I just don't buy the proposition that Bitcoin will be more valuable in the future because it will be more valuable in the future therefore the price will be higher in the future therefore the value is higher now, without first asserting some cause for the future rise in value or some cause for the present value.
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Look at this statement: USD will have a relatively stable value in the future because it have a relatively stable value in the past and now therefore the price will be relatively stable in the future
The value of money is decided by a consensus, and when people reached a consensus, it will just hold that value even the supply and demand changes. In USD's case, that consensus is reached through people's historical experience, so even the gold that originally backed USD have been removed, its value still kept relatively stable (In theory when the gold back it was removed, it should drop to zero)
Not to zero, there is no theory that suggests unbacked currency are always worth zero (or bitcoin would be zero as well)... The dollar plunged by a third during the '70s, though.
At about the time the gold backing for the dollar was removed, there was also the establishment of the EPA, and massive federal government appropriation of land and land use rights associated with that. This was a genius move by Nixon to co-opt his hippy opponents into giving him a new backing other than gold, by taking much land into the government treasury. December 2, 1970 The wilderness Act seized a bit over 9 million acres. (Now over 100 million, and growing).
To end the effect of Gresham's law on the dollar vs gold, and to prevent a run on the dollar, stabilize the economy, and decrease unemployment and inflation rates, on August 15, 1971, Nixon issued Executive Order 11615, pursuant to the Economic Stabilization Act of 1970, which imposed a 90-day maximum wage and price ceiling, a 10% import surcharge and most importantly, "closed the gold window", ending convertibility between U.S. dollars and gold, leaving only "Full faith and credit" in its wake.
In bitcoin's case, the consensus will be that this money will always rise in value because of its limited supply and unlimited demand. People won't reach such consensus if they don't know about supply and demand theory in economics, but I suppose that more and more people will gain such basic economy knowledge over time
So, the consensus about USD's value is reached by historical experience, while the consensus about bitcoin's value is reached by economics theory, they are both psychological phenomenon but that's what essentially drives people's behavior
They act similarly for those reasons. The difference being the "legal tender" issue. Taxes must be paid in dollars, and any debt may be discharged by payment in dollars (thus all debts public and private).
You are free to specify other terms contractually, but in a legal court dispute, unless you can get "specific performance" the best you are going to get is dollars as a debt satisfaction, though the amount may be based on the value of something else (such as bitcoin).