Yes, corn prices are today lower, but it is important to note the lags in production for cattle, and to a lesser extent pork, and to a much lesser extent poultry. Let's say you're a cattle rancher back in 2008 and you're facing much higher corn prices and drought that limits forage and hay to feed. What do you do? You start selling off part of your herd. As other ranchers make the same decision, prices initially fall but then start climbing. Then, in 2013 corn prices start falling and drought conditions subside in many parts of the country. So, you can feed cattle, but you don't have any excess sitting around. In fact, if you want to capitalize on higher beef prices, you might have to forgo current profits for future profits and hold back some of your female breeding stock (further tightening supplies). It might be another year till that new heifer is pregnant, another (almost) year till a calf is born, and another year and a half or so until you've got an animal that finally goes to the dinner table. Of course, what I'm describing is just the biological production lag that often leads to cattle and hog price cycles. This kind of cycle doesn't much occur with poultry because flock sizes can be changed relatively quickly, and that might explain why in the above graph, the price of chicken has been much more stable. (On the pork side, the porcine epidemic diarrhea virus, PEDv, is also partially responsible for the smaller inventories).
What about other explanations that are often presented for the price increases? I agree that consumer demand remains steady, something we've found in our Food Demand Survey (FooDS). But, it isn't increasing. You'd have to have increasing demand for consumers to be responsible for higher prices.
What about consumers in other countries? Exports? Here is data from the US Meat Export Federation on beef exports: