeting, President Obama called for a $100 million spending cut in 90 days from the various federal departments as a sign of budget discipline. While this is nominally quite a large number, it was pointed out correctly by many people that this was in fact a negligible fraction of the total federal budget; for instance, Greg Mankiw noted that the cut was comparable to a family with an annual spending of$100,000 and a deficit of $34,000 deciding on a spending cut of$3.  (Of course, this is by no means the only budgetary initiative being proposed by the administration; just today, for instance, a change in the taxation law for offshore income was proposed which could potentially raise about $210 billion over the next ten years, or about$630 a year with the above scaling, though it is not clear yet how feasible or effective this change would be.)

I thought that this sort of rescaling (converting $100 million to$3) was actually a rather good way of comprehending the vast amounts of money in the federal budget: we are not so adept at distinguishing easily between $1 million,$1 billion, and $1 trillion, but we are fairly good at grasping the distinction between$0.03, $30, and$30,000.  So I decided to rescale (selected items in) the federal budget, together with some related numbers for comparison, by this ratio 100 million:3, to put various figures in perspective.

This is certainly not an advanced application of mathematics by any means, but I still found the results to be instructive.  The same rescaling puts the entire population of the US at about nine – the size of a (large) family – which is of course consistent with the goal of putting the federal budget roughly on the scale of a family budget (bearing in mind, of course, that the federal government is only about a fifth of the entire US economy, so one might perhaps view the government as being roughly analogous to the “heads of household” of this large family).  The implied (horizontal) length rescaling of $\sqrt{100 \hbox{million}:3} \approx 5770$ is roughly comparable to the scaling used in Dubai’s “The World” (which is not a coincidence, if you think about it; the purpose of both rescalings is to map global scales to human scales).  Perhaps readers may wish to contribute additional rescaled statistics of interest to those given below.

One caveat: the rescaling used here does create some noticeable distortions in other dimensional quantities.  For example, if one rescales length by the implied factor of $\approx 5770$, but leaves time unrescaled (so that a fiscal year remains a fiscal year), then this will rescale all speeds by a factor of $\approx 5770$ also.  For instance, the circumference of the Earth has been rescaled to a manageable-looking 6.9 kilometres (4.3 miles), but the speed of, say, a commercial airliner (typically about 900 km/hr, or 550 mi/hr) is rescaled also, to a mere 150 metres (or 160 yards) or so per hour, i.e. two or three meters or yards per minute – about the speed of a tortoise.

All amounts here are rounded to three significant figures (and in some cases, the precision may be worse than this).   I am using here the FY2008 budget instead of the 2009 or 2010 one, as the data is more finalised; as such, the numbers here are slightly different from those of Mankiw.  (For instance, the 2010 budget includes the expenditures for Iraq & Afghanistan, whereas in previous budgets these were appropriated separately.)  I have tried to locate the most official and accurate statistics whenever possible, but corrections and better links are of course welcome.

FY 2008 budget:

• Total revenue: $75,700 • Individual income taxes:$34,400
• Social security & other payroll taxes: $27,000 • Total spending:$89,500
• Net mandatory spending: $48,000 • Medicare, Medicaid, and SCHIP:$20,500
• Social Security: $18,400 • Net interest:$7,470
• Net discretionary spending: $34,000 • Department of Defense:$14,300
• DARPA: $89 • Global War on Terror:$4,350
• Department of Education: $1,680 • Department of Energy:$729
• NASA: $519 • Net earmarks:$495
• NSF: $180 • Maths & Physical Sciences:$37.50
• Budget deficit: $13,800 • Additional appropriations (not included in regular budget) • Iraq & Afghanistan:$5,640
• Spending cuts within 90 days of Apr 20, 2009: $3 • Air force NY flyover “photo shoot”, Apr 27, 2009:$0.01
• Additional spending cuts for FY2010, proposed May 7, 2009: $510 • Projected annual revenue from proposed offshore tax code change:$630

Other figures (for comparison)

• National debt held by public 2008: $174,000 • Held by foreign/international owners 2008:$85,900
• National debt held by government agencies, 2008: $126,000 • Held by OASDI (aka (cumulative) “Social Security Surplus”):$64,500
• National GDP 2008: $427,000 • National population 2008: 9 • GDP per capita 2008:$47,000
• Land mass: 0.27 sq km (0.1 sq mi, or 68 acres)
• World GDP 2008: $1,680,000 • World population 2008: 204 • GDP per capita 2008 (PPP):$10,400
• Land mass: 4.47 sq km (1.73 sq mi)
• World’s richest (non-rescaled) person: Bill Gates (net worth $1,200, March 2009) • 2008/2009 Bailout package (TARP):$21,000 (maximum)
• Amount spent by Dec 2008: $7,410 • AIG bailout from TARP:$1,200
• AIG Federal Reserve credit line: $4,320 • AIG bonuses in 2009 Q1:$4.95
• GM & Chrysler loans: $552 • 2009/2010 Stimulus package (ARRA):$23,600
• Tax cuts (spread out over 10 years): $8,640 • State and local fiscal relief:$4,320
• Education: $3,000 • “Race to the top” education fund:$150
• Investments in scientific research: $645 • Pandemic flu preparedness:$1.50 (was initially $27, after being dropped from FY2008 and FY2009 budgets) • Additional request after A(H1N1) (“swine flu”) outbreak, Apr 28:$45
• Volcano monitoring: $0.46 (erroneously reported as$5.20)
• Salt marsh mouse preservation (aka “Pelosi’s mouse“): $0.00 (erroneously reported as$0.90)
• Market capitalization of NYSE
• May 2008 (peak): $506,000 • March 2009:$258,000
• Largest company by market cap: Exxon Mobil (approx $10,000, Apr 2009) • Value of US housing stock (2007):$545,760
• Total value of outstanding mortgages (2008): $330,000 • Total value of sub-prime mortgages outstanding (2007 est):$39,000
• Total value of mortgage-backed securities (2008): \$267,000
• Credit default swap contracts, total notional value: