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The exchange ratio of gold to other goods is not fixed, but fluctuates with changes in people’s preferences with respect to gold coins relative to other goods. The dollar is just a name for a weight of gold, so the dollar must have a fixed definition in terms of gold. In a pure gold standard, money is gold coins. As Rothbard points out, we can dispense with the name “dollar” altogether and just name the gold coins by their weight. In other words, we could call a gold coin “1/20th of an ounce.” Or we could call the gold coin of 1/20th of an ounce of gold some made up name like “Hayek.” Then two Hayeks would refer to 1/10th of an ounce of gold or two 1/20th of an ounce coins. Neither the Hayek nor the dollar is a fixed “value” for the coin. Instead it refers to the fixed weight of gold that the coin contains.