Thursday, May 07, 2009

Scaling large numbers

Several blogs (Greg Mankiw's and Terence Tao's) have introduced the
following length scaling, sqrt(100million/3)~5773, as a good way to
understand very large numbers. In particular, this is useful for
getting an everyday feel for the US government budget in normal
everyday life quantities. Essentially, this factor converts 100
million dollars to 3 dollars, and scales the US economy to roughly the
budget of a US household of 9 people.

Here's Tao's calculations for various US budget (and non-budget) items:

FY 2008 budget:

* Total revenue: $75,700
o Individual income taxes: $34,400
o Social security & other payroll taxes: $27,000
* Total spending: $89,500
o Net mandatory spending: $48,000
+ Medicare, Medicaid, and SCHIP: $20,500
+ Social Security: $18,400
o Net interest: $7,470
o 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)
o Iraq & Afghanistan: $5,640
* Spending cuts within 90 days of Apr 20, 2009: $3

Other figures (for comparison)

* National debt 2008: $174,000
* National GDP 2008: $427,000
o National population 2008: 9
o GDP per capita 2008: $47,000
o Land mass: 0.27 sq km (0.1 sq mi, or 68 acres)
* World GDP 2008: $1,680,000
o World population 2008: 204
o GDP per capita 2008 (PPP): $10,400
o 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 Bailout package (TARP): $21,000 (maximum)
o Amount spent by Dec 2008: $7,410
o AIG bailout from TARP: $1,200
+ AIG Federal Reserve credit line: $4,320
+ AIG bonuses in 2009 Q1: $4.95
o GM & Chrysler loans: $552
* 2009 Stimulus package (ARRA): $23,600
o Education: $3,000
+ "Race to the top" education fund: $150
o Investments in scientific research: $645
+ NSF allocation: $90 (was initially $42)
+ ARPA-E: $12
o 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
o Volcano monitoring: $0.46 (erroneously reported as $5.20)
o Salt marsh mouse preservation (aka "Pelosi's mouse"):
$0.00 (erroneously reported as $0.90)
* Market capitalization of NYSE
o May 2008 (peak): $506,160
o March 2009: $258,180
o Largest company by market cap: Exxon Mobil (approx
$10,000, Apr 2009)
* Value of US housing stock (2007): $545,760
o 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:
o April 2008: $1,320,000
o Oct 2008: $1,040,000
o Credit default swaps related to mortgages: less than
$10,000
* US trade balance (2007)
o Exports: $49,400
o Imports: $70,400
o Trade deficit: $21,000