Who guarantees the value of the one dollar bill or coin?

Answer 1

In theory it is the Federal Government, in practice though, no one.

Prior to 1933, one dollar was equal to ~1/20 of an ounce of gold (or ~3/4 an ounce of silver). Anyone could take a paper gold or silver certificate to a bank (or the US treasury) and get gold (or silver) for their paper money.

From 1933 until the 1970s, the US dollar was equal to ~1/35 of an ounce of gold, however, private citizens were not allowed to own gold and so you could not redeem paper dollars for gold coin. However, until ~1968 (the minting of 90% silver US Coins stopped in 1964, but silver certificates were redeemable in silver dollars until 1968) the US would redeem paper dollars for silver at the rate of $1 for ~3/4 of an ounce of silver. All US quarters, dimes, half dollars and dollars dated 1964 and prior are 90% silver and they are set at a rate so $1 (be it 4 quarters, 10 dimes, 2 half dollars, etc.) would equal ~3/4 of an ounce of silver. However, by 1968 the government's stock of silver ran out and paper dollars could not be redeemed for silver dollars. Both worthless copper-nickel coins (the ones we have today) and silver coins circulated until the late 1970s when a large increase in silver price meant that silver was worth more than face value.

Today, the dollar is essentially worthless, completely unbacked by any commodity such as gold and silver. The Federal Government "guarantees" the value of the currency only by agreeing to accept it for tax purposes.