I am planning to design a livestock trading website. Obviously it will contain dynamic content as new stock is added and old stock is sold, hopefully on a continual basis. How do I prevent the stock pages from being cached, or what should I do to prevent historic pages showing while the current page has already been updated?

Why would you not want old pages to show? You want as much as you can get into the search engines as possible.

Remember this is not like an online shop where you have a steady supply of stock in unlimited quantities, all available at one premises. As and when a farmer wants to sell say 100 sheep, it needs to be added to the site with a full description of type, price and location. Prospective buyers browsing the site will find an acceptable lot and buy it, but then that lot will have to be removed from the site as I will not be able to offer the same lot to another buyer.
At the same time I might get another lot available in another area that needs to be added to the site and be visible immediately to prospective buyers. This way I will have a lot of sheep/goats/cattle available in the area, all different in quantity, type and location. Prospective buyers will find a lot acceptable in quantity, type and location at an acceptable price whereafter the deal can continue, but I need the site to be as updated as possible for it to work.
If I allow old pages to show, my new lots will not be visible to prospective clients, while old lots which will probably have sold by then, will still be showing.

Doesn't seem to bother Ebay.

Site management is about using ALL the resource available to your advantage, and you are considering throwing away a valuable resource.

USE THEM!!!!

When lots are sold your site should mark them as ended and at the site time add links to currently active lots in the same category or type.
This gets visitors (real and robotic) to new pages much quicker that YOU could promote them.