Your question is a very good one and is almost more about economics than geology.

Prices are not set by any one organization, but are a balance between the cost of producing a mineral (extracting it from the ground and purifying it) and what people are willing to pay for it.

Gold is very rare and relatively expensive to produce, so the base price must be fairly high. If lots of people want to use gold and are trying to buy it, they will have to compete with each other for the gold and that will drive the price up. If not so many people want the gold, the price will stay closer to the actual cost of production.

Aluminum is much more common in the earth's crust than gold (8% of Earth's crust), so it is cheaper to produce. Iron (another cheaper one) makes up 5% of Earth's crust.

If you want more information on this, I would try asking an economics teacher.

There are two major factors that go hand in hand to determine the value of different elements: abundance & popularity. Another major factor is work.

Elements that are very abundant such as Aluminum are very cheap. This is because aluminum can be found everywhere. Although Gold is still quite abundant because of its popularity it has become very valuable. There are some elements that are not very abundant and are not very valuable --but as popularity of these elements increases, so does the value. An example of this is Ruthenium.

Now work, a person's time is of some value so if a lot of work goes into mining or harvesting different elements, this adds to the value of these elements as well.

This answer is going to involve both some chemistry and some economics, so get ready!

It's the same thing with precious metals -- gold is a very rare element, so it's more valuable than common elements such as iron.

Rarity also lets gold work well as a currency. Currencies only function well if they have a relatively stable 'volume' (when economists talk about volume, they mean the total amount in circulation). This is why the US Government controls the supply of dollar bills so there are only a certain number in circulation at any given time. If everyone could just print their own money, it would quickly lose value and be a worthless currency (think about it -- right now you'd take $10 to mow your neighbor's lawn, because you can then use that $10 to buy something else. But if you can just print your own $10, you'll no longer accept dollars as payment for any service you perform). Gold is really hard to come by -- you can't just go dig up a bunch of gold in your back yard -- so it has a stable volume and therefore maintains a relatively constant value.

We are still mining gold, so the global volume of gold is increasing, but only very slowly.

The other reason gold works so well as a currency is chemical -- gold is one of those metals that do not readily oxidize, so gold coins will maintain a constant weight. Iron coins wouldn't work very well -- if you aren't careful with them, your money will rust away. Copper coins aren't especially good either, because when they oxidize they will gain some weight (from the extra oxygen atoms). So if the weight of a copper coin will depend on how old it is and how long it's been sitting out in the air and turning into copper oxide. If you want a currency to be based on the weight of coins (which is really the only option) this is bad news.

So gold is rare, has a fairly stable volume, and doesn't rust away. This makes it a useful currency and so it was our primary currency for thousands of years (actually until the 1970s when President Nixon stopped the direct link between the value of the US Dollar and the value of the US gold reserves).

You might have noticed that I have used iron instead of aluminum as a counterexample to gold. Humans have only been able to isolate aluminum from bauxite ore relatively recently, so it was not around in ancient times to compete with gold. If it had been, it might have actually fared quite well -- aluminum is a very handy metal that is harder and lighter than gold, so it makes better tools and weapons. It's also not terribly common -- most of our aluminum comes from a few mines in Australia, I believe. But aluminum does oxidize (although only very slowly) so gold would still have the upper hand there.

This is a very interesting question. Gold is relatively rare in the earth's crust, and particularly because of its value in making jewelry, it has always been worth a lot of money. Aluminum is very common, and is nowadays, easily formed as the pure metal, so it is not very cheap. However, about 150 years ago, the current process of extracting aluminum from its oxide did not exist, and it was actually more expensive than gold. So it is important to recognize that the process by which an element is obtained plays a big part in what it costs.

Rarity is definitely one issue. H₂O is not very expensive because there is a lot of it around. Silver and Gold on the other hand, like, say, diamonds are very rare. On top of that, the usefulness of a substance makes its price high. Au (gold) is very useful because it has some excellent chemical properties (very inert) and also its malleable and can be worked as body decoration (rings and bracelets etc.) Diamonds have industrial use because they are very hard and are good abrasives.

So the common elements of rarity and usefulness to humans make for their great worth. Al(aluminum) is all over the place ...about 15% of any rock is Al₂O₃... hence its very common and easy to get.

The price of metals depends on their value to humans, their availability, and how difficult it is to extract them. Gold has always been valued because it is pretty; it does not tarnish, so you can make statues and jewelry and it does not turn black with age; it is soft so you can mold it, and it melts fairly easily. It has been used in jewelry and worship for thousands of years.

Aluminum is more abundant, and lighter than gold, but is getting depleted from the ground, so it's getting more expensive, but is not considered a precious metal.

The short answer is because the market says so. Over the course of thousands of years of trial and error, consenting adults engaging in commercial acts settled on it to perform the function of money. Why did people choose gold? Because, over time it was identified as having the greatest liquidity of all possible contenders. A person bringing a relatively illiquid item to market could swap it for gold, secure in the knowledge that he could later use that gold to get whatever he wanted. So for example if someone wanted to get rid of a boat, they could exchange it for gold, knowing that they would be able to reuse the gold later to buy something else. Theelement gold was probably chosen for the following reasons:

Rarity. Gold constitutes only about 5 parts per billion of the Earth's crust. It is also difficult, dangerous and expensive to extract. Anyone who has actually been down a mineshaft knows just how precious a metal it is.

Indestructibility. Gold doesn't tarnish or decay.

Density. Gold doesn't take up much space. All the gold mined in human history amounts to about 130 thousand metric tons, an amount which would only fill about a 100 foot cube if gathered in one place.

Malleability and divisibility. You can stretch it, pound it thin, and divide it into multiple tiny amounts.

Controlled expansion. This is the most important quality. Gold can only be produced in limited quantities, currently at a peak rate of about 2,500 metric tons, or roughly 2%, each year. No matter what wars or social programs urgently need funding.

You must also remember that gold is not valuable to all cultures. The Maya had plenty of gold but didn't value it highly. They used various shells to act as currency.