Intrinsic value means, in simple terms, "real value." For example paper dollars do not have intrinsic value. It is only the goods and services you can purchase with said paper that does have "real value." However, gold does have intrinsic value because the gold itself is valuable.
Or is?
This is the problem I think very few economists think through about currencies, intrinsic value, and specifically gold and silver. We always assume gold and silver are valuable unto themselves, which made them the "ultimate" form of currency. But if you look throughout history, especially in places where there was no gold or silver, you'll find other "substitute currencies" popped up. Salt, shells, etc. Even today in prisons cigarettes manifest themselves as the default currency. In other words, the value of a currency isn't its "intrinsicness," but rather the physical qualities it has that makes it the ideal tool of exchange.
This results in a debate and is the essence of the debate Stefan Molyneux was having with Schiff - does a currency even need to have intrinsic value or just really good traits that makes it a superior currency.
Schiff argued that currencies like bitcoin and the dollar are not backed up by anything, which makes gold superior. But this then brings us back to whether or not gold actually has intrinsic value. However Schiff pointed out several times something that made me realize gold (and silver) do indeed have intrinsic value. Namely, gold can be used for ornamentation.
Now when I say, "ornamentation" that is the polite was of saying, "sex and ego." For while, yes, humans have always sought gold and silver, you have to ask why would they do so? What is in it for men to grab a hunk of metal that has not the function of iron or the usefulness of bronze?
You can get laid.
Gold was (and still is) nothing more than peacock-feather currency. It was a way to demonstrate you had wealth and power. With gold you could either directly purchase sex (either prostitution, supporting a concubine, or a wife...or 6) or at least demonstrate you were wealthy and powerful by adoring yourself or your house with it. Thus, gold, and by default, intrinsic value does not derive it's worth from something like "scarcity" (though it does need to be scarce) as much as it does play and ego.
If you don't believe me, think about a world without women.
What would happen to the price of silver, gold, and diamonds? Yes they have some industrial uses, and their scarcity and malleability would make them a decent currency, but they would not be trading anywhere near what they are today if there were no women to woo.
Therefore, we need to realize that functional currencies do not necessarily have to have intrinsic value. Gold and silver have adequate enough characteristics on their own that make them great currencies, just as bitcoin, shells, cigarettes and salt. But if you want something to have genuine "intrinsic value," something that goes beyond currency-functionality, then it needs to either stoke your ego or get you some play.
The rest are all truly fiat currencies or commodities.
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