Clearly the main focus of discussion of gold is on its extrinsic value - the value placed on it by investors and others who prize it as a store for wealth. However, it's conceivable that society could one day be in a state where gold is no longer considered valuable for those reasons. What intrinsic value does gold have, or to put it another way, what uses does it have in the sense of being a material commodity as opposed to an investment opportunity?
The answer is that other than a small number of applications (the approx. 10% of gold production that goes to 'industrial uses') gold does not have intrinsic value beyond being pretty and rare (and useful for making jewelry.) There are a number of 'industrial' applications and uses for gold (see other answers for a list) but the volume consumed this way is fairly small, especially relative to the capacity to mine new gold and reclaim existing gold. If you removed investment, and jewelry usage (especially culturally driven jewelry usage) then there's no way the remaining uses for industry and dentistry could sustain the price levels we currently see for gold.
Furthermore, and perhaps more importantly, the best data I can find for this shows the total number of tons consumed for industrial uses has been shrinking for several years now, and that was prior to recent price increases, so it is difficult to tie that reduced demand to increasing prices. And one might postulate in a 'collapsed society' you seem to be referring to in your question, that a lot of the recent industrial demand (e.g. the '50 cents of gold in each cellphone') could quite possibly disappear entirely.
The argument many people use for gold having value is usually 'been used as money for thousands of years'. But this confuses gold having a value of its own with the reasons why something makes a useful currency. Gold has a large number of characteristics that make it an ideal currency, and of all the elements available it is perhaps the best physical element to serve as a currency.
- it isn't a gas or liquid
- it doesn't burn
- it's non-reactive
- it doesn't have an absurdly high melting point (as with platinum)
- it's rare but not TOO rare (like rhodium)
- it won't kill you (as with a radioactive metal)
- it doesn't corrode or tarnish
- it's relatively easy to test with a 'touchstone' and 'the acid test'
- it's easy to divide, or 'mint' in various sizes (an issue with gems, diamonds etc) recall 'pieces of eight'
BUT just as with a dollar bill, just because it is a good currency, does NOT give it an intrinsic value. Any currency is only worth what someone will trade you for it. The value is set by the economy etc., not the medium used as a currency. So yes, people will probably always use gold as money, but that doesn't make the money worth anything, it's just a medium of exchange.
Incidentally two other things should be noted. The first is that you have a problem when the medium itself used for a currency becomes worth more than the face value. Hence why we stopped using silver in coins, and there were concerns over pennies due to the price of copper.
This leads to the second point, which is that currently, gold is TOO RARE to suffice as a world currency, hence why all countries went off the gold standard years ago. The size of national and global economies was growing faster than the supply of gold, and hence it was becoming impossible to have enough gold to back all the currencies (inflation concerns aside).
Borrowing Wikipedia for a bit, it seems like the intrinsic uses are these. I've ordered these approximately in technology-level order:
- Decorative uses as jewelry, gold foil on metal objects, solid gold objects, gold thread, and the like
- Gold crowns
- Heat dissipation material
- As a toner in photography
- De-icing conductor for aircraft
- Corrosion-resistant or high-energy electrical conductors and contacts
- Certain high-tech medical applications for scanning electron microscopes and antigen detection
- Reflection of EM radiation for military, space, and other high-tech applications
The importance of any of these uses largely depends on the state of a civilization and the level of technology of that civilization. However, most of these applications have far cheaper substitutes available.
This site shows a list of (mostly) industrial uses of gold:
If you ignore the first two uses, jewelry and coinage, there remains aerospace, computers, electronics, dentistry and medicine.
It's worth noting that gold comes in the same chemical family as both copper and silver, meaning that gold can serve most of their uses, although not as well.
Extrinsic value is not a factor with respect to gold.
Intrinsic value by definition is the natural value of a commodity set by the market -- extrinsic value is externally set. The "extrinsic" value of gold in the United States is $50/oz. If the market value of gold fell below $50/oz, a US American Eagle coin would be worth $50 in the US.
If you take away the attributes that make a commodity valuable, the value drops.
Substitutes of equal or better quality for most industrial or other uses of gold exist, so if if the popularity of gold declines, or if the hoarders of gold have to liquidate, it's value will diminish. I have no idea what that value would be, but it would set by the market demand for gold jewelry and other valuable industrial uses.
Gold has no "intrinsic" value. None whatsoever.
This is because "value" is a subjective term. "Intrinsic value" makes just as much sense as a "cat dog" animal. "Dog" and "cat" are referring to two mutually exclusive animals, therefore a "cat dog" is a nonsensical term.
"The actual value of a company or an asset based on an underlying perception of its true value ..."
Intrinsic value is perceived, which means it is worth whatever you, or a group of people, think it is. Intrinsic value has nothing, I repeat, absolutely nothing, to do with anything that exists in reality.
The most obvious example of this is the purchase of a copy-right. You are assigning an intrinsic value to a copy-right by purchasing it. However, when you purchase a copy-right you are not buying ink on a page, you are purchasing an idea. Someone's imaginings that, for all intensive purposes, doesn't even exist in reality! By definition, things that do not exist do not have "intrinsic" properties - because things that don't exist, don't have any natural properties at all.
"Intrinsic" according to Websters Dictionary:
"Belonging to the essential nature or constitution of a thing ... (the intrinsic brightness of a star)."
An intrinsic property of an object is something we know that exists because it is a natural property of that object. Suns emit light, we know this because we can measure the light coming from it. It is not subjective.
"Intrinsic Value" is the OPPOSITE of "Intrinsic"