http://www.mckinsey.com/insights/high_tech_telecoms_internet/internet_mattersThe reference above estimates today's internet contribution to global GDP as 3.4%.
Using an order of magnitude estimate of global GDP of 100 trillion USD, the internet's contribution today is 3 trillion USD.
Using an optimistic guess that a fully evolved BTC economy will embody 50% of the internet economy the optimistic fully evolved BTC "GDP" will reach 1.5 trillion USD.
Using 15 million BTC to make the math easy, one BTC will be worth 100,000 USD in a fully evolved BTC economy.
(Applying this argument to today's price results in an estimate of 0.2% of today's internet economy transacted in BTC. This is a huge overestimate, which I think can be explained by today's BTC price reflecting investment based on the potential of BTC.)
I think you forgot to divide by the velocity of money.
Put another way, GDP is the value of goods and services sold in a year. But the same coins might be used for more than one transaction in a year, so a 1.5 trillion USD contribution to GDP doesn't mean a bitcoin money suppy ('market cap') or 1.5 trillian dollars. Some coins might be used in many transactions in the space of a year - hence requiring a significantly lower valuation to be able to account for all those transactions. Of course, this is balanced by the fact that other coins won't be spent at all in any given year.
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