I take a common-sense view of monetary value, as a measure of ``how much someone would pay to obtain'' an entropic item on offer from some vendor. This is distinct from the notion of monetary cost, which measures ``how little someone would take as compensation for'' releasing an entropic item to some buyer. In both cases, the ``someone'' must be informed enough to make a rational decision: the buyer must know somehow what an item would be ``worth'' to them, and the vendor must know how much they would lose by revealing the item.
Curiously, entropic items may have a negative monetary cost: it may actually be rational to underwrite the cost of broadcasting such items to a large audience, if a benefit accrues thereby to the vendor. Most advertising falls into this category.
It is also curious that entropic items with negative monetary cost may have a positive monetary value. Some advertising falls into this category. For example, when I'm trying to purchase an expensive computer product, I'm willing to spend some money on trade magazines in order to obtain their advertisements.
Please note that monetary value and cost is an individualised measure. Each individual buyer and vendor will, in general, have a different assessment of the monetary value and cost of an entropic item. This assessment will, in general, change with time. In particular, a second offering of an item will almost surely have zero value to someone who has just received that item.
A market can be made, in the usual economic fashion, finding individual vendors and buyers for entropic items, such that the buyer's value exceeds the seller's cost by a sufficient amount to defray the cost of distribution and advertising.