Utility Threshold Property

Utility is expressed as preference for the coin over substitutes, for transfers of a comparable value. Increasing utility implies a rising fee level. A person with higher marginal utility for a confirmation offers a higher fee than another. Given differences in the market fee level over time, another person may offer a lower fee in expectation of a longer time to confirm. Others will not transact on the chain, relying instead on substitutes.

Increasing utility therefore implies increasing average transfer value, as rising fees will otherwise cause the cost of transfer to exceed the value transferred. Greater depth implies greater confirmation security. Therefore time can be traded for higher security against double spend. However time cannot be reduced below one block period to achieve lower security. The lowest levels of security are none (unconfirmed) and minimal (one confirmation). There is no trade to be made between these levels.

As fees rise hash rate follows, mitigating the need to increase confirmation depth for higher value transfers. But given there is no way to reduce security for lower value transfers, the useful minimum value transfer rises with utility. Failure to support transfers in a certain value range implies substitutes are cheaper in that range. This implies the possibility of coexisting moneys to service distinct value ranges.

Rule differences in terms of block period or size do not change this relationship. The effect of these coin variations is strictly proportional. Even unlimited size blocks must produce fee levels that price out low value transfers given rising utility.