Supply is perfectly elastic if any change in price causes quantity supplied to fall to zero. At the market price P* producers are willing and able to sell an infinite amount of the good. The supply curve is horizontal.
Many factors determine PES:
1) Availability of Resources and Labour.
If resources and labour are easily/quickly/cheaply available then supply can easily increase so supply is elastic.
2) Factor Substitutability.
As it becomes easier for producers to switch resources from producing one good to a substitute good, PES becomes more elastic.
3) Spare Capacity.
As producers get closer to full capacity, PES becomes more inelastic. A large degree of spare capacity means there is space to produce more with the current resources and technology so quantity supplied can easily be increased. But at full capacity, supply is at its maximum and cannot rise any more (this could cause PES to be perfectly inelastic in the short-run).
4) Availability of Substitutes.
As the number of substitutes rises, PES becomes more elastic. Assume goods X and Y are substitutes. As the price of Y falls, X becomes more profitable relative to Y, producers switch to producing less of Y and more of X.
As the time period increases, PES becomes more elastic. If producers are at full capacity in the short-run, they can increase investment to build more machines and buildings, increase their productive capacity in the long-run and increase quantity supplied in the long-run.
A production lag is the length of time between using the factors of production and producing the final output. As the production lag increases, PES becomes more inelastic because producers cannot change quantity supplied quickly when price changes (this could cause PES to be perfectly inelastic in the short-run). An oil drill and pump may take a long time to set up, making oil supply very inelastic.
As producers keep more stocks and inventories, producers can increase quantity supplied when price rises even if they are at full capacity so PES becomes more elastic.