1gp is 1gp is 1gp.
1 gp is worth 10 sp, 50 ep or 100 cp.
That's it.
Gold is defined to be worth that amount, and that's all there is to the economy in D&D.
Though the specific items that you can purchase differ widely, the prices are set by the designers. So an item that costs 1gp has the same worth in the economy as another item that costs 1gp. Obviously, if your DM wants to change the prices, he's totally in bounds to do that, it's his game, and prices can and should vary by setting.
So basically, if a goat and a whip are each worth 1gp, a farmer would likely consider a (nice, adventurer quality) whip handed in trade for a goat to be a fair deal.
It's worth noting that D&D is a complete and utter command economy. And designing a functional, working, economy is not generally regarded as a design goal for D&D. Things are given prices with some regard to fictional reality, but not very much. Ultimately, if you're concerned with the economy being functional, you probably want to import another economic scheme or find a different game.
As shown in other answers, trying to relate 1 gp to a current dollar value is nigh pointless, there's not going to be a consistent currency exchange to be found based on the items that you can purchase in the game (And the economies are so drastically different it's not remotely comparable). The best way to think about it is that 1gp is something like the $20 of the D&D world, it's not the largest unit of currency (that'd be astral diamonds), and it's not the smallest (that'd be the copper piece, the equivalent of a dollar, or maybe even a quarter..it's probably not a penny).
All that to say, trying to do a direct conversion from gp to dollars (or other modern currency), just isn't productive. Think of it as a unit of currency and not much more.