Price Elasticity of Supply, HELP!?

Well, the PES measures how responsive supply is to a change in price, so you're focusing on the supply side of the market, here.

Imagine you're a potato farmer, and the upward sloping supply curve holds true for you. Price increases by, say, 10%: how should you respond to this? Textbook answer: by increasing the quantity of potatoes supplied. But, in the short-run, you can't magic up new potatoes overnight, you need to invest in more land, machinery, hire workers, and so on, so you might not be able to increase supply a lot, even with an increase in price.

This is just applying the concept of short-run fixed factors of production, which makes PES inelastic, and in the long-run all factors should be free, so PES is relatively more elastic because you can better respond to a change in price. The agricultural case above is usually used an example the extreme situation of near perfectly inelastic PES.