To avoid having people set up 10 accounts and send themselves lots of free daily gifts, my Facebook restaurant game limits you to trading ingredients 1-for-1. You can set up extra accounts, and you can all send each other those daily gifts, but you cannot then go to each of those 10 accounts and send yourself the 10 gifts each received. Ignore the multi-account question and consider what this does to the game’s economy.
The best way to get what you want is to give it to someone else. First, if you need lots of beef, the easiest way to signal this is to send everyone beef. (You could also post it explicitly.) The default Facebook “send one back” option will get you beef. Let’s say you still want more beef. If the people you sent it to did not want it, you can trade with them, your whatever for the beef you just sent them.
To me, the interesting part is the deflation in the meat market. Flood the game with as much beef as you can for as many days as you can. This is entirely given away, so while you have lost nothing, you have gained no beef. But you still want beef, which other people now have excess amounts of. You can trade anything for beef, because people have more than they know what to do with.
In an MMO, when you flood the market with something, you are a seller and are driving down your own price. In a social media game, when you flood the market with something, you are a gifter and are driving down the price you pay.