Shutting down a whole city to search for one man arguably sends the message that the terrorists have won: they have succeeded in closing a major metropolis. I don't know how much this will cost in lost productivity, but millions and millions would be a conservative guess.
On the other hand, it also sends another message: if you set off bombs in a public space, we will shut down the city and hunt you like vermin until we find you.
I doubt it's necessary to shut the city down in order to catch Tsarnaev. Unless he's got a plastic surgeon stashed in his back pocket, the next time he goes out in public, someone will recognize him, and he'll be caught.
On the other hand, the brothers seem to have had a lot of explosives with them. How many more people are we willing to see blown up in order to keep normal life flowing in the city? The incentives for the police and the government are pretty clear, and I'm not willing to second-guess them. Boston lost one Friday. But no one else lost their lives.