Shrimp are scavengers. They will eat anything they come across dead or alive. Their diet is usually plants and small animals. They even eat each other.
1 Additional Answer
The size of the shrimp depends on what their diet is. A small shrimp is probably limited to plankton. Plankton is comprised of very small animals and plants floating in the ocean. Large shrimp are able to eat other shrimp, small animals, and even scavenge dead animals. You can find more information here: http://www.heiploeg.nl/wat-eet-een-garnaal.en_US.html