The Player's Handbook lists some commodities on Table 7–3: Trade Goods (112), including iron at 2 sp per lb. (therefore 6 sp for 3 lbs., although this table doesn't mention whether this is iron ore or iron in another form, iron apparently being a rather complicated substance and available in many forms).
The Dungeon Master's Guide lists an item made of mithral as costing an additional 500 gp per lb. (284), so probably mithral can either be purchased for 50 gp per 1/10 lb. or be sold for 50 gp per 1/5 lb. (because Dungeons and Dragons 3.X economics is weird that way).
The Arms and Equipment Guide also has a list of trade goods and corresponding values (40).
Underdark (for use with the Forgotten Realms campaign setting) on the lower darklands village Dupapn, Waters of Deep Hunger, describes the Mithral Pit, one of the village's important sites, partly as follows:
Anyone with the means to empty out the wells and the will to challenge a village full of [foes] would find a total of 1d4 × 5,000 gp each in gold ore, mithral ore, and platinum ore. The rocks are heavy, though, weighing about 1 pound per gp (gold), 1 pound per 10 gp (platinum), or 1 pound per 50 gp (mithral). (146)
A DM wanting to make his PCs' lives miserable (well, PCs without access to a portable hole, anyway) could extrapolate from these figures.
Somewhere between 250,000 GP and 125,000,000 GP. *
And it sells for full price.
Gemstones are small, lightweight, and easily secured compared to their same value in coins.
- DMG 133
The DMG does not give the weight of gems, unfortunately, but it does say that they are lightweight compared to coins, so for my calculations, I used the same weight as coins: fifty to the pound. This gives us a total of$$
500~\mathrm{pounds}~{\times}~50\frac{\mathrm{gems}}{\mathrm{pound}}~=~25,000~\mathrm{gems}.
$$
On the following page, there is a table to roll on for gems as treasure, and gives the value of each type. There's a lot of them, so they're listed at the bottom of the answer. What matters is they vary in price from 10 GP (e.g. Obsidian) to 5,000 GP (e.g. Ruby).
If your pile of gems is completely made out of Rubies, for example, you're looking at around$$
25,000~\mathrm{gems}~{\times}~5,000\frac{\mathrm{GP}}{\mathrm{gem}}~=~125,000,000~\mathrm{GP}.
$$
On the other hand, if your pile of gems is completely made out of Obsidian, you're only looking at$$
25,000~\mathrm{gems}~{\times}~10\frac{\mathrm{GP}}{\mathrm{gem}}~=~250,000~\mathrm{GP}.
$$
Don't sell it all at once, though. It's not that supply and demand is a problem, but that money is heavy, by comparison. Gem prices are static, and they are at least as efficient as Platinum by weight. It's only worth selling them when you need the money.
* Your DM might decide that you need to perform an Intelligence check to know this in character, though.
- 10 GP gems: Azurite, Banded agate, Blue quartz, Eye agate, Hematite, Lapis lazuli, Malachite, Moss agate, Obsidian, Rhodochrosite, Tiger eye and Turquoise.
- 50 GP gems: Bloodstone, Carnelian, Chalcedony, Chrysoprase, Citrine, Jasper, Moonstone, Onyx, Quartz, Sardonyx, Star Rose Quartz and Zircon.
- 100 GP gems: Amber, Amethyst, Chrysoberyl, Coral, Garnet, Jade, Jet, Pearl, Spinel and Tourmaline.
- 500 GP gems: Alexandrite, Aquamarine, Black pearl, Blue spinel, Peridot and Topaz.
- 1,000 GP gems: Black opal, Blue sapphire, Emerald, Fire opal, Opal, Star ruby, Star sapphire and Yellow sapphire.
- 5,000 GP gems: Black sapphire, Diamond, Jacinth, Ruby.
Best Answer
It's nearly impossible to put a modern-world value on 1 GP
...because things don't have the same relative values in our world as they do in a typical medieval-style adventuring world that is pre-industrial, but has magic.
As you've already noted, 1 GP is worth about 1 goat or about 1 whip. It's also good for 2 nights' stay in a modest inn, or 5 gallons of ale. On the other hand, it's only 1/25th of the price of a 1 lb hourglass, 1/50th the cost of a chain shirt, or 1/1000th the price of a spyglass. These aren't items that are all of equivalent values in modern terms, so it doesn't make sense to try to assign a modern value to a gold piece. The gold piece has value exactly in relation to what kinds of items one can purchase with it.
Today (May 2015) you could get:
So, by using modern item values, we might say that 1 GP is worth somewhere between 15 cents and $200 in $US.
But before you dismiss the prices as being "inconsistent" with modern values, consider your setting. Relative prices are much different now. Many things are much easier to make, and the cost of hand labor is reduced. Other things may be more in demand or uncommonly made now, and cost relatively more. If you want to build a more modern setting for your world, you might as well just use a modern currency.
As @KRyan notes in the comments:
See Were iron nails at one time so scarce that pioneers in America burned down their cottages to retrieve them? on [skeptics] for more information on that.
Additionally, as other answers have noted, the developers set prices with game balance as a higher priority than the creation of a realistic economy.