[Shaun]

The value of shares is based on demand, generally.

Generally speaking, the value of an object, in $, is the amount of $ equal to that object. In such, you find a trade. If one has an object, another has $, and they both agree to trade the object for the $, then the object and the $ are seen as equivalent and are thus equal. This must be true because if the $ and the object were not equal, then the person with the higher valued good (either object or $) would be realizing a loss due to trade and would decline to trade.

What does this mean?

The value of an object, to the purchaser, in $ units, is the amount of $ the purchaser would agree to pay. The value of the object, to the seller, in $ units, is the amount of $ the seller would agree to receive. When the purchaser and the seller agree to an amount of $ to be traded with an object, then they both agree that the value of that object is equal to the traded amount of $. Thus that object could be established as being worth that amount of $ in the most recent tradeoff.

A share is just the same as any object and the most recent value of the share is the most recent amount of $ paid for a share.