We should start by saying that math was never our strong suit, and we didn't progress past Trig. (in which we got a D+ our senior year of high school). Nevertheless, we shall endeavor to analyze the question. We'll focus on lost productivity due to traffic, if only because it's a straightforward figure, and we'll limit ourselves to the Central Artery: 16 minutes and 42 seconds a day comes to 69 hours and 35 minutes of time per year per car, if we assume 250 work days. Of course, only half of that is lost in the morning, so we have 34 hours and 42 minutes of actual lost work time. (OK, you can see where this is going. If you're ready for more number-crunching, click below.)
Photo courtesy of Rene Schwietzke. Some rights reserved.
According to the City of Boston, there were 184,000 daily car trips, on average, through the Central Artery in 1987, and 197,000 in 1999. Call that a regular increase of about 6,500 cars a year, and you're talking about 203,500 trips a day in 2005. Bostonist will make things easy (and be generous in our estimates) by assuming all of those trips are work-related.
According to the Bureau of Transportation Statistics, 90% of those trips will be single drivers and the bulk of the remaining ten percent will be two-person carpooling arrangements. So let's say that for 203,500 car trips, there are 225,000 actual commuters.
So we have 225,000 commuters, each of whom works an extra 34 hours and 42 minutes per year. With an average wage in Massachusetts of $44,954, that's $749.95 per commuter, which amounts to $168,738,750 in lost wages/productivity each year. At that rate, the Big Dig will pay for itself, in increased productivity alone, in just 83 years and three months!
OK, not so good. But like we said, we're no math wiz. Hopefully, the eggheads at the Turnpike Authority will crunch the numbers in a way that actually makes Bostonist feel good about 15 billion dollars and 15 years of construction misery.
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OK, this is fun.
So, in addition to productivity gains, you probably need to also account for productivity *losses* due to everything being a mess for 15 years.
I know you said you were just going to limit your equation to productivity gains. But one other number that it would be realtively easy to get a less-than-precise but interesting number is in gas consumption. Assume that all 203,500 cars were cars, and actually got the CAFE-required 27.5 MPG (so, no light or heavy trucks, which include SUVs). Also assume an average speed of 20 MPH (which I just pulled out of thin air). That means a savings of 41,193 gallons of gas, or about $99K. Wow. That didn't add up to much. Even if I use an average MPG of 15 to factor in SUVs, I still only get about $182K.
If you take into account that the people who drive into Boston for work are probably at the high-end of the MA average wage, it's probably really only 60 years til it pays for itself.
The big return on investment will not be in reduced commuting time, but in increased traffic handling as the commuting time returns to it's pre-Big Dig equilibrium. I know that this is really awful, so enjoy the fast ride while you can.
Eventually, people will realize that they CAN live on the North Shore and work towards the South Shore (or vice versa), so they'll start shuffling jobs, and new jobs will be created in new areas because they will have a larger workforce catchment area. Traffic congestion will increase, but tax revenues from all the development and new jobs will rise as well.
That's what will make the Big Dig pay off. Remember, the Romans rebelled when asked to pay for the big Tarquin sewer project, but they are still using that old sewer system today.