I'm probably being obtuse about this. Can you tell me what the advantages are for transacting in BTC? If there's dollars on either side, the only advantage to dealing in BTC is different (as opposed to lesser) transaction fees… and Square and others are whittling away at that already. Yes, the "traditional transactional protocols" are convoluted and expensive, but the Check 21 act eliminated their necessity in 2004. That's why Square can exist.

One advantage is that rather than numerous closed networks, bitcoin offers a open distributed ledger. Like HTTP and SMTP, a standard protocol reduces costs of fragmentation, and lowers the barrier to entry. Fees of the bitcoin network itself can be near zero, whereas Coinbase currently charges 1% for buying and selling (currently for merchants, the first $1M is free). PayPal charges 2.9% + $0.30 per transaction. As the protocol is open and won't change quickly, others can easily get into the wallet game, and likely keep a downward pressure on these fees, perhaps like webmail; Hotmail couldn't get away with $20/yr for 20MB for long, it was just too easy to undercut. Another thing that could exert downward pressure, is that anyone can transfer BTC without a processor. For example, if you have a paywall, you can accept numerous BTC payments for free, and cash out to USD at the end of the day (or hour), running around any 'per-transaction fees', which most credit card processors include. On top of the advantages that come from letting anyone tinker with an open protocol, bitcoin has other built in functionalities such as m of n transactions whereby a transfer won't occur unless m of n parties approves the transaction. Escrow, arbitration, and pledge functionalities exist as part of the protocol. As one example, you could crowd fund a project, where the money only transfers if a certain total value is pledged. You can use the ledger for a notary stamp. This is part of the protocol.

It gets even deeper, and my knowledge of the protocol is limited. However, the more I look, the more I find shit that is pretty compelling. The short version to the argument is that with bitcoin, you can have an internet rather than a bunch of intranets patched together. Techies can then go to work on that, and take it to the next level and the next. As an example, look at namecoin, using the bitcoin protocol, they are creating an ICANN-free DNS registry among other things; there's talk that this could be used for an verifiable voting ledger.

At this point, I'm basically saying the bitcoin P2P network offers potentially transformative innovation and cohesion in the transactional space. There's a story under all this talk about bitcoins, and I think Krugman is remiss to gloss over it. Maybe he has considered all of these aspects of bitcoin, but as the dude said:

By 2005 or so, it will become clear that the Internet's impact on the economy has been no greater than the fax machine's.

I think it's likely he hasn't.

BTW, I think Square is going public this year.