Do caterpillars eat the skin they shed?

YES, they do eat the skin they have shed. I've watched this occur in my garden & I have a video of it. It's probably filled with nutrients for the growing caterpillar. There are 5 instars, or stages of growth. After they shed their skin, they grow to the next instar, then shed their skin again. This happens 5 times, then the caterpillar goes into a chrysalis and eventually emerges as a butterfly.