Economics of Anti-Ballistic Missile Defenses

References

The True Cost of Road Crashes: Valuing life and the cost of a serious injury (2.1 MB PDF)

Recently in the news (as of Spring 2011), there is a lot of talk going on about Israel's newly deployed IRON DOME low-level ABM system.

Much is being made of the cost of a typical HAMAS Quassam rocket (estimated to be €500 per rocket back in 2008; which translates into about $740 USD in 2011) versus the cost of the Tamir interceptor missiles which are estimated to cost between $35,000 and $50,000.

During the 2006 Lebanon War, about 4,000 rockets were fired into Israel for 43 KIA and 101 WIA.

(I am excluding the 1,300~ who received 'light wounds' and the 2,770 who were treated for shock and anxiety)

This breaks down to a crude yardstick of:

1 Death for every 93 rockets during an intense bombardment
1 Serious Wound for every 39.6 rockets during an intense bombardment
From 2000~ to 2010, about 4,728 rockets were fired from Gaza into Israel, causing 23 fatalities, or about:
1 Death for every 205.5 rockets fired during a sporadic bombardment

With no ABM system in place to protect Israel, it only costs Islamic groups $64,820 to $152,440 to kill an Israeli and about $29,600 to $65,100 to seriously wound one.

According to the True Cost of Road Crashes, the official Value of Statistical Life (VSL) in several countries is:

United States: $3 million USD (82.6 times per capita GDP)
United Kingdom: $2.11 million USD (70.4 times per capita GDP)
Germany: $1.67 million USD (43.4 times per capita GDP)
Likewise, the Value of Serious Injuries (VSI) is:
United States: $464,600~ USD (12.8 times per capita GDP)
United Kingdom: $253,000~ USD (12.9 times per capita GDP)
Germany: $126,000~ USD (4.7 times per capita GDP)

Israel's per capita GDP is about $29,500 USD; so you end up with:

VSL: $1.28 to $2.4 million USD
VSI: $138,600 to $380,500 USD

Without ABM, the Islamic groups can easily and cheaply wage economic war on Israel – It only costs them $152,000~ to cause at least $1.28 million dollars worth of damage to the Israeli economy.

We haven't even touched on the productivity that's lost from people being forced to leave work and run to bomb-shelters at any moment of the day to escape death or serious injury in the areas under rocket fire.

With ABM however, the entire equation changes, particularly since the Quassams are so inaccurate that the majority of them fired simply hit empty fields.

It's why the numbers for missiles per injury/death are so high – the Palestinians have to fire dozens of rockets to get that solitary triplet that will impact within a city.

IRON DOME takes advantage of this by allowing operators to pre-define “keep out” zones for the system. If a rocket's trajectory has it impacting outside that “keep out” zone, the system doesn't fire on the rocket and lets it impact harmlessly in a field.

The ABM cost/benefit equation isn't “Fire 60 Quassams for a cost of $44,400 to cause the Israelis to expend $2.4 million dollars worth of interceptors to shoot down each Quassam.”

It's actually “Fire 60 Quassams for a cost of $44,400 to get five on a trajectory that will have them impact in a city center.”

Total cost to the Israelis of firing ten interceptors to negate the threat of those five rockets in the salvo that are actually going to hit something? Only $400 grand. Considering that the VSI for an Israeli is between $138 and $380 grand if a rocket inflicts a serious injury, it's a bargain.

As an added bonus, the IRON DOME system is capable of providing backtracked trajectory data (as is any ABM system worth it's salt) to other military units, such as helicopter gunships or unmanned drones, so they can be on the scene and attacking the launching teams in much less time.

The equation just gets even better in favor of the defense when you move up to a nuclear threat.

Hiroshima was a mere 15 kilotons or so, yet it killed about 100,000 people and seriously wounded about 60,000 more. In terms of a US economy, that's $327.87 billion from the personnel casualties alone.

September 11th destroyed about 16 acres in the US totally and caused about $30 billion in direct damages for a crude cost of $1.875 billion/acre destroyed.

Hiroshima reduced about 3,200 acres to smoking radiated ashes. Even if we cut that by 40% due to much better modern US fire codes, that's still 1,920 acres that's going to be destroyed utterly, or about $3.6 trillion in property damage.

Against the $3.9 trillion cost of a mere 15 kiloton device successfully initiating over a major U.S. city, the $32.7 billion that we've spent on GBI/GMD in Alaska is a bargain.