From the NYTimes (New Orleans Floodplan Upgrade Urged):
Federal officials outlined plans yesterday for a significant improvement to the New Orleans flood-protection system by 2011, but said the total cost would be more than double the $7.1 billion that Congress has already appropriated for repairs and upgrades.
I'm wondering ... what is the breakeven willingness to pay that would justify this expense?
By spending an additional $7.6 billion, the Army Corps of Engineers could build higher, tougher floodwalls and gates to seal off waterways like the city’s enormous Inner Harbor Navigation Canal from storm surges, officials said. Permanent pumping stations at the mouths of the city’s drainage canals would block surging water from Lake Pontchartrain and effectively pump water out of the city during storms as well.
The officials said the upgraded system would result in a widespread reduction in water levels should the city be hit by the kind of flood that might have a 1 percent chance of occurring in any year. It would not eliminate flooding, however — rainwater could still accumulate to two or four feet in some sections of the city — and very intense storms could still do major damage.
Suppose the present value of costs (PVC) is $14.7 billion. The present value of benefits in perpetuity is:
- PVB = (P x B x N)/r
where the P is the annual probability of a flood, B is the annual individual level benefit, N is the population and r is the discount rate. According to the article, P = .01. According to my favorite mistake-free source, the greater New Orleans population is 1.2 million (the city population is 273k). The question is, what is the individual level benefit that equates PVB and PVC at various discount rates? Using simply my brain to calculate these values*:
- r = .02, B = $24,500
- r = .07, B = $61,250
In order for the net benefits to be positive, annual willingness (and ability) to pay (B) must be greater than these breakeven benefit estimates, much greater for net benefits to look like a good investment. Whether the greater New Orleanian's annual willingness to pay to avoid the flood risk is much greater than these estimates is an empirical question.
Suppose we looked at this as a national problem. Using 300,000,000 for N we get:
- r = .02, B = $98
- r = .07, B = $343
Would you be willing to pay $98 in higher taxes every year?
As always, corrections to my math and assumptions in the comments section are much appreciated.
*Note: I also used MS Excel.
