I believe there is a point of view from which things as loans, mortgages, etc. are impossible in a Bitcoin economy: and that is anonymity.
If two peers know each other in person, they could choose to agree on a mortgage contract if the currency was stable enough, or if there was a real Bitcoin economy.
Suppose subject A has lots of coins, subject B wants to buy a house from C who accepts 1000 coins (probably he is able to make profit from selling a house for coins). B could request A to send him 1000 coins with promise of returning them plus interests.
A is surely interested in making such profit, but must deal with the risk of B being unable to pay back. In current economy, a mortgage agreement is made with a contract that allows A to take property over the house in case B doesn't pay, with a court order.
So if we suppose that a Bitcoin economy exist (there is lot of discussion about it) certainly these practices are possible, because instead of writing a check you could ask your destination's Bitcoin address, send the money and expect monthly payments.
But Bitcoin is based on distribution, anonymity and absence of control. Since transactions are final and not revokable, no authority in the Bitcoin's virtual world has the power of seizing property.
Lending Bitcoins is like lending a bike in exchange of it and some accessories, and Bitcoin can just be a currency like others when buying a house in a real-world economy with real-world regulations.
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I think this question would be better answered on Economics SE: http://economics.stackexchange.com/ .
– ThePiachu – 2011-11-05T13:12:07.8171@ThePiachu: I agree that this is a better fit for the Economics SE since the question is actually "How are loans possible in a deflationary economy?". I'll let the community decide if this one should be closed though. It's certainly of interest to the community and there are some good answers already. – D.H. - bitcoin.se – 2011-11-05T21:34:46.437
I think it should stay open here, because it is an excellent example of loan operations within the context of 100% reserve banking as opposed to fractional reserve banking. Bitcoin economists will have to deal with this issue as the economy matures. – matonis – 2012-02-03T19:03:42.330